Report on the Research at the Institute of Informatics of the University of Szeged

Report on the Research at the Institute of Informatics of the University of Szeged

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Szeged, 2007 A Short Introduction of the Institute

I. HISTORY AND MISSION Computer Economist, BSc

Systematic education in computer science was The normal duration of the program is 7 launched within the Mathematical Institute at the end semesters. The program produces experts who are of the 1950’s by László Kalmár. The Institute of In­ well versed in the information society, and are able formatics was founded as an independent unit in 1990. to understand and solve the problems arising in real The head of the Institute: Prof. Zoltán Fulöp. The business processes. They can manage the informa­ deputies of the head: Dr. Eva Gombás (student af­ tion technology supporting the business needs, such fairs) and Dr. Karoly Devenyi (management) as to improve on the knowledge base and business The Institute consists of five departments and a intelligence of companies, model the cooperation of research group: info communication processes and technologies, con­ trol those processes, identify problems, and develop • Department of Applied Informatics, head of the applications (and also maintain and monitor their department: Dr. Tibor Csendes 1 quality). Moreover the graduates are equipped by • Department of Computer Algorithms and Arti­ the theoretical basics to continue their studies at MSc ficial Intelligence, head of the department: Prof. level. Janos Csirik Computer Engineer, BSc • Department of Foundations of Computer Sci­ The normal duration of the program is 7 ence, head of the department: Prof. Zoltan Esik semesters. The goal of the program is to train com­ • Department of Image Processing and Computer puter experts with solid engineering skills. The grad­ Graphics, head of the department: Dr. Eoörs uates are expected to install and operate complex sys­ M áte2 tems, especially in the information infrastructure area, • Department of Software Engineering, head of and also to plan and develop the data and program the department: Dr. Tibor Gyimáothy system of such systems. This means skills both in hardware and advanced software technology, involving • Research Group on Artificial Intelligence of the modeling, simulation, performance, reliability, config­ Hungarian Academy of Sciences, head of the re­ uration, trouble shooting, maintenance, and develop­ search group: Prof. Jáanos Csirik ment of systems. They are also provided with ap­ The main activities of the institute are the edu­ propriate basic knowledge to continue their studies at cation and research of modern informatics and com­ MSc level. puter science knowledge. Here we provide a sketch of Computer Program Designer, BSc our educational programs and research activities. The normal duration of the program is 6 II. EDUCATION semesters. The graduates are supposed to have high skills in planning and development of company infor­ The institute offers BSc, MSc, and PhD degrees. The mation systems using modern software tools. Further­ curricula consist mainly of mandatory courses for un­ more, they are trained in the planning, development dergraduates and a broad spectrum for specialization and operation of decision support systems, expert sys­ at graduate level. The curricula have already been tems, and multimedia systems. The graduates also re­ adjusted to conform to the so-called Bologna project, ceive firm basis in Computer Science knowledge in or­ embracing most of the topics of modern informatics der to have suitable knowledge to continue their stud­ and computer science. ies at MSc level. The informatics/computer science and some of the engineering courses belong to the departments of the GRADUATE PROGRAMS Institute of Informatics. The Institute of Mathemat­ Computer Program Designer, MSc ics and the Faculty of Economics and Business Ad­ ministration are responsible for the mathematics and The normal duration of the program is 4 economics courses. The physics courses are taught by semesters. The goal of the training is to produce infor- the Departments of Physics. In the Computer Engi­ matics/computer science experts who have firm theo­ neer BSc program we cooperate w ith the Kecskemáet retical basis, and they are able to expand their knowl­ College. edge autonomously in a long run. They can work in teams or on their own, to develop, produce, apply, in­ BSC PROGRAMS troduce, maintain, and to service information systems Presently we have three programs at undergradu­ at high level. Furthermore, they possess the necessary ate level: Computer Economist, Computer Engineer, cooperation and model making skill that are needed and Computer Program Designer. for solving of the informatics problems arising in their fields. They are also able to conduct research work, and to continue their studies at PhD level. There are six offered fields for specializations: Image Processing, Artificial Intelligence, Model Making for Informati- 1 Dr. Balázs Imreh was the head between 2003-2005. cians, Operations Research, Computer Science, and 2 Prof. Attila Kuba was the head between 2003-2006. Software Development.

1 PhD program in Computer Science Process synthesis. Optimization problems arising in chemistry, biology and industry. In addition of the above programs, a doctoral pro­ gram in Computer Science is available since 1993. The Research Group on Artificial Intelligence aim of this program is to support graduate studies, Machine learning, Computational learning theory. leading to the degree of PhD in computer science, Natural language procession, Language technology, with an emphasis on theoretical aspects. The pro­ Speech technology, Peer-to-peer algorithms and sys­ gram is part of the Doctoral School in Mathemat­ tems. ics and Computer Science of the Faculty of Science of the University of Szeged. It is composed of three The members of the Institute of Informatics pub­ subprograms: Theoretical Computer Science, Opera­ lish about 150 scientific papers in highly respected in­ tions Research and Combinatorial Optimization, and ternational journals/proceedings anually. Applications of Computer Science. The possible re­ search topics include mostly come from those parts of P artn ers computer science and related areas, which are being The Institute of Informatics has joint pro­ investigated at the Institute of Informatics. The nor­ grams and research cooperation (e.g. CEEPUS, mal duration of the program is 6 semesters. Students SOCRATES/ERASMUS) with the following higher are required to take entrance examinations for the ad­ education institutes from North-America, Europe, mittance. The State of Hungary usually supports up and Asia. to 5-6 new fellowships every year that is offered to Hungarian citizens. Foreign students are not entitled C anada: University of Waterloo, Canada, Queen’s for that fellowship, their tuition and other expenses University, Canada. have to be supported from other sources. U SA : Boston University, MA, City University of New York, NY, Columbia University, New York, NY, The III. RESEARCH THEMES AND CO­ University of Iowa, Iowa City, IA, University of Illi­ OPERATIONS nois at Urbana-Champaign, IL, Stevens Institute of Technology, Hoboken NJ, AT&T Labs. The departments of the Institute conduct research in A ustria: Technische Universität Wien, Medizinische the following areas. Universitat Graz, Technische Universitat Graz. Czech Republic: Charles University, Prague. Department of Applied Informatics D enm ark: University of Aalborg. Reliable computing, interval optimization, dis­ E ngland: University College London, GB. crete optimization, PNS problems, extremal graph F inland: University of Turku, Lappeenranta Univer­ theory, combinatorial games, and history of mathe­ sity of Technology. matics. France: University of Bordeaux, INRIA, Sophia An­ tipolis, University of Paris 6 and 7. Department of Image Processing and Com­ G erm any: Technische Universitaät Ilmenau, Technis­ puter Graphics che Universitat Dresden, Universität Hamburg, Tech­ Image models based on random Markov fields, nische Universitat Munchen, Universität Erlangen- Parametric estimation of transformations, Higher or­ Nfirnberg, Universität Mannheim, Universität Karl­ der active contour models, Analysis of satellite pic­ sruhe, Universität Stuttgart. tures, Digital spatial models. Vectorization of scanned Switzerland: University of Bern. drawings, Computer-Aided surgery. Medical image Italy: University of Rome La Sapienza. analysis, Skeletonization by thinning, Image registra­ Netherlands: Technical University of Eindhoven. tion, and Discrete tomography. Serbia: University of Nis, University of Novi Sad, Institut Mihajlo Pupin, Belgrad. Department of Foundations of Computer Sci­ Slovenia: University of Maribor. en ce Spain: Universidad de Almeria, Universidad de Tar­ Algebra and logics in computer science, Automata ragona. and formal languages. Tree-automata and tree- China: Hong Kong University of Science & Technol­ transducers. Term rewriting systems, and fixed points ogy. in computer science. Process algebras, Temporal log­ Israel: Ben-Gurion University of the Negev, Univer­ ics. Structures in computer science: semirings and sity of Haifa. semi-modules, and categorical algebras. Japan: Kyoto Sangyo University, University of Aizu. Department of Computer Algorithms and Ar­ IV. OTHER ACTIVITIES tificial Intelligence Automata theory, Fuzzy theory, Bin packing, CONFERENCE ORGANIZATION Meta heuristics, String matching, On-line algorithms, We have organized several conferences from the Machine Learning and Computational Learning The­ foundation of the Institute. In the last years the fol­ ory, Multi-Criteria Decision Making, Scheduling, lowing conferences were organized. Robotics, and Mechatronics. 16th International Symposium on Fundamentals of Department of Software Engineering Computation Theory, Budapest, 2007. 13th International Conference on Discrete Geometry Static and dynamic analysis of software systems. in Com puter Imagery, 2006. Slicing for imperative languages and logical program­ Logic and Combinatorics, Szeged, 2006. ming. Reverse engineering. Open source software de­ Computer Science Logic 2006, Szeged, 2006. velopment. Linux file system and GCC compiler op­ Algebraic Theory of Automata and Logic, Szeged, timization. Embedded systems. Ad-Hoc networks. 2006.

2 1. 2. 3. and 4. Hungarian Computer Linguistics switches with speed 100Mbps, while those switches are Conference, Szeged, 2003, 2004, 2005, and 2006. hooked by optical cables (1Gbps) to the main switch AFL 05 - 11th International Conference on Automata to the University Computer Center. The Institute also and Formal Languages, Dobogókő, 2005. operates the following servers: 2 Sunfire 280R, 1 IBM International Workshop on Soft Computing Applica­ eServer, 1 Compaq Alphaserver DS20, 3 HP Proliant, tions, Szeged-Arad, 2005. 1 Sun Ultra Enterprise 2. (The servers are driven by International Conference on Software Maintenance, Solaris 9, Linux, Windows 2000 Server or Windows 2005. 2003 Server.) A cluster, consisting of 4 HP Proliant DLT’03 - Developments in Language Theory, Seventh server, has been working from the September of 2005. International Conference, Szeged, 2003. Its mass storage device is an MSA 500 disc array of European Symposium on Algorithms, Budapest, capacity 1 TB. 2003. http://www.inf.u-szeged.hu/starten.xml Conference of PhD Students in Computer Science, Szeged, 2004 and 2006. Summer School on Image Processing, SSIP, Szeged, 2004, 2005, and 2006. Veszprém Optimization Conference: Advanced Algo­ rithms, Veszprém, 2004 and 2006. Between the years 2000 and 2006 the people of the Institute served in program committees of more than 50 international conferences. ACTA CYBERNETICA A scientific journal, Acta Cybernetica has been published since 1969 by the Institute in English. The journal is available in about 150 university departments worldwide, its homepage is: www.inf.u-szeged.hu/actacybernetica/starthu.xml OTHER SCIENTIFIC SERVICE Several members of the faculty work as editors in international scientific journals; they play significant roles in major scientific organizations and serve in pro­ gram committees of major conferences. Some of those journals: Acta Cybernetica, Cen­ tral European Journal of Operations Research, Gram­ mars, IEEE Transactions on Image Processing, Infor- matica, Pure Mathematics and Application, Theoret­ ical Computer Science, Theoretical Informatics and Applications, Optimization Letters, and Oriental J. of Mathematics. Organizations in which the Institute is repre­ sented: European Association for Theoretical Com­ puter Science, European Association for Computer Science Logic, Gesellschaft fr Angewandte Mathe­ matik und Mechanik, International Federation of In­ formation Processing, and Association for Computing Machinery.

V. RESOURCES

LIBRARIES The Institute of Informatics has a library of which holds about 5000 Hungarian and English volumes and subscribes over 200 scientific journals. The recently renewed University Library also an invaluable resoure for both our faculty and our students. It offers not only numerous scientific books, journals but it serves as a place for study and host of conferences. The directories of all libraries at the University are con­ nected together, and their shelfed items are searchable by browsers. HARDWARE/SOFTWARE The Institute provides computer access for about 3700 users. The students may use 220 worksta­ tion (Pentium4 based or IBM machines), in which both Mircosoft and Linux operation systems are avail­ able. All machines run by the Institute are linked to

3 Research by Departments Department of Applied Informatics

I. COMPUTER-ASSISTED PROOFS All of these proved to be valid - as expected. The FOR CHAOTIC AND STABILITY BE­ amount of function evaluations (for the transforma­ HAVIOUR IN DYNAMICAL SYSTEMS tion, i.e. for the seventh iterate of the Henon mapping (H (x1, x2) = (1 — A x 2 + x 2,B x i) ) in each case) were 273, 523, and 1613, respectively. The algorithm INTRODUCTION stores those subintervals for which it was impossible An important question is while studying approx­ to prove whether the given condition holds, these re­ imations of the solutions of differential equations, quired further subdivision to achieve a conclusion (see whether the given problem has a stable solution or Figure 1). The depth of the stack necessary for the chaotic behaviour. We study verified computational checking was 11, 13, and 14, respectively. The CPU methods to check regions the points of which fulfill time used proved to be negligible, only a few seconds. the conditions of some behaviour. We have proven that this algorithm is capable to In this case the verification means mathematical provide the positive answer after a finite number of verification. In the computer part, hence rounding steps, and also that the given answer is rigorous in and other errors were considered. Instead of real num­ the mathematical sense. Once we have a reliable com­ bers, we can also calculate with intervals. In case the puter procedure to check the conditions of chaotic be­ bounds of the result interval are not computer repre­ havior of a mapping it is straightforward to set up an sentable, then they are rounded outward. optimization model that transforms the original chaos location problem to a global optimization problem. INVESTIGATION OF CHAOTIC REA- The key question for the successful application of a GIONS FOR THE HENON MAP global optimization algorithm was how to compose the The problem is usually solved by careful study­ penalty function. On the basis of earlier experiences ing the given problem with much human interaction, collected with similar constrained problems, we have followed by an estimation of the Lipschitz constant, decided to add a nonnegative value proportional to bounding the rounding errors to be committed, and how much the given condition was hurt, plus a fixed finally a number of grid points are checked one by one penalty term in case at least one of the constraints by a proper computer program [15]. Instead of that, was not satisfied. we introduce a new - interval arithmetic based - au­ We have applied the global optimization model for tomatized method. the 5th iterate Henon mapping. Note that the less the iteration number, the more difficult the related prob­ lem: no chaotic regions were reported for the iterates less than 7 till now. Table 1 presents the numerical results of the ten search runs.

LO ZO FE PE T 12 4 13,197 4,086 17 12 1 12,913 3,365 16 12 1 13,569 4,303 19 12 2 12,918 3,394 16 12 1 14,117 5,083 18 12 3 21,391 7,400 25 12 2 12,623 3,296 16 12 0 15,388 6,221 30 12 3 13,458 3,858 15 12 2 14,643 5,002 16

Table 1. Numerical results of the search runs (Here LO stands for the number of local optima found, ZO Figure 1. The parallelograms and the starting interval for the number of zero optimum values, FE for the covered by the verified subintervals for which either number of function evaluations, PE for the number the given condition holds, or they do not contain a of penalty function evaluations, and finally T for the point of the argument set. CPU time used in minutes.)

To check the existence of chaotic reagions we We applied successfully this method to locate sev­ have set up an adaptive subdivision algorithm based eral chaotic regions of Henon map, and gave a lower on interval arithmetic. First the algorithm deter­ bound for topological entropy. The topological en­ mines the starting interval, that contains the region tropy characterizes the mixing of points by the Henon to be checked. Then the three inclusion relations are map. The numerical results are publised in [2-6,11]. checked one after the other.

4 CHAOTIC BEHAVIOUR OF THE FORCED where a is a positive number, and the initial function DAMPED PENDULUM 0 (s) is a constant, c > —1 , i.e. 0 (s) = c for s e [—1 , 0]. To simplify the further calculations use the sub­ Recently, a few papers considered real dynamical stitution z(t) = ey(t^ — 1. Then z'(t) = ey(t)y'(t) and problems and give a mathematical proof to chaotic be­ z(t — 1) = ey(t-1) — 1. We obtain the delay differential haviour [13]. In this research we investigated a forced damped pendulum as the mechanical model, i.e. we equation have a body on a weightless solid rod, forced to move y'(t) = —a(ey(t-1) — 1), on a vertical circle around the center point. The mass where the initial function is 0 (s) = c, s e [—1 , 0]. and the length of the pendulum are equal to 1. We E.M. Wright conjectured in a paper [14] published have a not negligible friction depending on the speed in 1955 that all solutions of this delay differential of the pendulum with a friction factor of b = 0.1. An equation converge to zero for a wide set of the pa­ external periodic force is applied to the body, cos(t), rameter a. He gave a proof of the statement for a where t is the time (it is independent of all other fac­ values between 0 and 1.5, and conjectured to be true tors). for further a values below n / 2. The related second order differential equation is We described and proved the correctness of a new, even more stronger bounding scheme that allows an x ' = cos(t) — 0.1x — sin(x), efficient shrinking of the possible extreme values of a where x is the angle of the pendulum, and X is the periodic solution. The present approach follow an­ angle speed of the pendulum. other line of thought, still it is a kind of extension of In the proof we will need certain quadrilaterals that of Wright. {Q k}kez “long” in the unstable and “short” in the We applied our Taylor series based algorithm to stable directions so that there are “exceptional” orbits bound the trajectories. This method was publised of the Poincare mapping P with the following proper­ in [ 1], and we illustrate the result in the case of a = 1.5 ties: on Figure 3. • an exceptional orbit is contained in UkeZQ k; • an exceptional orbit visits the quadrilaterals consecutively: if Pn(x0,X0) e Qk for some k ,n e Z , then either Pn+1(xo,x'0) e Qk-1 or P n+1(xo,Xo) e Qk or P n+1(xo,Xo) e Qk+1. In the main step of the proof of chaotic behaviour we will show that for an arbitrary consecutive order {Q ik }kez of quadrilaterals there is an exceptional or­ bit visiting the quadrilaterals in the prescribed order. To this end we have to know forward images P (Q k) and backward images P - 1 (Qk) (see Figure 2).

Figure 3. The bounded trajectory in y, y' coordinate systems.

After the theoretical investigations the remaining problem to be solved is to prove that for a values between 1.5 and n/2 no periodic solution exists with M and m absolute extreme values larger than 0.075. We implemented a new parallel Branch and Bound algorithm, which is able to prove the remaining prob­ lem, so we prove Wright original conjecture. The com­ puter part of the proof is published in [9,12]. ACKNOWLEDGEMENTS Figure 2. Forward and backward Poincare map in t = ±2n time points of Q0. The authors are grateful to Barnabás Garay (BME, Budapest, Hungary), Laszlo Hatvani (SZTE, We applied the earlier mentioned subdivision Szeged, Hungary), Tibor Krisztin (SZTE, Szeged, method, which was able to prove the chaotic beha­ Hungary), and Arnold Neumaier (University of Vi­ viour of the considered systems. The details of the enna) for their contribution and support. proof was published in [7,8]. This works have been partially supported by the Bilateral Austrian-Hungarian project öu56011, and INVESTIGATION OF A DELAY DIFFER­ Hungarian Science and Technology Fundaton No. E- ENTIAL EQUATION 25/2004, as well as by the Hungarian National Science E.M. Wright considered the delay differential Foundation Grant OTKA No. T 048377 and No. T equation 046822.

z (t) = — az(t — 1)(1 + z(t)),

5 REFERENCES II. OPTIMIZATION OF COMPLEX TRANSPORTATION PROCEDURES [1] B. Bánhelyi: Egy késleltetett differenciálegyenlet vizsgálata megbázhátá számátogepes eljárással (In During the organization of the transportation proce­ Hungárián). Alkalmazott Matematikai Lapok , dures many optimization problems arise. The deci­ 2007. Accepted for publicátion. sion maker has to assign goods to different vehicles [2] B. Bánhelyi, T. Csendes, ánd B.M. Gáráy: Op- and the optimal paths in the road system has to be timizátion ánd the Mirándá ápproách in detect­ determined. The optimal path and also the cost of ing horseshoe-type cháos by computer. Interna­ the path may depend on the type of the used vehi­ tional Journal of Bifurcation and Chaos, 2007. cle. In [1] we suppose that two places are given the Accepted for publicátion. destination point and the termination point and some amount of good must be transported between these [3] B. Bánhelyi, ánd T. Csendes: A verified com- places. We have a practical packing problem that the putátionál technique to locáte cháotic regions of goods are packed into three dimensional boxes, a box Henon systems. Proceedings of the 6th Interna­ can be described by its size and its weight. Vehicles tional Conference on Applied Informatics, Eger, belonging to different types can be used for the trans­ 297-304, 2004. portation of the boxes. [4] B. Bánhelyi, T. Csendes, ánd B.M. Gáráy: A We also consider [2,3] the model where a vehicle globál optimizátion model for locáting cháos: has to visit the places but it can be used for internal numericál results. Proceedings of the In­ transports. This means that in the case when a place i ternational Workshop on Global Optimization, is visited before a place j then the vehicle can be used Almería (Spain), 35-39, 2005. to transport some goods from i to j. The profit which can be achieved by such a transport is denoted by B ij. [5] B. Bánhelyi, T. Csendes, ánd B.M. Gáráy: A Thus the goal is to find an ordering of the places which verified optimizátion technique to bound topo- maximize the total profit which can be achieved by logicál entropy rigorously. 2007. Submitted for the internal transports according to the cost of travel­ publicátion. ling. We call this problem min-cost Hamiltonian path [6] B. Bánhelyi, T. Csendes, ánd B. M. Gáráy: E 2 problem with internal transport, HPPIT in short. cháos for iterátes of the clássicál Háenon mápping. 2007. Mánuscript. A BIN PACKING APPROACH OF A SHIP­ MENT CONSTRUCTION [7] B. Báánhelyi, T. Csendes, B.M. Gáráy, ánd L. Hátváni: Computer ássisted proof of cháotic Our optimization subproblem can be formulated beháviour of the forced dámped pendulum. 2007. as a generalized version of the three-dimensional bin Submitted for publicátion. packing problem. In box packing problem three di­ mensional boxes must be packed without overlapping [8] B. Bánhelyi, T. Csendes, B.M. Gáráy, ánd into the minimal number of three dimensional unit L. Hátváni: A computer-ássisted proof for E3- cube. This problem was defined in previous papers cháos in the forced dámped pendulum equátion. and later many algorithm were developed for the so­ 2007. Mánuscript. lution of the problem. In our model there are different [9] B. Bánhelyi, T. Csendes, T. Krisztin, ánd boxes which can be used for packing the items, thus A. Neumáier: Proof for á conjecture of Wright our model is related to the variable sized bin pack­ on á deláy differentiál equátion II. - Computer ing problem, where the bins which can be used to Aided Párt. 2007. Submitted for publicátion. pack the elements may have different size. The no­ [10] T. Csendes, B. Bánhelyi, ánd B.M. Gáráy: A tion of bin packing and its multidimensional versions globál optimizátion model for locáting cháos. with variable sizes and heuristic algorithms to it were Proceedings of the International Workshop on developed as we noted in references of [1]. The new Global Optimization, Alm ería (Spain), 81-85, model differs in two ways from the variable sized mul- 2005 tidimensonal model. In this model there is a further restriction on the bins, each type of bins has a weight [11] T. Csendes, B. M. Gáráy, ánd B. Bánhelyi: A limit and the total weight of the boxes assigned to a verified optimizátion technique to locáte cháotic bin (vehicle) cannot be more than the weight limit of regions of á Háenon system. Journal of Global the vehicle. Moreover in the new model we have a Optimization , 145-160, 2006. more general cost function, the cost of a bin depends [12] T. Csendes, B. Bánhelyi, ánd L. Hátváni: To- on its type, but it can be an arbitrary value it is not wárds á computer-ássisted proof for cháos in á the volume of the bin. forced dámped pendulum equátion. Journal of HAMILTON PATH PROBLEM WITH IN­ Computational and Applied Mathematics , 378­ TERNAL TRANSPORTS 383, 2007. [13] J.H. Hubbárd: The forced dámped pendulum: Important combinatorial optimization problems Cháos, complicátion ánd control. Amer. Math. require finding a permutation of vertices of a com­ Monthly, 741-758, 1999. plete digraph that minimizes a certain cost function. The most familiar one is the min-cost Hamiltonian [14] E. M. Wright. A non-lineár difference-differentiál path problem - or its closed-path version, the Travel­ equátion. Journal für die Reine und Angewandte ling Salesman Problem (TSP) -, when the cost of a Mathematik, 194:66-87, 1955. permutation depends on consecutive node pairs only. [15] P. Zgliczynski: Computer ássisted proof of the Another problem is known as the Linear Ordering horseshoe dynámics in the Háenon máp. Random Problem (LOP) when we want to find a linear or­ Comput. Dynam., 5:1-17, 1997. der of the nodes of a digraph such that the sum of the arc weights, which are consistent with this order,

6 is as large as possible. Now we consider a new op­ of TSP and LOP, 6th Joint Conference on Math­ timization model using a mixed linear cost function ematics and Computer Science, Pecs, July 12-15, from these two. Motivation of this common general­ (2006) submitted for publication. ization of TSP and LOP is the above practical ques­ tion. Thus the goal is to find an ordering of the places III. GRAPHS AND GAMES which maximize the total profit which can be achieved by the internal transports according to the cost of EXTREMAL GRAPH THEORY travelling. We call this problem min-cost Hamilto­ nian path problem with internal transport, HPPIT In [1] we considered the interval number, an im­ in short. Heuristics on TSP or LOP can be modify portant graph parameter. Partial characterization is to our problem and give new ones. The vehicle rout­ given for the extremal cases of the degree formula, ing problem with inner transportation leads to the and we also give bounds on the interval number i(G) following mathematical model. Let G(V,A) be a di­ if certain induced subgraphs are not present in G. The paper [3] generalizes the classical theorem of rected complete graph, where V = v 0 ,v \ , . . . , v n is the set of vertices, (v 0 is the depot, and the other vertices Nash-Williams asserting that any planar graph can be are the places which should be visited by the vehicle). covered by three forests. We show that additionally Furthermore two (n+1)x(n+1) nonnegative matrices one of those forests has maximum degree at most 8. Similar results are obtained for outerplanar, series­ are given, B and D. B ij is the possible profit which parallel and K 3,2 minor-free graphs. can be achieved by the inner transportation from vi We investigate the edge-bandwidth of grid-type to vj if vi is visited before vj (B ii = 0 for each i). D ij graph in [4]. Those are the n x n planar grid Pn © Pn gives the cost of travelling from v i to v j (D ii = 0 for each i). and tori Cn © Cn, the n-dimensional cube P2 , and the In the HPPIT problem we would like to find a K n © K n . In all cases asymptotically sharp bound on tour which visits each city exactly once and starts at the edge-bandwidth are given. the depot and returns there at the end of the tour. POSITIONAL GAMES The objective is to maximize the total profit achieved by the inner transportation taking into account the In [2] we introduce the idea of the recycled version cost of the tour. A feasible solution can be defined of games and prove some results on those. The main as a permutations p of the set {1,..,n}. The per­ results are a logarithmic upper and lower bounds on mutation describes the tour where the vehicle starts the recycled line game, and a 3ydi upper bound on the and ends at vo and visits the other vertices in the or­ recycled Kaplansky game if the players use n marks. The paper [5] solves some biased graph games. der vp ( i ), vp (2) , ..,v p (n ) . Then the objective function is given by the formula It extends the result of Szekely and Beck on degree game, and the method has consequences for the bal­ ance games. We discuss the general diameter games on the complete graph on n vertices. It defies the z (p ) = B p(i),p(j) + 5 Z (B o,p(i) + B p (i), 0) heuristic intuition for the 1:1 case, but the acceleration 0

7 IV. NEW APPROACHES TO CIRCLE PACKING IN A SQUARE

The optimization problem of the densest packing of equal circles in a square arises from discrete geo­ metry, it has become a well-studied problem in the past decades. The research in this topic on our part began nearly 10 years ago. During the 2003-06 period we have summarized our results in a book (with a CD) and some articles. In this time period P.G. Szabo fin­ ished his Ph.D. thesis about the circle packings [10].

INTRODUCTION Figure 4. A grid circle packing for 39 circles. It is easy to understand what the densest circle packing is: to position a given number of equal circles in such a way that the circles fit fully in a square with­ relationship of the number of the circles. We studied out overlapping. We gave some geometrical forms of separately a conjecture on an infinite circle packing se­ the problem and we proved their equivalence. Since we quence of the literature and we investigated the grid studied the problem as a global optimization problem, packing class too. Based on the pattern classes we we classified its mathematical models into the suitable have improved also the theoretical bounds. We gave problem classes of mathematical programming. An sharp constant lower and upper bounds of the den­ important experience of our research was to realize sity [5]. that those methods were efficient which strongly used MINIMAL POLYNOMIALS the geometrical properties of the problem 11[ ]. BOUNDS We worked on the minimal polynomials of the packings. We have investigated the question whether First of all, we investigated how theoretical bounds a circle packing contains optimal substructures, how can be determined for the optimum value. It was the minimal polynomial of the packing can be deter­ a natural idea to improve the lower bounds by ap­ mined based on the general minimal polynomials of plying computer and using global optimization tech­ the substructures. This problem was solved by us­ nology. We checked the numerical results by inter­ ing the resultants. We demonstrated some examples, val arithmetic computations using the PROFIL/BIAS how the method can be used. The minimal polynomi­ C ++ library, so their reliability is now proved by com­ als were published and also the exact values for some puter. Based on E. Specht’s modified billiard simula­ cases until 100 circles. We studied separately the al­ tion method approximate circle packings up to 200 gebraic solution of the Pn (m) = 0 equation, where were given. We have investigated the problem of the we guessed the suitable quadratical field based on the existency of the structure of the circle packings based structure of the packing and we have found the ex­ on the theory of Groebner bases, namely how the ex- act value by a CAS (Computer Algebra System). We istency of a circle packing can be proved with a given have also given a classification of the linear, quadrati- structure [1-3,12]. cal and quartical packing classes and the connection is OPTIMAL PACKINGS explained with the previous studied pattern classes [7]. Our summarized results are published in a book at A new verified optimization method was presented Springer [13]. One especially important feature of the for the circle packing problem. The developed algo­ book is the inclusion of all the open source program­ rithm is based on interval analysis. As one of the ming codes used on an enclosed CD. The wider scien­ most efficient parts of the algorithm, an interval-based tific community has already been involved in checking version of a previous elimination procedure is intro­ the codes and has helped in having the computational duced. This method represents the remaining areas proofs accepted. The main results we have summa­ still of interest as polygons fully calculated in a reli­ rized in a survey article, too [ 8]. able way. Currently the most promising strategy of finding optimal configurations is to partition the orig­ REFERENCES inal problem into subproblems. Still as a result of the highly increasing number of subproblems, earlier [1] Szabo, P.G.: On proving existence of some cir­ computer-aided methods were not able to solve prob­ cle packings in a square using computer algeb­ lem instances where the number of circles was greater ra systems. In: 6th International Conference on than 27. M.Cs. Markot provided a carefully devel­ Applied Informatics (January 27-31, 2004, Eger, oped technique resolving this difficulty by eliminating H ungary), Vol. I, 2004. p. 487. large group of subproblems together. This elimina­ [2] Szabo, P.G.: Egybevágó körök pakolásai tion method played a key role in solving the previ­ negyzetben - korlatok es minimálpolinomok. ously open problem instances of packing 28, 29, and In: XXVI. Operációkutatási Konferencia (2004. 30 circles [4,6,9]. majus 26-28, Győr). Előadás kivonatok, 2004, p. REAPETED PATTERNS 26. Using the proven and the best known circle pack­ [3] Szabá, P.G.: Packing Equal Circles in a Square - ings, we have investigated the structures of the pack­ bounds, minimal polynomials and classification. ings, determined some pattern- and structure classes In: Volume of extended abstracts of Conference and included the special cases into them. The clas­ of PhD Students in Com puter Science (July 1-4, sification was based on a common algorithmical de­ 2004, Szeged, Hungary), 2004, pp. 110-111. scription of the structures and a number theoretical

8 [4] Markot, M.Cs. - Csendes, T.: A reliable method (1929-2006) on János Bolyai’s number theoretical for verifying structural optimality of circle pack­ gems. We found the proof of F. Bolyai for the Wilson’s ing configurations in the unit square. SCAN-2004 Theorem and its conversion, results on the conversion Conference Book of Abstracts, Fukuoka, 2004, of Fermat’s little Theorem, about the perfect num­ 81. bers, etc. These collected results show a strong con­ [5] Szabó, P.G.: Packing Equal Circles in a Square nection between the father and his son in their com­ - Bounds, Repeated Patterns and Minimal Poly­ mon last years too. We tried to give an answer for the nomials. In: Volume of abstracts of SCAN 2004, following question: “How did János Bolyai know that 11th GAMM-IMACS International Symposium 4 272 943 is a prime number?” E. Kiss refereed our on Scientific Computing, Computer Arithmetic, investigations in his works (e.g. in the second edition and Validated Numerics (October 4-6, 2004, of his Bolyai-book). Later, we have written a common Fukuoka, Japan), 2004, p. 110. paper with Kiss about the manuscripts of Bolyais on the Mathematical Analysis. The research was based [6] Markót, M.Cs. - Csendes, T.: A new verified op­ on the Bolyai’s collections in Marosvásarhely (Tirgu- timization technique for the ’’packing circles in a Mures, Roumania) and Budapest (Hungary) [1-11]. unit square” problems. SIAM J. on Optimization 16(2005) 193-219. LÁSZLÓ KALMÁR’S LEGACY [7] Szabó, P.G.: Optimal substructures in optimal In 2005 Laszlo Kalmar’s (1905-1976) correspon­ and approximate circle packings. Beitrage zur Al­ dence with Hungarian mathematicians has been is­ gebra und Geometrie 46 (2005) No. 1. pp. 103­ sued by us with notes, titled KALMÁROM. In 2006 118. we have continued this work for to publish the second [8] Szabó, P.G. - Markót, M.Cs. - Csendes, T.: part of this book, titled KALMARIUM II, and we Global Optimization in Geometry - Circle Pack­ wrote some other articles about the life and works of ing into the Square. In: Essays and Surveys in L. Kalmar. This research was based on the Kalmár’s Global Optimization (GERAD 25th Anniversary legacy at the University of Szeged [12-17]. Series). Ed. by C. Audet, P. Hansen, and G. MARCEL RIESZ’S LEGACY Savard. New York, 2005. Springer. pp. 233-266. Continuing our general research direction, we have [9] Markot, M.Cs. - Csendes, T.: A reliable area re­ examined Marcel Riesz’s (1886-1969) legacy in the duction technique for solving circle packing prob­ Swedish town of Lund. This research is a continu­ lems. Com puting 77 (2006) 147-162. ation of the work of L. Filep (1941-2004). By do­ [10] Szabó, P.G.: Egybevógo körök pakolasai ing this, documents from Hungarian mathematical negyzetben - korlatok, ismetlődő mintak es schools of international significance become available minimóalpolinomok (In Hungarian). Ph.D. Thesis. to the public and scholars, including important cor­ Szeged, 2005. University of Szeged. 99 p. (2006). respondence by Frigyes Riesz (1880-1956) and Mar­ [11] Szabo, P.G.: Grid circle packings - a global opti­ cel Riesz. We have concluded in earlier studies that mization approach. In: Volume of abstracts of these materials definitely contain items of mathemat­ ISMP 2006, 19th International Symposium on ical and historical worth, which help us understand Mathematical Programming (July 30-August 4, the history of mathematical problem solving in the 2006, Rio de Janeiro, Brazil), 2006, p. 34. twentieth century. This is of a great significance, be­ cause the Riesz brothers are famous in the world of [12] Szabó, P.G. - Specht, E.: Packing up to 200 mathematics. Their articles are still cited, but not Equal Circles in a Square. In: Models and Al­ much is publicly known about their life and times. gorithms for Global Optimization: Essays Ded­ Most know only a few scant details about their sci­ icated to Antanas Zilinskas on the Occasion of entific correspondence. They also worked in foreign His 60th Birthday (Springer Optimization and scientific academies and circles, so these are of inter­ Its Applications, Vol. 4). Ed. by A. Törn, J. Zilin- national interest [18]. skas. 2006. Springer. pp. 141-156. FURTHER RESEARCH [13] Szabó, P.G. - Markót, M.Cs. - Csendes, T. - Specht, E. - Casado, L.G. - Garca, I.: New Ap­ Some other research topics arised from different proaches to Circle Packing in a Square. W ith Pro­ kind of requests. gram Codes. Springer, Berlin, 2007. PANNONIAN PHOENIX V. HISTORY OF MATHEMATICS AND Pannonian Phoenix, or The Hungarian Language INFORMATICS Arisen From The Ashes - Our Earliest Printed Scientific Books from the 16th - 19th Centuries [19]. During the period 2003-06, we worked on some books, book chapters and articles, based on our research on The National Szechenyi Library and the Hunga­ the history of mathematics and informatics. A big rian Academy of Sciences organized the ’Pannonian part of the research on the History of Mathematics Phoenix’ exhibition. We gave the analytic descrip­ is often an investigation of the correspondence and tions of the following mathematical books: legacy of scientists. In the following topics, we have summarized, shortly, the studied scientific legacies. • Aritmética, az az A szamvetesnec tvdomania, mell(y) az tvdos Gemma Frisivsnac szam-vetesboel FARKAS BOLYAI’S LEGACY magyar nyelure... forditattot. Debrecen, 1577. We found some interesting unknown mathematical • Tolvay Ferenc: Az Arithmetikanak; avagy A notes of Farkas Bolyai (1775-1856) in his manuscripts Számlálasnak ot Speciesinek rövid Magyar on number theory from the second part of the 1850’s Reguiakban foglaltatott Mestersege. Kolozsvár, years. These results joined to the work of E. Kiss 1698.

9 • Onadi János: Practici algorithmi erotemata me- [9] Kiss E. - Szabó P.G.: A matematikai analízis thodica, az az olly cselekedő számok, mellyek könyü problémái a ket Bolyai kéziratos hagyatekaban. kérdések es feleletek által rövid utat mutatnak arra (Submitted for publication). a tudomanyra, melyben akár mely fele adasnak [10] Szabó P.G. - Oláh-Gól R.: Bolyai Farkas kezirata s vetelnek, osztálynak, vagy egyeb kereskedesben, csak a legg-kissebb summáanak-is bizonyos száama a kockakettőzes problemójóról (Submitted for tanitattik. Kassa, 1693. publication). • Maráthi György: Arithmetica, vagy szamvetesnek [11] Kiss E. - Olóh-Gal R.: Újabb leveltari ku­ mestersege. Debrecen, 1743. tatósok Bolyai Jónos eletmuvehez. A sajto ala rendezesben közreműködő: Szabo P.G. • Maká Pal: Bevezetes a számvetesre a’ magyar es hozza tartozandá tartományok’ nemzeti iskoláinak [12] Szabo P.G.: KALMARIÚM. Kalmór Lószlo leve- szamára. Buda, 1780. lezese magyar matematikusokkal (Dóvid Lajos, • Dugonics András: A’ tudakosságnak első konyve, Erdős Pól, Fejer Lipót, Grunwald Geza, Kertesz mellyben foglaltatik a’ betovetes (algebra). A’ Andor, Kőonig Dóenes, Róedei Lóaszlóo, Róenyi Alfróed, tudákossagnak masadik könyve, mellyben foglal­ Riesz Frigyes, Szele Tibor, Turan Pól, Varga tatik a föld-merés (geometria). Pest, 1784. Tamas), Szeged, 2005. Polygon. 476 p. • Bolyai Farkas: Az arithmetica eleje. Marosvasar- [13] Szabo P.G.: KALMARIÚM II. Kalmór Lószló le- hely, 1830. velezese magyar matematikusokkal (Aczel Janos, • Brassai Sámuel: Euklides Elemei XV konyv. Pest, Fenyo Istvón, Gyires Bela, Hajos György, Lazar 1865. Dezso, Lakatos Imre, Neumann Janos, Radó Ti­ bor, Surónyi Jónos, Szenóssy Barna, Szőkefalvi- JOHN VON NEUMANN Nagy Bela, Vincze Istvan). (Submitted for pub­ lication). In the year of von Neumann (2003) we have writ­ [14] Szabó P.G.: Kalmór Laszló hagyateka. In: XLV. ten some papers about the life and works of John von Ratz Lószlo Vandorgyules (2005. julius 5-8, N eumann (1903-1957) [20-23]. Salgótarjan) eloadas kivonatok, 2005. pp. 14-15. OTHER WORKS [15] Bohus M. - Makay A. - Sóntane-Tóth E. - There are some other works on Japanese History Szabó P.G.: ”Kretaprogramozós” Kalmór Lószlo of Mathematics (Sangaku problems) [24], a forgot­ vezetóesóevel (Az informatika oktatóasóanak kezde­ ten Hungarian book on the ’upward’ continued frac­ tei Szegeden). In: Informatika a felsoőoktataósban tions [25], magic squares [26,27], an old astronomical 2005 Konferencia (2005. aug. 24-26, Debrecen) instrument “Jacob’s Ladder” [28], and we edited the eloőadóas kivonatok, 2005. p. 81. last unpublished work of L. Dávid (1881-1962) on the [16] Bohus M. - Muszka D. - Szabó P.G.: A szegedi Cauchy-equation at János Bolyai’s work [29,30]. informatikai gyujtemeny, Új Kep 9, 2005, No. 10. pp. 35-40. REFERENCES [17] Szabo P.G.: Ki rejtőzik a mor ólszakall [1] Szabá P.G.: Bolyai Farkas szamelmeleti vonatko- mogott? (Vólogatas Kalmar Laszló feljegyze- zasu keziratos hagyateka, Termeszet Világa seibol), SZEGED 17, 2005, No. 3. pp. 18-19. Bolyai-emláekszáam, 2003, pp. 57-61. [18] Riesz Frigyes óes Riesz Marcell levelezóese. Filep [2] Szabá P.G.: A 4 272 943 ,,edi szam”, Termeszet Laszló gyujteset sajtó ala rendezte es jegy­ Vilaága Bolyai-emláekszaám, 2003, p. 62. zetekkel ellatta: Szabó P.G. (Submitted for pub­ lication). [3] Szabó P.G.: A Bolyai-negyzetek, Termeszet Vila- [19] Szabo P.G.: Matematikatörtenet + History ga Bolyai-emláekszáam, 2003, p. 61. of Mathematics descriptions. In: Pannóoniai [4] Szabá P.G.: Idősebb Zeyk Miklás, az ismeretlen Feniksz, avagy hamvóból fel-tómadott magyar nagyenyedi tudás, Termeszet Vilaga 134, 2003, nyelv. Elsőo nyom tatott tudomóanyos koönyveink No. 8, pp. 372-373. (16-19. szazad). Szerk. Gazda I., Stemler A. Bu­ [5] Szabo P.G.: Pávay Vajna Miklás levele uno­ dapest, 2005. OSZK - MTA pp. 153-170. kájához, Bolyai Farkashoz, Muszaki Szemle (His­ [20] Szabo P.G.: Neumann Janos eletutja es toria Scientiarum - 1, Special Issue in History of munkóssaga, Pi-Matematikai folyóirat, Miskolci Sciences) 27 (2004) pp. 44-45. Egyetem I/II (2002/2003) pp. 1-13. [6] Szabo P.G.: A Wilson-tetelnek es megfordí- [21] Szabó P.G.: Neumann Jónos ajanlja Szőkefalvi- tasának bizonyítasa Bolyai Farkas keziratos Nagy Belót, Termeszet Vilóga Neumann-emlek- hagyatáekáaban, Polygon 13, 2005, No. 2, pp. 1­ szóam, 2003. p. 47. 10. [22] Szabó P.G.: Neumann Jónos es Szeged, Ter­ [7] Szabo P.G.: ”Kiss Elemer: Matematikai kin­ meszet Vilaga Neumann-emlekszóm, 2003. pp. csek Bolyai Jaános káeziratos hagyatáekáabáol” cámuő 48-51. könyveről, Termeszet Világa 137, 2006, No. 4. p. [23] Szabó P.G.: Neumann Jónos (szocikk), In: Nem­ 188. zeti óevforduloóink 2007, Balassi Baólint Kulturóalis [8] Szabo P.G.: Bolyai Farkas keziratos hagyateka. Intezet Nemzeti Evfordulók Titkarsaga, Bp., In: A Magyar Tudomáany Napja Erdáelyben. 2006, p. 56. Bolyai Farkas Emláekkonferencia. (2006. novem­ [24] Szabo P.G.: Szangaku, a japan matematika kin­ ber 25-26, Csíkszereda, Románia) eloadas csei, Szaku 9, 2003, pp. 8-9. kivonatok, 2006, p. 19. [25] Szabo P.G.: A felfele menő lónctortek, Polygon 12, No. 1-2. pp. 71-80.

10 [26] Szabó P.G.: Bűvös négyzetek, ABACUS 10, 2004, Nó. 7. pp. 27-29. [27] Szabó P.G.: Bűvós négyzetek, ABACUS 10, 2004, Nó. 8. pp. 23-26. [28] Szabó P.G.: Jakób bótja, Műszaki Szemle (His­ tória Scientiarum - 1, Special Issue in Históry óf Sciences) 27, 2004, pp. 39-43. [29] Szabó P.G.: David Lajós ,,hattyűdala”. (Submit­ ted fór publicatión). [30] David L.: Az F (x 1) + F (x2) = F (x 1 + x 2) fűggvenyegyenlet Bólyai Janósnal. (Sajtó ala ren­ dezte David P. es Szabó P.G.). (Sűbmitted fór pűblicatión).

11 Department of Computer Algorithms and Artificial Intelligence

I. AUTOMATA THEORY [5] Gecseg, F. and Imreh, B.: On asynchronous tree automata. Journal of Automata, Languages and We have continued to study complete systems of tree Combinatorics, accepted for publication. automata. In [5] we gave necessary and sufficient con­ ditions under which a system of tree automata is iso- II. ANALYSIS OF ALGORITHMS morphically complete with respect to the a i -products for the class of asynchronous tree automata. Little is known about the general properties of tree BIN PACKING languages recognized by deterministic root-to-frontier In the classical bin packing, we are given a list L tree recognizers (DR tree languages). Therefore, we of items (ai,a2, ...,an) each item ai e (0, 1] and the have started to study special classes of DR tree lan­ goal is to find a packing of these items into a mini­ guages the counterparts of which are well-known in mum number of unit-capacity bins. In [ 6] we present the theory of finite state recognizers (definite, nilpo­ the theoretical results on the on-line Sum-of-Squares tent, monotone languages). Paper [3] contains our algorithm. SS is applicable to any instance of bin results concerning closedness of nilpotent DR tree lan­ packing in which the bin capacity B and the item sizes guages under Boolean operations. s(a) are integer (or can be scaled to be so), and runs We say that a class M of finite monoids deter­ in tim e O (nB ). It performs remarkably well from an mines a class K of tree languages recognizable by tree average case point of view: For any discrete distribu­ recognizers if a tree language is in K if and only if its tion in which the optimal expected waste is sublinear, syntactic monoid is in M . Classes of monoids deter­ SS also has sublinear expected waste. For any dis­ mining the classes of definite and nilpotent DR tree crete distribution where the optimal expected waste is languages are given in [4]. bounded, SS has expected waste at most O(logn). We Results of [4] show that the class of definite DR also discuss several interesting variants on SS, includ­ tree languages can be determined by the same class of ing a randomized O (nB log B)-time online algorithm monoids as the class of definite string languages. The SS* whose expected behavior is essentially optimal for same is true for the class of nilpotent DR tree lan­ all discrete distributions. Algorithm SS* depends on guages. This was the observation which motivated us a new linear-programming-based pseudopolynomial­ to give general conditions in [ 2] under which a class time algorithm for solving the NP-hard problem of de­ of tree languages with a given property can be de­ termining, given a discrete distribution F , just w hat is termined by the same class of monoids as the class of the growth rate for the optimal expected waste. In [5] string languages having the same property. The result it is proven that the asymptotic worst case bound of has been applied to certain classes of tree languages. the SS algorithm is at most 2.777. In [1] a novel classi­ CONNECTIONS OF RESEARCH TO EDU­ fication scheme is presented for bin packing problems. CATION Classification of the papers and results in fields of re­ search are helpful in placing new results in a historical Tree automata and tree languages constitute dif­ context and in identifying open problems. The paper ferent graduate and PhD courses. The open prob­ contains several examples on using the classification lems can serve as research subjects for PhD students. scheme for the known results on the area of bin pack­ The textbook [1] gives a systematic treatment of fi­ ing. nite state recognizers, string languages, tree recogniz­ ers and tree languages. SCHEDULING ACKNOWLEDGEMENTS In [9] the following scheduling problem is investi­ gated. There are two sets of identical machines, the Research sketched above was supported by the jobs have two processing times one for each set of ma­ Hungarian National Foundation for Scientific Re­ chines. We consider two different objective functions, search, Grant T 48786. in the first model the goal is to minimize the maximum of the makespans on the sets, in the second model we REFERENCES minimize the sum of the makespans. We investigate the online and the offline versions. In the offline case [1] Gecseg, F.: Automata and Formal languages (in an FPTAS is given for both objective functions. In Hungarian). Polygon, Szeged, 2005. the online case we characterize the competitive ratio [2] Gecseg, F.: Classes of tree languages determined of a load greedy algorithm which assigns every job to by classes of monoids. International Journal of the set, where the job has smaller load. The com­ Foundations of Computer Science, submitted for petitive ratio of this algorithm tends to to for both publication. problems as the ratio m /k grows. We show that the post greedy algorithm has also unbounded competi­ [3] Gecseg, F. and Gyurica, Gy.: On the closedness tive ratio as m /k grows. Finally we analyze a modi­ of DR tree languages under Boolean operations. fied greedy algorithm and we show that it is constant Acta Cybernetica, 17(2006), 449-457. competitive for arbitrary number of machines. Lower [4] Gecseg, F. and Imreh, B.: On definite and nilpo­ bound for the possible competitive ratios are also pre­ tent DR tree languages. Journal of Automata, sented. Languages and Combinatorics, 9:1(2004), 55-60.

12 For most scheduling problems the set of machines by probabilistic and empirical analysis. is fixed initially and remains unchanged for the dura­ LEARNING ALGORITHMS tion of the problem. Recently online scheduling prob­ lems have been investigated with the modification that In [7] we investigate the problem of learning the initially the algorithm possesses no machines, but that order of criteria of lexicographic decision under var­ at any point additional machines may be purchased. ious reasonable assumptions. Although the lexico­ In all of these models the assumption that each ma­ graphic decision is very simple, it is the most common chine has unit cost have been supposed. In [11] we and used decision model in everyday life. Even if the consider the problem with general machine cost func­ decision-makers use another model, they translate it tions. Furthermore we also consider a more general (if it is possible) to lexicographic, because for the ver­ version of the problem where the available machines bal communication only this approach is good. For have speed, the algorithm may purchase machines learning the order of criteria we give a sample evalua­ with speed 1 and machines with speed s. We de­ tion and an oracle based algorithm. In the worst case fined and analyzed some algorithms for the solution analysis of the sample evaluation algorithms we are of these problems and their special cases. Moreover dealing with the adversarial models. We show that some lower bounds on the possible competitive ratios if the distances of the samples are less than 4, then are presented. In [15] we define and investigate a fur­ samples are not learnable, but 4-distance samples are ther scheduling model. In this new model the number polynomial learnable. of machines is not fixed; the algorithm has to purchase SURVEYS the used machines, moreover the jobs can be rejected. We show that the simple combinations of the algo­ We wrote surveys on several areas of the analysis rithms used in the area of scheduling with rejections of algorithms. An overview on the results concerning and the area of scheduling with machine cost are not the area of median strings is given in [14]. A survey constant - competitive. We present an exponential on the basic results competitive analysis of online al­ time 2.618-competitive algorithm called OPTCOPY. gorithms is published in the book chapter [10]. The surveys [2], [3], [4] summarize some parts of the bin STRING ALGORITHMS packing research field. In [2] the different versions of In [13] the problem of finding the generalised me­ classical one dimensional bin packing and the basic dian string is considered. The generalised median results are presented. The paper [3] gives an overview string is defined as a string that has the smallest sum on the area of variable sized bin packing and bin cov­ of distances to the elements of a given set of strings. It ering. In this models it is not supposed that the size is a valuable tool in representing a whole set of objects of each bin is 1. In [4] the basic results on the per­ by a single prototype, and has interesting applications formance guarantees for one dimensional bin packing in pattern recognition. All algorithms for computing are summarized. generalised median strings known from the literature ACKNOWLEDGEMENTS are of static nature. That is, they require all elements of the underlying set of strings to be given when the The mentioned research tasks were supported by algorithm is started. In this paper, we present a novel the following grants: the Hungarian National Founda­ approach that is able to operate in a dynamic environ­ tion for Scientific Research Grant F048587 and Grant ment, where there is a steady arrival of new strings T046405. belonging to the considered set. Rather than com­ puting the median from scratch upon arrival of each REFERENCES new string, the proposed algorithm needs only the me­ [1] E. G. Coffman, J. Csirik A classification scheme dian of the set computed before together with the new for bin packing Acta Cybernetica, (2006) to ap­ string to compute an updated median string of the pear new set. Our approach is experimentally compared to a greedy algorithm and the set median using both [2] E. G. Coffman, J. Csirik, Y. T. Leung, Variants of synthetic and real data. classical one dimensional bin packing Approxima­ tion algorithms and metaheuristics, Taylor and SERVER PROBLEMS Francis Group (2006) to appear We investigated some combinatorial optimization [3] E. G. Coffman, J. Csirik, Y. T. Leung, Variable problems on routing servers. In [ 8] we consider a gen­ sized bin packing and bin covering Approxima­ eralized online 2-server problem on the uniform space tion algorithms and metaheuristics, Taylor and in which servers have different costs. Previous work fo­ Francis Group (2006), to appear cused on the case where the ratio between these costs [4] E. G. Coffman, J. Csirik, Performance guaran­ was very large. We give results for varying ratios. For tees for one dimensional bin packing Approxima­ ratios below 2.2, we present a best possible algorithm tion algorithms and metaheuristics, Taylor and which is trackless. We present a general lower bound Francis Group (2006), to appear for trackless algorithms depending on the cost ratio, proving that our algorithm is the best possible track­ [5] Csirik, D. S. Johnson, C. Kenyon, On the worst- less algorithm up to a constant factor for any cost case performance of the sum of squares algorithm ratio. The results are extended for the case where we for bin packing DS/0509031, 1 (2005) have two sets of servers with different costs. In [12] we [6] J. Csirik, D. S. Johnson, C. Kenyon, J. B. Orlin, recall the patching technique, which is a basic method P. W. Shor, R. R. Weber, On the sum-of-squares in the area of developing heuristic algorithms for the algorithm for bin packing Journal of ACM 53: 1 traveling salesman problem and its generalization. We (2006) 1-65 summarize some known applications and we present a [7] J. Dombi, Cs. Imreh, N. Vincze, Learning lexico­ new application of the technique for the p-TSP prob­ graphical order, European Journal on Operation lem. We demonstrate the efficiency of this application Research to appear

13 [8] L. Epstein, Cs. Imreh, R. van Stee, More on class, the Generalized Dombi operator was introduced, Weighted Servers or FIFO is better than LRU, which unites well-known operators of fuzzy theory Theoretical Computer Science 3 0 6, 2003, 305­ such as min/max, product/algebraic sum, Einstein, 317. Hamacher, Dombi and drastic. Its formula is as fol­ [9] Cs. Imreh, Scheduling problems on two sets of lows.

identical machines, Computing, 7 0, 2003, 277­ J a ) 1 (x) = 294, Y 1 — Xx ex 1 / a ’ 1 + 1 + Y I 1 [10] Cs. Imreh, Competitive analysis (in Hungarian), 1 rr 1 )) in Algorithms in Informatics II., ed. A. Ivnyi, where x e [0,1]n and Y ,a £ R. Also, a new form of (2005), 1350-1383 the Hamacher operator was given, which makes multi­ [11] Cs. Imreh, On-line scheduling with general ma­ argument calculations easier. chine cost functions Electronic Notes in Discrete We also examined the De Morgan identity which Mathematics V ol 2 7, 2006, 49-50 connects the conjunctive and disjunctive operators by [12] B. Imreh, Cs. Imreh, Sz. Imreh The patching a negation. It is shown that in some special cases technique and its applications, (in Hungarian), (min/max, drastic and Dombi) the new operator class Alkalmazott Matematikai Lapok , 2 2, 2005, 85-96. forms a De Morgan triple with any rational involutive negation. [2] [13] X. Jiang, K. Abegglen, H. Bunke, J. Csirik, Dy­ namic computation of generalized median strings REASONING WITH APPROXIMATED Pattern Analysis and Applications 6 (3,) (2003), FUZZY INTERVALS 185-193. We have investigated the two fundamental ap­ [14] X. Jiang, H. Bunke, J. Csirik, Median strings: A proaches to approximate reasoning, the compositional review In: Bunke H (ed.) Data mining in Time rule of inference (CRI) and fuzzy truth value based Series Databases, : World Scientific, 2004. 173­ reasoning. They are common in the sense that the 192 so-called indetermination of the conclusion appears in [15] J. Nagy-Gyorgy, Cs. Imreh, On-line scheduling both models. We have argued that this phenomenon with machine cost and rejection, Discrete Applied is acceptable only in the logic view of reasoning, and Mathematics , submitted so it should be avoided regarding the similarity based view. Sigmoid-like membership functions were intro­ III. RESEARCH IN MULTICRITERIA duced to avoid the indetermination of the conclusion. DECISION MAKING AND FUZZY The generalized CRI reasoning scheme was investi­ LOGIC gated for all three representative t-norms. Only the Lukasiewicz t-norm based CRI scheme is not closed A COMMON PREFERENCE MODEL FOR under sigmoid-like functions and from all three, the VARIOUS DECISION MODELS minimum is the best regarding computational com­ plexity. The Membership Driven Inference (MDI) rea­ Decision-makers use aggregation procedures using soning scheme was introduced by modifying the min- value functions or preference relations. However, the based CRI on sigmoid-like functions in order to get a aggregation procedure can not be independent from simple yet powerful reasoning scheme. It was shown the value function or the preference relation. Conjoint that it has a series of good properties, it fulfills the measurement can handle both. The advantage of this generalized modus ponens, the generalized modus tol- model is that it gives a general modeling framework lens, the generalized chain rule, and more. Also, we for the decision situation. But it does not tell us much have focused on the efficient computation of the MDI about how we should make the decision-making. If a reasoning scheme. The class of squashing functions decision-maker is facing an aggregation problem he was introduced. This class of membership functions doesn’t know which aggregation procedure is he going can arbitrarily approximate piecewise-linear member­ to use. To choose the MCDM method also seems to ships functions of fuzzy sets. Moreover, we have shown be a multicriteria decision problem. The conclusion is that by using squashing membership functions, the that a more general framework is needed. MDI reasoning scheme can be calculated on the pa­ We proposed a general multicriteria decision tool rameters of the memberships instead of a pointwise which contains the classical procedures (ELECTRE, computation. This efficient calculation of a rule’s out­ PROMETHEE, TACTIC, MAUT, Lexicographic de­ put can be applied to approximated trapezoidal and cision) as special cases. The so-called Bounded Sys­ triangular fuzzy intervals, too, by an LR decomposi­ tem is based on the class of nilpotent t-norms ex­ tion of them. [3,4] tended by hedges and mean and preference operators. With the Bounded System a heterogenous decision ADVANCES IN TYPE-2 FUZZY LOGIC system can be built up i.e. on some criteria we can Fuzzy logic in narrow sense is a generalization of make a lexicographic decision, on some others we can classical two-valued logic, it considers a range of truth use an outranking approach with veto threshold and values, usually the unit interval. In recent years, re­ maybe on the remaining criteria the utility approach. search related to type -2 fuzzy logic has become even Our Bounded System is easy to understand and its pa­ more active than ever. Type-2 fuzzy logic takes the rameters (weights, thresholds etc.) can also be easily generalization a step further by considering truth val­ assessed by a learning algorithm. [1] ues that are themselves fuzzy. This means that ev­ THE GENERALIZED DOMBI OPERATOR ery truth value (i.e. every element of [ 0, 1]) has a fuzzy membership degree (which is again an element The multiplicative utility function is extensively of [0,1]). This mapping from the unit interval to itself used in the theory of multicriteria decision mak­ is the truth value, hence its name fuzzy truth value. ing. As its generalization a new fuzzy operator

14 We have studied type-2 logical operations (such as conjunctions, disjunctions and implications) on non­ interactive fuzzy truth values. Our investigations are intended to provide a theoretical background for type- 2 approximate reasoning applications. Regarding type-2 t-norms and t-conorms (i.e. con­ junctions and disjunctions), sufficient conditions were given on the continuity of the resultant fuzzy truth values. We have shown easy-to-implement point- wise formulas for the type -2 conjunction and disjunc­ tion of fuzzy truth values with different monotonic­ ity. As an important special case, we considered the extended Lukasiewicz operations on interactive lin­ ear fuzzy truth values. It was shown that the com­ putationally complex convolutions of the extended Lukasiewicz operations are equivalent to simple oper­ ations on the parameters on the linear fuzzy truth val­ ues. We have given necessary and sufficient conditions when these operations preserve continuity and linear­ ity. These results can be directly applied to type-2 fuzzy systems and also to approximate reasoning sys­ tems based on fuzzy truth values. Our investigations on implications have shown that type-2 S-implications have similar properties on the lattice of convex normal fuzzy truth values like type-1 S-implications on the unit interval. Residual implications (i.e. residuals of conjunctive operations) are fundamental in fuzzy logic. Type-2 residual im­ plications are approached from two distinct views: as extended residual implications of t-norms, and as gen­ eral residuated structures. Extended type-2 implica­ tions are compared to type-2 S-implications, and it turned out that regarding the lattice of convex nor­ mal fuzzy truth values the latter seem more adequate for approximate reasoning purposes. [5-7]

REFERENCES

[1] J. Dombi. A common preference model for various decision models. In B. De Baets and J. Fodor, editors, Principles of Fuzzy Preference Modelling and Decision Making, pages 143-164. Academia Press, 2003. [2] J. Dombi. Towards a general class of operators for fuzzy systems. submitted for publication, 2006. [3] J. Dombi and Zs. Gera. The approximation of piecewise linear membership functions and Lukasiewicz operators. Fuzzy Sets and Systems, 154:275-286, 2005. [4] Zs. Gera. Computationally efficient reasoning us­ ing approximated fuzzy intervals. Fuzzy Sets and Systems, 158(7):689-703, 2007. [5] Zs. Gera and J. Dombi. Exact calculations of ex­ tended logical operations on fuzzy truth values. submitted for publication. [6] Zs. Gera and J. Dombi. Type-2 residual implica­ tions on non-interactive fuzzy truth values. sub­ mitted for publication. [7] Zs. Gera and J. Dombi. Type-2 s-implications on non-interactive fuzzy truth values. submitted for publication.

15 Department of Foundations of Computer Science

THEORETICAL COMPUTER SCIENCE LOGIC ON WORDS The research performed in the Department of Linear temporal logic has the same expressive Foundations of Computer Science lies in the intersec­ power as aperiodic automata. In order to be able tion of algebra, logic and computer science. The main to express modular counting and other properties of themes are automata and formal languages, tree au­ words, Wolper introduced Extended Linear Tempo­ tomata and term rewriting, weighted tree automata, ral Logic. In [7], we bridged W olper’s logic and logics on words and trees, finite model theory, fixed the Krohn-Rhodes decomposition theory of finite au­ point operators in computer science, and axiomatic tomata and gave an algebraic characterization of questions. W olper’s logic.

I. ALGEBRA & LOGIC IN COMPUTER LOGIC ON TREES SCIENCE Temporal logics can be classified into linear time and branching time logics. The latter logics can SEMIRINGS AND SEMIMODULES be viewed as logics on trees. Important branching In [12], we introduced inductive ‘-semirings as a time logics are CTL (Computational Tree Logic) and generalization of Kozen’s Kleene algebras, We proved CTL‘ . In both logics, one can define only regular that inductive ‘-semirings are iteration semirings and properties. However, it is an open problem to give a they are closed under several algebraic constructions. decidable characterization of those regular properties In [10, 14, 15] we studied semiring-semimodule pairs (given by a finite tree automaton) definable in these equipped with a ‘- and ^-operation. We estab­ logics. An algebraic approach to deal with this and lished several algebraic properties of these structures related problems in formal logic has been developed and studied several subclasses where the ‘- and ^ - in the papers [4-6, 8,9] using pseudovarieties of finite operations are defined using a partial order, a com­ algebras and the cascade product (wreath product). pletely additive structure and/or an infinite prod­ The method developed in these papers reduces the uct. We used these algebraic structures to give an characterization of the expressive power to the mem­ abstract treatment of Buchi-automata and weighted bership problem in pseudovarieties of finite algebras. Buchi-automata on infinite words. In [13], we ap­ ACKNOWLEDGEMENTS plied these structures to context-free languages over w-words. In [16], we defined algebraically complete The above research has been supported by semirings as an extension of inductive ‘ -semirings. the grants 53ou1 and 60ou12 of the Austrian- One of the most fundamental nontrivial normal form Hungarian Action Found, the grant T046686 of the theorems for context-free languages is the Greibach National Foundation of Hungary for Scientific Re­ normal form theorem. We established Greibach’s nor­ search (OTKA), and the ESF Research Network AU- mal form theorem in all algebraically complete semir­ TOMATHA. ings. REFERENCES CATEGORICAL ALGEBRAS [1] S. L. Bloom and Z. Esik. Axiomatizing omega In [3], we generalized the notion of partially or­ and omega-op power on words, Theoretical In­ dered algebras to categorical algebras. An important formatics and Applications, 38(2004), 3-18. result in partially ordered algebras that has many ap­ plications in Computer Science is that each ordered [2] S. L. Bloom and Z. Esik. The equational theory algebra can be completed into a continuous ordered of regular words, Information and Computation , algebra preserving all valid inequalities. We extended 197(2005), 55-89. this result to categorical algebras and discussed sev­ [3] S. L. Bloom and Z. Esik. Completing Categori­ eral applications in Computer Science. cal Algebras, Proc. Fourth IFIP Conf. Theoreti­ REGULAR WORDS cal Computer Science TCS-2006, Springer, 2006, 231-250. Regular words were introduced by Courcelle in the [4] Z. Esik. An algebraic characterization of the ex­ late 70’s. His motivation came from recursive program pressive power of temporal logics on finite trees, schemes. They were subsequently studied by Thomas P art 1, Proc. 1st International Conference on Al­ and Heilbrunner. Courcelle raised several important gebraic Informatics , Aristotle University of Thes­ problems regarding the equational axiomatization of saloniki, 2005, 53-78. regular words and the decidability of the equational theory. Courcelle’s questions for axiomatization were [5] Z. Esik. An algebraic characterization of the ex­ completely solved in [1,2]. We also gave a P-time al­ pressive power of temporal logics on finite trees, gorithm to decide the equational theory. This greatly P art 2, Proc. 1st International Conference on Al­ improves an earlier algorithm of Thomas with no ex­ gebraic Informatics , Aristotle University of Thes­ plicit upper bound for its complexity. saloniki, 2005, 79-100. AXIOMATIC THEORY OF AUTOMATA [6] Z. Esik. An algebraic characterization of the ex­ pressive power of temporal logics on finite trees, In [ 11], we gave an introduction to the axiomatic P art 3, Proc. 1st International Conference on Al­ theory of automata and languages developed earlier gebraic Informatics , Aristotle University of Thes­ by Conway, Bloom, Esik and Kuich. saloniki, 2005, 101-110.

16 [7] Z. Esik. A note on W olper’s logic, Proc. Work­ TREE SERIES TRANSDUCERS shop on Semigroups and Automata, Lisboa, 2005, The first definition of the semantics of a tree series electronic. transducer, called algebraic semantics, is based on a [8] Z. Esik. Characterizing CTL-like Logics on Finite tree series substitution that does not take into account Trees, Theoretical Computer Science, 356(2006), the number of the occurrences of the substitution vari­ 136-152. ables. In [16] we introduced tree series transducers of [9] Z. Esik. Cascade Products and Temporal Logics which the semantics takes into account that number. on Finite Trees, Electronic Notes in Theoretical We compared the computation power of the two mod­ Computer Science, 162(2006), 163-166. els. In [17] we defined a tree series transducer model [10] Z. Esik and W. Kuich. An algebraic generaliza­ with an operational style semantics and called this tion of omega-regular languages,Proc. MFCS 04, model weighted tree transducer. We showed that LNCS 3153, Springer, 2004, 648-659. tree series transducers with algebraic semantics and [11] Z. Esik and W. Kuich. Equational Axioms for a weighted tree transducers are semantically equivalent. Theory of A utom ata, Formal Languages and Ap­ In [11] we generalized the famous tree transducer plications, Studies in Fuzziness and Soft Com­ hierarchy of J. Engelfriet for tree series transducers puting 148, Carlos Martin-Vide, Victor Mitrana, over commutative, idempotent and positive semirings. Gheorghe Paun (Eds.), Springer, 2004, 183-196. [12] Z. Esik and W. Kuich. Inductive ‘-semirings, ALGEBRAIC PROPERTIES OF REGULAR Theoretical Computer Science, 324(2004), 3-33. TREE LANGUAGES [13] Z. Esik and W. Kuich. A semiring-semimodule In [3], we showed that regular tree languages can generalization of w-context-free languages, The­ be axiomatized by a few simple equations and the least ory is Forever, LNCS 3113, Springer, 2004, 68­ fixed point rule. This extends a result of Kozen from 80. words to trees. In [ 8], we introduced a new algebraic [14] Z. Esik and W. Kuich. A semiring-semimodule framework for the study of varieties of tree languages generalization of w-regular languages, Part 1, in relation to logic. J. Automata, languages, and Combinatorics, MULTI BOTTOM-UP TREE TRANSDUC­ 10(2005), 203-242. ERS [15] Z. Esik and W. Kuich. A semiring-semimodule In [12] we defined deterministic multi bottom-up generalization of w-regular languages, Part 2, tree transducers and showed that they are seman­ J. Automata, languages, and Combinatorics , tically equivalent with deterministic top-down tree 10(2005), 243-264. transducers with regular look-ahead. Then in [13] we [16] Z. Esik, H. Leiss. Algebraically complete semir­ compared the computation power of linear determin­ ings and Greibach normal form, Annals of Pure istic multi bottom-up tree transducers and eight well- and Applied, Logic, 103(2005), 173-203. known classes of deterministic bottom-up and deter­ ministic top-down tree transducers. II. AUTOMATA AND FORMAL LAN­ SHAPE PRESERVING TREE TRANSDUC­ GUAGES ERS WEIGHTED TREE AUTOMATA Shape-preserving tree transducers generalize length-preserving sequential machines. In [10] In [1], we proved a general Kleene theorem ap­ we showed that shape-preserving top-down tree plicable to weighted tree automata and formal power transducers are equivalent to finite-state relabelings. series over trees, finite or infinite. In [5] we gave a Moreover, we proved that it is decidable if a top-down survey of results on weighted tree automata and tree tree transducer is shape preserving. In [20] it was transducers. In [4], we studied fuzzy subsets of alge­ proved that shape-preserving bottom-up tree trans­ bras including algebras of trees and established a triple ducers are also equivalent to finite-state relabelings. equivalence between equational, rational and recog­ The decidability of the shape-preserving property for nizable fuzzy sets. bottom-up tree transducers was proved in [ 21]. In [2] we showed that the cost-finiteness of tree au­ tomata with costs over finitely factorizing and mono­ PEBBLE TREE TRANSDUCERS tonic semirings is decidable. We showed that it is also decidable whether a tree automaton with costs over a In [14,15], we investigated pebble tree transduc­ finitely factorizing, monotonic, and naturally ordered ers and macro pebble tree transducers. We showed semiring is bounded with respect to the natural order. that the circularity problem and the strong circularity In [18], we compared the classes of tree series problem for pebble tree transducers is decidable and which are recognizable by (a) multilinear mappings that the weak circularity problem for pebble macro over some finite dimensional K -vector space, where K tree transducers is decidable. Moreover, we proved is a field, (b) K-E-tree automata, where K is a com­ several decomposition results for macro pebble tree mutative semiring, (c) weighted tree automata over transducers. K , where K is a semiring, (d) finite, polynomial tree In [ 22], n-pebble tree-walking automata with al­ automata over K, where K is a commutative and con­ ternation were defined. It was shown that tree lan­ tinuous semiring, (e) polynomially-weighted tree au­ guages recognized by these devices are exactly the tomata, where K is a semiring, and (f) weighted tree regular tree languages. Then it was shown that the automata over M-monoids. deterministic and noncircular pebble alternating tree­ walking automata are strictly less powerful than their nondeterministic counterparts.

17 STORAGE-TO-TREE TRANSDUCERS OTHER In [19] it was shown that the class of tree trans­ In [9] we gave a short introduction to tree trans­ formations induced by regular storage-to-tree trans­ ducers for those who just would like to get an insight ducers with positive look-ahead is equal to the com­ into the field. position of the class of transformations induced by ACKNOWLEDGEMENTS regular storage-to-tree transducers with the class of linear homomorphisms. It was also proved that the The above research has been supported by the classes of transformations induced by both IO and OI grants 53ou1 and 60ou12 of the Austrian-Hungarian context-free-storage-to-tree transducers are closed un­ Action Found, the grants 36/2005 and 45/2002 of the der positive look-ahead and composition with linear Deutsche Akademische Austauch Dienst (DAAD) and homomorphisms. the Hungarian Scholarship Committee (MOB), the TREE AUTOMATA AND TERM REWRITE grants T046686 and T030084 of the National Foun­ SYSTEMS dation of Hungary for Scientific Research (OTKA), and a Szechenyi Istvan Scholarship of the Hungarian In [27] several characterizations and decidability Ministry of Education. results were obtained for ground tree transformations and congruence relations induced by tree automata. REFERENCES

TERM REWRITE SYSTEMS PRESERVING [1] S. L. Bloom and Z. Esik. An Extension Theo­ RECOGNIZABILITY rem with an Application to Formal Tree Series, Salomaa showed that linear monadic term rewrite J. of Automata, Languages and Combinatorics systems effectively preserve recognizability. We [31] 8(2003), 145-185. showed that there are finitely many descendants of [2] B. Borchardt, Z. Fulop, Z. Gazdag, and A. any recognizable tree language L for all linear monadic Maletti. Bounds for Tree Automata with Polyno­ term rewrite systems, and we gave these descen­ mial Costs, J. of Automata, Languages and Com­ dants through finitely many linear monadic term binatorics, 10(2005), 107-157. rewrite systems. We [29] showed that right-linear half­ monadic term rewrite systems effectively preserve rec- [3] Z. Esik. Axiomatizing the equational theory of ognizability. Using this property, we [29] showed that regular tree languages, J. Logic and Algebraic termination and convergence are decidable properties Programming, to appear. for right-linear half-monadic term rewrite systems. [4] Z. Esik and L. Gwangu. Fuzzy Tree Auotomata, Fuzzy Sets and Systems, to appear. GROUND TERM REWRITING [5] Z. Esik and W. Kuich. Formal Tree Series, We [28] showed that for any given finitely gener­ J. of Automata, Languages and Combinatorics ated congruences p and t over the term algebra, it is 8(2003), 219-285. decidable if the intersection of p and t is a finitely gen­ erated congruence. If the answer is yes, then we can [6] Z. Esik and Z. L. Nemeth. Higher dimensional effectively construct a finite relation U over ground autom ata, J. of Automata, Languages and Com­ terms such that the congruence closure of U is equal binatorics., 9(2004), 3-29. to the intersection of p and t . [7] Z. Esik and Z. L. Nemeth. Algebraic and graph- We [30] showed that for a given left-linear right- theoretic properties of infinite n-posets, Theoret­ ground term rewrite system R it is decidable if there is ical Informatics and Applications , 39(2005), 305­ a ground term rewrite system S such that the restric­ 322. tion of the rewriting relation of R to ground term s is equal to the rewriting relation of S. If the answer is [8] Z. Esik and P. Weil. Algebraic recognizability yes, then one can effectively construct such a ground of regular tree languages, Theoretical Computer term rewrite system S . Science, 340(2005), 291-321. [9] Z. Fuoloop. An Introduction to Tree Transducers, HIGHER DIMENSIONAL AUTOMATA Formal Methods in Computing (Eds. M. Ferenczi, In [ 6], we defined parenthesizing automata, that A. Pataricza and L. Ronyai), Akademiai Kiado operates on higher dimensional words (i.e., on ele­ Budapest, 2005, 199-258. ments of free algebras with several independent as­ [10] Z. Fuoloop and Zs. Gazdag. Shape Preserving Top- sociative operations). We have extended several basic Down Tree Transducers, Theoretical Computer results of the classical theory of automata to parenthe­ Science, 304(2003), 315-339. sizing automata including the equivalence to algebraic recognizability and monadic-second order definability. [11] Z. Fulop, Zs. Gazdag, and H. Vogler. Hierarchies In [7], we described infinite higher dimensional words of Tree Series Transformations, Theoretical Com­ in algebraic frameworks and gave graph-theoretic de­ puter Science, 314(2004), 387-429. scriptions of them. Based on these results parenthesiz­ [12] Z. Fuoloop, A. Kuoehnemann, and H. Vogler. A ing Buchi-automata was defined with generalization of bottom-up characterization of deterministic top- the above mentioned classical results [24,25]. In [23], down tree transducers with regular look-ahead, it was shown that the classes of languages that can be Information Processing Letters, 91(2004), 57-67. accepted by parenthesizing automata with at most i [13] Z. Fuoloop, A. Kuoehnemann, and H. Vogler. Lin­ pairs of parentheses form a strict hierarchy, for i > 0. ear Deterministic Multi Bottom-up Tree Trans­ The aim of [26] is to relate parenthesizing automata to ducers, Theoretical Computer Science, 347(2005), the work of Hashiguchi, Ichihara and Jimbo on binoid 275-287. languages.

18 [14] Z. Fulop and L. Muzamel. Recent Results on Peb­ OTHER ACTIVITIES ble Macro Tree Transducers, Proc. of the 1st In­ ternational Conference on Algebraic Informatics, I. EDITED BOOKS Thessaloniki, 2005, 281-284. In the period 2003-3006, the members of the Depart­ [15] Z. Fulop and L. Muzamel. Circularity, Com­ ment of Foundations of Computer Science edited or position, and Decomposition Results for Pebble co-edited the following books and special journal is­ Macro Tree Transducers, J. of Automata, Lan­ sues. guages and Combinatorics, to appear. 1. AFL 05, Special Issue of Acta Cybernetica, Vol­ [16] Z. Fulop and H. Vogler. Tree Series Transforma­ ume 17, Number 4, 2006. tions that Respect Copying, Theory of Comput­ 2. Automata and Formal Languages, Special Issue ing Systems, 36(2003), 247-293. of Theoretical Computer Science, Volume 366, [17] Z. Fulop and H. Vogler. Weighted Tree Trans­ Number 3, 2006. ducers, J. of Automata, Languages and Combi­ 3. Recent Advances in Formal Languages and Ap­ natorics, 9(2004), 31-54. plications, Studies in Computational Intelli­ [18] Z. Fulop and H. Vogler. A Comparison of Several gence 25, Springer-Verlag, 2006. Models of Weighted Tree Automata, Technical 4. Computer Science Logic, Proceedings of CSL Report, Technical University of Dresden, Faculty 2006, LNCS 4207, Springer-Verlag, 2006. of Informatics, TUD-FI06-08, 2006. 5. Automata and Formal Languages, Proceedings [19] T. Hornung and S. Vagvolgyi. Storage-to-tree of the 11th International Conference, AFL 2005, transducers with look-ahead, Theoretical Com­ Dobogoko, May 17-20, 2005. puter Science, 329(2004), 115-158. 6. Process Algebra, Special Issue of Theoretical [20] Zs. Gazdag. Shape Preserving Bottom-up Tree Computer Science, Volume 335, Number 2-3, Transducers, J. of Automata, Languages and 2005. Combinatorias, 10(2005), 483-534. 7. Proceedings of the 4th Conference for PhD Stu­ [21] Zs. Gazdag. Decidability of the Shape Preserv­ dents, CSCS 2004, Special Issue of Acta Cyber- ing Property of Bottom-Up Tree Transducers, In­ netica, Volume 17, Number 2, 2005. ternational Journal of Foundations of Computer 8. Developments in Language Theory, DLT 2003, Science, 17(2006), 395-413. Special Issue of Theoretical Computer Science, [22] L. Muzamel. Pebble Alternating Tree-Walking Volume 327, Number 3, 2004. Automata and Their Recognizing Power, Acta 9. Fixed Points in Computer Science 03, Warsaw, Cybernetica, to appear. Special Issue of Theoretical Informatics and Ap­ plications, Volume 38, Number 4, 2004. [23] Z. L. Nemeth. A hierarchy theorem for regular languages over free bisemigroups, Acta Cybernet- 10. Fixed Points in Computer Science 02, Copen­ ica , 16(2004), 567-577. hagen, Special Issue of Theoretical Informatics and Applications, Volume 37, 271-391, 2003. [24] Z. L. Nemeth. Automata on infinite biposets, Proc. Automata and Formal Languages, 11th Int. 11. Process algebra: Open problems and future Conf., AFL 2005, Szeged, 2005, 213-226. directions, PA’03, Bologna, Italy, July 21-25, 2003, BRICS Notes Series NS-03-3, 2003. [25] Z. L. Nemeth. Automata on infinite biposets, 12. Developments in Language Theory, Proceedings Acta Cybernetica,, 18(2006), 765-797. of the 7th International Conference, DLT 2003, [26] Z. L. Nemeth. On the regularity of binoid lan­ LNCS 2710, Springer, 2003. guages: A comparative approach, Preproc. 1st 13. Proceedings of the 3rd Conference for PhD Stu­ International Conference on Language and Au­ dents, CSCS 2002, Special Issue of Acta Cyber- tomata Theory and Applications, LATA 2007, netica, Volume 16, Number 2, 2003. Tarragona, 2007, to appear. [27] S. Vagvolgyi. On Ground Tree Transformations II. ORGANIZED CONFERENCES and Congruences Induced by Tree automata, Theoretical Computer Science , 304(2003), 449­ In the period 2003-3006 the Department of Founda­ 459. tions of Computer Science has organized the following conferences and workshops: [28] S. Vagvolgyi. Intersection of Finitely Gener­ ated Congruences over Term Algebra, Theoretical 1. Computer Science Logic, CSL 2006, Szeged, Computer Science, 300(2003), 209-234. Hungary, September 25-29, 2006. 2. Logic and Combinatorics, Satellite Workshop of [29] S. Vagvolgyi. Right-Linear Half-Monadic Term CSL 2006, Szeged, Hungary, September 23-24, Rewrite Systems, Theoretical Computer Science , 2006. 309(2003), 195-211. 3. Algebraic Theory of Automata and Logic, [30] S. Vágvolgyi. Term Rewriting Restricted to Satellite Workshop of CSL 2006, Szeged, Hun­ Ground Terms, Theoretical Computer Science , gary, September 30 and October 1, 2006. 302(2003), 135-165. 4. Automata and Formal Languages, 11th Interna­ [31] S. Vaágvoolgyi. Descendants of a recognizable tree tional Conference, AFL 2005, Dobogoko, Hun­ language for sets of linear monadic term rewrite gary, May 17-20, 2005. rules, Information Processing Letters, 99(2006), 5. Developments in Language Theory, 7th Interna­ 111-118. tional Conference, DLT 2003, Szeged, Hungary, July 7-11, 2003.

19 Department of Image Processing and Computer Graphics

I. MEDICAL AND NEUTRON TOMOG­ we have to resample image intensities of image B RAPHY APPLICATIONS OF AN AUTO­ in Oa . The simplest resampling method is to select MATIC REGISTRATION METHOD the intensity value of the closest grid position of O b . Linear or more complex interpolation methods Registration is a fundamental task in image process­ (cubic spline, B-Spline, Sinc) can also be used. Let ing. Its purpose is to find a geometrical transforma­ T denote the transformation that maps both the po­ tion that relates the points of an image to their corre­ sition and the associated intensity value at that posi­ sponding points of another image. Many registration tion, and BT the resampled image B. algorithms have been proposed in the past decade. The selection of the similarity measure is probably Automatic methods become more and more popular the most crucial part of a registration algorithm. We due to their convenient usability and with the com­ need a function which optimally has one global op­ puting power of today’s computers the running time is timum at perfect alignment, has no local optimums, acceptable for many applications. We have developed and is ’’smooth enough” to find this optimum fast. a fast, fully automatic algorithm that is capable of Practically it is very hard, or even impossible to find solving linear registration of 2D and 3D images of dif­ such a similarity measure, especially when the images ferent sources. For medical images, we joined the Ret­ are taken by different imaging devices. Many similar­ rospective Registration Evaluation Project conducted ity measures were proposed in the past decade. We by Vanderbilt University, USA. We also applied the chose the measures based on the mutual information method to register 2D neutron tomography images of the images proposed by Collignon et al. [3] and Vi­ with success. The evaluations show that our method ola and Wells [11,12], and on the normalized mutual has the potential to produce satisfactory results, but information of the images proposed by Studholme et visual inspection is necessary to guard against large al [8]. errors. Both measures utilize the entropy of image A,

II. REGISTRATION METHOD H (A) = - X pA(a) ■ logpTA(a), a First we describe the fully automatic, iterative regis­ tration method that is capable of finding linear trans­ the entropy of image B, formations to align images from the same or different modalities (i.e., taken by the same or different imaging H (B) = - X Pb (b) • logpB (b), devices). b We follow the notations of [4]. Let X denote the and the joint entropy of images A and B, object to be imaged, and let A and B be 3D images of X taken by the same or different imaging devices. H(A,B) = - X ^ p Ab (a,b) • logp Ab (a,b), The images usually have different fields of view, thus a b the domains O a and O b will be different. A (x a ) and B( x b ) are referred to as the intensity values at spa­ where pA and p B are the histograms, and pAB is the tial positions x a and x b , respectively. Intensity values co-occurrence matrix of the intensity values of images represent some kind of measurement of the material A and B. in spatial positions of X , such as attenuation of X- Mutual information is computed as ray beams in case of Computed Tomography (CT), changes in states of protons under changing the mag­ M I (A, B ) = H (A) + H (B) - H (A, B ), netic field properties in Magnetic Resonance Imag­ ing (MRI), or distribution of nuclear tracers in case and the normalized mutual information as of Positron Emission Tomography (PET) and Single H(A ) + H(B) Photon Emission Computed Tomography (SPECT). N M I(A , B) As the images A and B represent the same object H(A,B) X , there is a relation between the spatial locations We found that when mutual information is calcu­ in A and B: position x e X is m apped to x a in lated over the overlapping domain QA,B , the failure image A, and to x b in image B. The registration rate is high 8 []. We decided to use the whole O a in­ process involves recovering the spatial transformation stead, in case of this measure, which solved the prob­ T which maps x b to x a over the entire domain of lem. interest, which can be the entire domain of image A To speed up the registration process and to avoid or the overlapping portion of the domains. falling into a local optimum, we use the Gaussian mul­ The medical images are discrete, they sample the tiresolution pyramid representation of the images [ 1]. object at a finite number of points. Sample spacing The search starts at the coarsest level. When an op­ can be different for different images. These grid po­ timum is found, the result is propagated to the next, sitions and the corresponding sample values together finer level. We use Powell’s direction set, iterative, are referred to as voxels. nonlinear optimization algorithm to find the optimum For any given T , the intersection of discrete do­ of the similarity measure [7]. Further optimizations of mains O a and O b might be the empty set, when no the algorithm can be found in [9]. sample points will exactly overlap. To overcome this,

20 III. EVALUATION OF MR-CT AND MR- PET REGISTRATION

It is necessary to measure the quality of alignment to be able to decide whether a registration algorithm is suitable for solving a given registration problem. The alignment need not be perfect, but the error must be below a certain (application dependent) threshold. The similarity measure cannot be used to judge this, since it is not guaranteed that it reaches its global optimum at perfect alignment. An other method, vi­ sual inspection is generally applicable. Although vi­ sual inspection is always necessary since the automatic methods occassionally might fall into a nonglobal op­ timum producing a bad result without any warnings, a more accurate evulation procedure based on some kind of measurements is necessary. An overview of such procedures can be found in [4]. To evaluate our registration method, we joined the Retrospective Registration Evaluation Project of Vanderbilt University, USA in 1999 [13]. The objec­ tive of that project was to perform blinded evaluation of retrospective image registration techniques using a prospective, marker-based registration method as a gold standard. A gold standard is a system whose Figure 5. Fusion of the CT to MR registration prob­ accuracy is known to be high. A fiducial marker sys­ lem for Patinet #5, before (top) and after (bottom) tem can serve as an excellent gold standard for rigid registration. CT data is shown in red, MR data in registration, since some of these systems can provide green color. submillimetric accuracy. The primary disadvantage is the high invasiveness i.e., bone-implanted markers [ 6]. In order to ensure blindness, all retrospective regis­ istration task, both of our methods produce accept­ trations were performed by participants who had no able results. Our MI method ranks high, the NMI knowledge of the gold-standard until after their results method produces average results. For PET to MR had been submitted. problems, the MI method tends to fail (five failures out The evaluation followed these steps. Image vol­ of 35 cases), and produces average results. The NMI umes of three modalities: X-ray computed tomog­ method gives stable results and ranks high among the raphy (CT), magnetic resonance (MR), and positron competing algorithms. The running time was about emission tomography (PET) were obtained from pa­ 30-120 seconds on a 800 Mhz Pentium-III PC. More tients undergoing neurosurgery at Vanderbilt Univer­ detailed results of the evaluation of our methods can sity Medical Center, on whom bone-implanted mark­ be found at ers were mounted. These volumes had all traces of the http://www.vuse.vanderbilt.edu/~image . markers removed and were provided to project collab­ orators outside Vanderbilt, who then performed reg­ IV. APPLICATION OF AUTOMATIC istration on the volumes. The investigators communi­ REGISTRATION IN SEGMENTING cated their results to Vanderbilt, where the accuracy ORGANS OF THE PELVIC REGION of each registration was evaluated. Two registration tasks were evaluated: CT to MR In a cooperation with General Electric Medical Sys­ and PET to MR, and these tasks were broken into tems Hungary, the algorithm had been modified to subtasks according to the type of MR and to whether solve pelvic CT-CT registration problems of different or not the MR image was corrected (rectified) for ge­ patients. When segmenting organs of the pelvic re­ ometrical distortion. The image data set of nine pa­ gion, transforming (or registering) CT studies of dif­ tients were used, seven of which contained both CT ferent patients to a common reference frame can be and MR, and seven with both PET and MR. used in two preprocessing tasks: The results of the project were published in [13] • Generating a probability atlas, or a deformable and [14]. Since we joined the project later, our results organ model (model creation), were not included in those papers, thus we compared • and in the clinical application, establishing our results against those evaluated earlier [9]. the voxel-to-voxel correspondence between the Before the evaluation of our results, we visually study to be segmented and the probability atlas inspected the quality of registration. Using the NMI or model (initial organ placement). method, all registration results were visually accept­ able. In case of mutual information, for the CT to In these cases precise alignment of all anatomical MR task, all 41 results were visually acceptable. In structures is not crucial, the focus is on proper align­ case of PET to MR, for five image pairs the results ment of the pubic bone area and fast execution. of registration was visually misregistered. The other Studies are registered against a previously selected 30 results were visually acceptable. In spite of these suitable reference study. The modified algorithm con­ clear misregistrations, all results were submitted for sists of two steps. First, a global nine degree of free­ evaluation to Vanderbilt University. Figure 5 show dom transformation (three rotation, three scale, and the result of a MR-CT registration problem. three translation) is to be found. Then this is locally The results show that in case of CT to MR reg- refined in the pubic bone area, modifying six of the pa­ rameters (three rotation and three translation). The

21 local neighbourhood of the pubic bone area is selected istration algorithm utilizes the normalized version of manually for the reference study only, as a preprocess­ mutual information as pixel similarity measure. One ing step. of the projection images is selected as the reference It has been shown that after the refinement step, image and the others are registered against it one by prostate regions are significantly (P < 0.05 using one. Although the algorithm is fully automatic, a pre­ Student t-test) closer to each other [10]. The study processing step is necessary. The center region of the database was provided by General Electric Medical images, where the projection of the object is visible Systems and consisted of 26 CT images with expert must be masked out and the similarity measure is segmented “gold-standard” prostate and bladder re­ evaluated only outside of it. This mask selection is gions. The failure rate was low (three out of 26), even necessary only for the reference image. The result of though many of the studies were distorted by artificial the preprocessing step is shown in Figure 6. metallic objects or not satisfying the assumed proto­ col. The running time is 20-40 seconds using a 3 Ghz Pentium IV desktop PC. It is possible to make it even faster by removing the unnecessary image regions (the border around the patient) of the reference study.

V. APPLICATION OF IMAGE REGIS­ TRATION IN NEUTRON TOMOGRA­ PHY

We could use the registration algorithm in an interest­ ing, non-medical problem [2,5]. Using neutron radio­ graphy, the inner regions of object made from metal, copper, or aluminum can be inspected, which is more useable than using conventional X-ray techniques due to their much lower contast properties. Similarly to X- ray, a neutron ray is passing through the inspected ob­ ject while it is attenuated more or less according to the object properties. An imaging plate is placed at the back of the inspected object which detects the inten­ sity of the passed ray. By rotating the object around its axis, a set of 2D projections is generated. Using discrete or conventional tomography algorithms, a 3D model of the object can be obtained. The imaging process consists of the following steps. The object is placed on a table which can be rotated around by a given angle after the 2D image is taken. At the back of the object a rail track is situ­ Figure 6. A 2D projection image of a gas pressure reg­ ated, in which the casing of the imaging plate can be ulator (top) and the manually selected masked region moved. After an image is taken, the casing is removed, (bottom). the imaging plate is taken out of the casing and the image data is read. After deleting the contents of the The running time is around 90-120 seconds for imaging plate, it is put back into the casing and moved images of size 5000 x 4000 pixels. Visual inspection to the back of the object using the rail track. confirmed that the registration provided acceptable The way the images are taken introduces geomet­ results, the markers align reasonably well and the re­ ric differences between the consecutive projections. It sult can be used for tomographic reconstruction. We means that the same projection directions from the can expect further improvements in precision if the source might pass the imaging plate at different pixel markers were attached to the rail track instead of the locations. Such geometric differences can degrade the casing. result of the reconstruction. The task of the image registration algorithm is to recover these geometric VI. CONCLUSIONS differences. If we take a closer look at the way the images In this paper we summarized our experiments using an are taken, we can conclude that placing the casing in automatic, voxel-similarity based registration method and out cannot produce significant errors. The rail for medical and non-medical problems. We can con­ track provides one way motion only, and an immobile clude that voxel-similarity measures, in our case the bumper stops the casing precisely enough. The main ones based on mutual information, can be success­ source of error is the moving of the imaging plate in fully applied to align multimodal medical images and and out from the casing. To track these movings, ex­ neutron tomography images also. Although the regis­ ternal markers attached to the casing are applied, the tration itself is fully automatic, in some cases manual projections of which are visible in the top, bottom, left selection of masked out regions is required as a prepro­ and right hand side of the images. Since the imaging cessing step. Especially when aligning neutron tomog­ plate moves with respect to these markers, we can ex­ raphy images using external markers, other solutions pect that when the markers are aligned, the image could also be considered by detecting those markers data is suitable for reconstruction. and aligning the extracted geometric features. Such It is assumed that a rigid-body transformation an approach could work without any preprocessing (translation along the axes and rotation about the steps and could be much faster than the approach we center of the image) can align the images. The reg­ used. The problem of such an approach is that it re­ quires special programming and it would require much

22 more development time. When the running time is [12] W.M. Wells, P. Viola, H. Atsumi, S. Nakajima, not crucial, our automatic approach is able to solve and R. Kikinis. Multi-modal volume regsitration the problem without any severe modifications. by maximization of mutual information. Medical Image Analysis, 1(1):35-51, 1996. ACKNOWLEDGEMENTS [13] J. B. West, J. M. Fitzpatrick, and et al. Compar­ We are grateful for the help we received from Pro­ ison and evaluation of retrospective intermodal­ fessor Fitzpatrick, Jay West and Ramya Balachandran ity brain image registration techniques. Journal from the Vanderbilt University in evaluating our regis­ of Computer Assisted Tomography, 21:554-566, tration results. The images and the standard transfor­ 1997. mations were provided as part of the project, ’’Evalu­ ation of Retrospective Image Registration”, National [14] J. B. West and et al. Retrospective intermodal­ Institutes of Health, Project Number 1 R01 NS33926- ity registration techniques for images of the head: 01, Principal Investigator, J. Michael Fitzpatrick, Surface-based versus volume-based. IEEE Trans­ Vanderbilt University, Nashville, TN. Parts of our action on Medical Imaging, 18(2):144-150, 1999. work have been funded by OTKA T023804, FKFP 0908/1999 and OTKA T048476 grants. VII. DISCRETE TOMOGRAPHY

REFERENCES Discrete Tomography (DT) deals with the reconstruc­ tion of discrete valued functions from their line inte­ [1] P. J. Burt and E. H. Adelson. The laplacian pyra­ grals along certain directions called projections. The mid as a compact code. IEEE Transactions on function itself usually represents a two-dimensional Communications, 31:532-540, 1983. cross-section of an object consisting of a small num­ ber of homogeneous materials, while the projections [2] M. Balaska, A. Kuba, A. Nagy, A. Tanacs, and can be regarded as the results of some imaging meth­ B. Schillinger. Comparison Radiography and To­ ods (like, e.g., X-ray, gamma, or neutron imaging). mography Possibilities of FMR-2 (20 MW) and Typical applications arise in non-destructing testing of Budapest (10 MW) Research Reactors. In Pro­ industrial parts, investigating of crystalline or macro­ ceedings of WCNR-8, page 4, 2006. molecule structures with electron microscopy or exam­ [3] A. Collignon, F. Maes, D. Delaere, D. Vander- ining the shape of blood vessels and heart chambers meulen, P. Suetens, and G. Marchal. Automated in human body with angiography. In all of these ap­ multi-modality image registration based on in­ plications there is a strong reason that restricts the formation theory. In Proceedings of Information number of available projections to at most about 10 Processing in Medical Imaging, pages 263-274, (often only 2 or 4). This usually yields ambiguous 1995. reconstruction, i.e., the result image of a classical re­ [4] J. V. Hajnal, D. L. G. Hill, and D. J. Hawkes. construction method can be quite dissimilar to the Medical Image Registration. CRC Press, Read­ original one. Another problem is that the reconstruc­ ing, M assachusetts, 2001. tion problem is in most cases NP-hard. Therefore, in [5] Z. Kiss, L. Rodek, and A. Kuba. Image recon­ DT more sophisticated methods are needed that can struction and correction methods in neutron and guarantee accurate and fast reconstruction despite the X-ray tomography. Acta Cybernetica, 17:557­ fact that there are a few available projections. Such 587, 2006. methods can be developed by exploit the prior knowl­ edge that the image to be reconstructed can contain [6] C. R. Maurer, J. M. Fitzpatrick, M. Y. Wang, only a small number of different intensity values. R. L. Galloway, R. J. Maciunas, and G. S. Allen. Registration of head volume images using im­ RECONSTRUCTION WITH GEOMETRI­ plantable fiducial markers. IEEE Transaction on C A L P R IO R S Medical Imaging, 16:447-462, 1997. One way to reduce ambiguity and to avoid in­ [7] W. H. Press, S. A. Teukolsky, W. T. Vetterling, tractability is to suppose that one wants to reconstruct and B. P. Flannery. Numerical Recipes in C: The a binary image (also called discrete set) that belongs Art of Scientific Computing. Cambridge Univer­ to a certain class of images having some geometrical sity Press, New York, NY, 2nd edition, 1992. properties (connectedness, convexity, etc.). The main [8] C. Studholme, D. L. G. Hill, and D. J. Hawkes. challenge here is to find geometrical properties that An overlap invariant entropy measure of 3D med­ drastically reduces the number of possible solutions of ical image alignment. Pattern Recognition, 32(1): the same reconstruction problem but still keeps the 71-86, 1999. reconstruction process tractable. [9] A. Tanoacs and A. Kuba. Evaluation of a fully Although a former result shows that the recon­ automatic medical image registration algorithm struction in the class of horizontally and vertically based on mutual information. Acta Cybernetica , convex (shortly, hv-convex) discrete sets from two pro­ 16:327-336, 2003. jections is NP-hard we have shown that it is possible to reconstruct all the solutions of the same reconstruc­ [10] A. Tanacs, E. Mate, and A. Kuba. Application of tion task with a quite fast algorithm in polynomial­ Automatic Image Registration in a Segmentation time if we have the additional information that the set Framework for Pelvic CT Images In Conference to be reconstructed is also 8-connected and consists of on Computer Analysis of Images and Patterns several components [5]. (CAIP2005), Lecture Notes in Computer Science For so called Q-convex sets a fast operation is also 3691, pages 628-635, Springer Verlag, 2005. presented that can speed up the reconstruction of such [11] P. Viola and W. M. Wells III. Alignment by maxi­ kind of sets [ 6]. Moreover we also investigated how the mization of mutual information. In Proceedings of knowledge that the Q-convex set is not 8-connected IEEE International Conference on Computer Vi­ can facilitate the reconstruction. sion, pages 16-23, Los Alamitos, CA, Jun. 1995.

23 We also generalised a uniqueness result of di­ DIRECT FRAMEWORK rected horizontally or vertically convex polyominoes Discrete REConstruction Techniques (DIRECT) and showed that this result also holds if the polyomino is a toolkit for testing and comparing 2D/3D re­ is diagonally convex. Additionally, a negative result is construction methods of discrete tomography. The also given showing that for any other direction of con­ toolkit involves generating projections of discrete ob­ vexity there can be exponentially many line-convex jects, running reconstruction methods, and visualiza­ polyominoes with the same horizontal and vertical projections [3]. tion of result. Most of the reconstruction techniques developed at our department are built-in into this The general task of reconstructing a discrete set framework which is updated from time to time. The from four projections is NP-hard, too. In [4] we in­ DIRECT toolkit can be reached at troduced the class of decomposable discrete sets and developed a polynomial-time reconstruction algorithm http://www.inf.u-szeged.hu/~direct/ for this class using four projections. We also anal­ ysed the possibility to adapt the developed technique with a full access for registered users. for the reconstruction problems in the classes of Q- convexes and hv-convexes. CONFERENCES ORGANIZED EMISSION DISCRETE TOMOGRAPHY The Workshop on Discrete Tomography and Its Applications was held in June 2005 in New York City Recently, a new field of DT called Emission Dis­ with the co-organization of Attila Kuba. This small crete Tomography (EDT) has been studied. In this conference attracted more than 60 participants from model the function to be reconstructed represents an 10 countries including all the authors of the present object having some radiation surrounded by a homo­ paper. The conference proceedings was published geneous material having certain absorption. Thus, the electronically [17] and includes 38 contributions from projections are depending not only the emission but which 9 were written by our collegues as a sole or coau­ the absorption, too. Uniqueness and non-uniqueness thor. Furthermore, based on some of the talks a book theorems for EDT was proved in [10] and [14]. More­ was edited entitled Advances in Discrete Tomography over, in [9] the surprising result was published that in and Its Applications that will be published in March the EDT model the reconstruction of hv-convex dis­ 2007 [7], in which 6 from the 15 chapters are writ­ crete sets from two projection can be done in polyno­ ten by the members of our group, solely or partially. mial time, at least for a certain absorption coefficient. Further informations on the conference are available at

RECONSTRUCTION WITH OPTIMIZATI­ http://www.dig.cs.gc.cuny.edu/ ON The 13th Conference on Discrete Geometry for The reconstruction process can also be formulated Computer Imagery was held in Szeged in October as an optimization task where the aim is to find the 2006. As part of the conference program one session global minimum of the objective functional was devoted to the topic of DT. Some of the authors of this paper has also publications in the conference * ( /) = E .y \ m ] w - p # w2 + Y \\f - / oil2 proceedings [11]. The homepage of the conference can where P$ denotes the input projection of angle ft, / be found at is the image function that approximates the solution, [R/](ft) denotes the projection of the image / taken http://www.inf.u-szeged.hu/dgci at angle ft, \\.\| is the Euclidean norm, and 7 > 0 is a regularizing parameter. / o is a prototype func­ ACKNOWLEDGEMENTS tion that has the same domain and range as /, and is similar to the expected reconstruction result. Such a The mentioned research tasks were supported model has the advantage that due to the second term by the following grants: NFS DMS0306215, OTKA on the right hand side prior information of the image T048476, FKFP 0908/1997, OTKA T032240, OTKA to be reconstructed can be incorporated. Moreover, T032241. it also can handle incorrect measurements of projec­ REFERENCES tions. The regularazing parameter 7 stands for con­ trolling whether prior information or the projections [1] M. Balasko, E. Svab, A. Kuba, Z. Kiss, L. Rodek, are more reliable in a certain reconstruction task. A. Nagy: Pipe corrosion and deposit study us­ Such kind of optimization problems can be solved, ing neutron- and gamma- radiation sources. 5th e.g., by a simulated annealing (SA) approach. A lot International Topical Meeting on Neutron Ra­ of work has been done at our department in this field, diography Nuclear Instruments and Methods in mostly concentrating on applications of neutron and Physics (Research A) 542 (2005) 302-308. X-ray tomography [1,2,8,12,13]. The same technique was applied to solve some reconstruction problems in [2] M. Balasko, A. Kuba, A. Nagy, Z. Kiss, L. Rodek, the case of so-called fan-beam projections [15,16]. L. Rusko: Neutron-, gamma-, and X-ray three­ However, SA is not the only method by which dimensional computed tomography at the Bu­ the above optimization problem can be solved. Very dapest research reactor site. 5th International recently, SA was compared to a dc-programming Topical Meeting on Neutron Radiography Nuclear m ethod from the viewpoint of reconstruction effi­ Instruments and Methods in Physics (Research ciency. It turned out that (for the images used in that A) 542 (2005) 22-27. comparison) there is no significant difference of accu­ [3] P. Balazs: The number of line-convex directed racy and running time between the two methods [18]. polyominoes having the same orthogonal projec­ tions. In [11] 77-85.

24 [4] P. Balázs: A decomposition technique for recon­ VIII. HIGHER-ORDER ACTIVE CON­ structing discrete sets from four projections. Im ­ TOURS AND ITS APPLICATION age and Vision Computing, accpeted. TO TREE CROWN DETECTION [5] P. Balazs, E. Balogh, A. Kuba: Reconstruction of OBJECTIVES, GOALS 8-connected but not 4-connected hu-convex dis­ crete sets. Discrete Applied Mathematics 147(2- The aim of our work is to introduce prior shape 3) (2005) 149-168. knowledge into existing image segmentation models. [6] S. Brunetti, A. Daurat, A. Kuba: Fast filling op­ To accomplish we extended the recently introduced erations used in the reconstruction of convex lat­ higher-order active contour framework for region and tice sets. In [11] 98-109. image modeling by introducing a model for a ‘gas of circles’, the ensemble of regions in the image domain [7] G.T. Herman, A. Kuba (Eds.): Advances consisting of an unknown number of circles, with ap­ in Discrete Tomography and Its Applications, proximately fixed radius and short range of interac­ Birkhauser, Boston, to appear in March 2007. tions. We applied the developed models of current [8] Z. Kiss, L. Rodek, A. Kuba: Image reconstruc­ interest in remote sensing image processing: the ex­ tion and correction methods in neutron and X- traction of tree crowns. Forestry services are inter­ ray tomography. Acta Cybernetica 17 (2005) 557­ ested in various quantities associated with forests and 587. plantations, such as the density of trees, the mean crown area and diameter, etc. [9] A. Kuba, A. Nagy, E. Balogh: Reconstruc­ To include more complex prior knowledge, longer- tion of hu-convex binary matrices from their ab­ range interactions are needed. There is a large body sorbed projections. Discrete Applied Mathemat­ of work that does this implicitly, via a template re­ ics 139(1-3) (2004) 137-148. gion or regions to which the segmented region R is [10] A. Kuba, M. Nivat: A sufficient condition for compared. However, such energies effectively limit non-uniqueness in binary tomography with ab­ R to a bounded subset of region space close to the sorption. Theor. Comput. Sci. 346(2-3) (2005) template(s), which excludes, inter alia, cases like tree 335-357. crown extraction in which R has an unknown number [11] A. Kuba, L. G. Nyul, K. Palagyi: Discrete Ge­ of connected components. ‘Higher-order active con­ ometry for Computer Imagery, 13th International tours’ (HOACs) provide a complementary approach. Conference, DGCI 2006, Szeged, Hungary, Octo­ HOACs generalize classical active contours to include ber 25-27, 2006, Proceedings, Lect. Notes. Com­ multiple integrals over the contour. Thus HOAC ener­ put. Sci. 4245 (2006) gies explicitly model long-range interactions between boundary points without using a template. This al­ [12] A. Kuba, L. Rodek, Z. Kiss, L. Rusko, A. Nagy, lows the inclusion of complex prior knowledge while M. Balaskáo: Discrete Tomography in neutron ra­ permitting the region to have an arbitrary number of diography. 5th International Topical Meeting on connected components, which furthermore may inter­ Neutron Radiography Nuclear Instruments and act amongst themselves. The approach is very gen­ Methods in Physics (Research A) 542 (2005) eral: classical energies are linear functionals on the 376-382. space of regions; HOACs include all polynomial func­ [13] A. Kuba, L. Ruská, L. Rodek, Z. Kiss: Prelimi­ tionals. nary studies of Discrete Tomography in Neutron In [2,3,6], a HOAC energy was used for tree crown Imaging. IEEE Trans. on Nuclear Sciences 52 extraction. In this ‘gas of circles’ model, collections (2005) 380-385. of mutually repelling circles of given radius ro are lo­ cal minima of the geometric energy. The model has [14] A. Kuba, G. J. Woeginger: Two remarks on re­ many potential applications in varied domains, but it constructing binary vectors from their absorbed suffers from a drawback: such local minima can trap projections. Lect. Notes. Comput. Sci. 3429 the gradient descent algorithm used to minimize the (2005) 148-152. energy, thus producing phantom circles even with no [15] A. Nagy, A. Kuba: Recontruction of binary ma­ supporting data. The model as such is not at fault: trices from fan-beam projections. Acta Cybernet- an algorithm capable of finding the global minimum ica 17/2 (2006) 359-385. would not produce phantom circles. This suggests two [16] A. Nagy, A. Kuba: Parameter settings for re­ approaches to tackling the difficulty. One is to find constructing binary matrices from fan-beam pro­ a better algorithm. The other is to compromise with jections. Journal of Computing and Information the existing algorithm by changing the model to avoid Technology 14/2 (2006) 100-110. the creation of local minima, while keeping intact the prior knowledge contained in the model. We solved [17] Proceedings of the Workshop on Discrete Tomog­ the problem of phantom circles in [2,3,6]’s model by raphy and its Applications, Elec. Notes Discr. calculating, via a Taylor expansion of the energy, pa­ Math. 20 rameter values that make the circles into inflection [18] S. Weber, A. Nagy, T. Schule, Ch. Schnorr, A. points rather than minima. In addition, we find that Kuba: A benchmark evaluation of large-scale this constraint halves the number of model parame­ optimization approaches to binary tomography. ters, and severely constrains one of the two that re­ In [11] 146-156. main, while improving the empirical success of the model [4,5]. THE ‘GAS OF CIRCLES’ MODEL HOAC energies generalize classical active contour energies by including multiple integrals over the con­ tour. The simplest such generalizations are quadratic

25 energies, which contains double integrals. There are greatly improve the results, and in conjunction with several forms that such multiple integrals can take, the region prior, the full model is considerably better depending on whether or not they take into account than that based on one band alone. The results can contour direction at the interacting points. The Eu­ be seen on figure 9. clidean invariant version of one of these forms is COLLABORATION E g (7) = *£(7) + a A (Y) This work is a joint research between ARIANA research group of INRIA Sophia Antipolis, France and “ f / / T(J5) ' T(J 5,)’If(\P>P\)dPdP> Institute of Informatics, University of Szeged; based on a bidirectional Ph.D. work. The project started in where 7 is the contour, parameterized by p; L is 2004. the length of the contour; A is the area; \p,p'\ = |y (p ) — y (p ')\; t = y is the (unnormalized) tangent ACKNOWLEDGEMENT vector to the contour; and T is an interaction function This work was sponsored by a Hungarian-French that determines the geometric content of the model. Bilateral Grant PAI Balaton (F-3/04), EU project With an appropriate choice of interaction function T, IMAVIS (FP5 IHP-MCHT99), EU project MUSCLE the quadratic term creates a repulsion between an­ (FP6-507752), Hungarian Scientific Research Fund - tiparallel tangent vectors. This has two effects. First, OTKA T046805 and a Janos Bolyai Research Fellow­ for particular ranges of a, ¡3 , and dmin (A = 1 wlog), ship of the Hungarian Academy of Sciences. Peter circular structures, with a radius r o dependent on the Horvath was having his scholarship through the Doc­ parameter values, are stable to perturbations of their toral School of the University of Szeged, Hungary and boundary. Second, such circles repel one another if the Ministry of Foreign Affaires, France. The CIR they approach closer than 2dmin. Regions consisting images were provided by the French Forest Inventory of collections of circles of radius ro separated by dis­ (IFN). tances greater than 2dmin are thus local energy min­ ima. We [2,3,6] called this the ‘gas of circles’ model. REFERENCES Via a stability analysis, we [2,3,6] found the ranges of parameter values rendering circles of a given radius [1] P. Horvath. A Multi-Spectral Data Model for stable as functions of the desired radius. Stability, Higher-Order Active Contours and its Application however, created its own problems, as circles some­ to Tree Crown Extraction. In Proceedings Scan­ times formed in places where there was no supportive dinavian Conference on Image Analysis (SCIA), data. To overcome this problem, in [4,5], the criterion 2007. Subm itted. that circles of a given radius be local energy minima [2] P. Horváth, I. H. Jermyn, Z. Kato, and J. Zerubia. was replaced by the criterion that they be points of A Higher-Order Active Contour Model for Tree inflexion. As well as curing the problem of ‘phantom’ Detection. In Proc. International Conference on circles, this revised criterion allowed the fixing of the Pattern Recognition (ICPR), Hong Kong, China, parameters a, 3 , and dmin as functions of the desired August 2006. circle radius, leaving only the overall strength of the prior term, A, unknown. For energy-based models, pa­ [3] P. Horváath, I. H. Jermyn, Z. Kato, and J. Zeru- rameter adjustment is a problem, so this is a welcome bia. A Higher-Order Active Contour Model of a advance. ‘Gas of Circles’ and its Application to Tree Crown To illustrate the behaviour of the prior model, fig­ Extraction. Pattern Recognition, November 2006. ure 7 shows the result of gradient descent starting from Submitted. the region on the left. Note that there is no data term. [4] P. Horváath, I. H. Jermyn, Z. Kato, and J. Zerubia. The parameter values in these experiments render the An improved ‘gas of circles’ higher-order active circles involved stable. With the parameter values cal­ contour model and its application to tree crown culated in [4,5], they would disappear. extraction. In Proc. Indian Conference on Vision, Figure 8 illustrates results using the published Graphics and Image Processing (ICVGIP), M adu­ models. rai, India, December 2006. A MULTI-SPECTRAL DATA MODEL [5] P. Horvaáth, I. H. Jermyn, Z. Kato, and J. Zerubia. Kör alaku objektumok szegmentálása magasabb In the above models we also described a likelihood rendu aktív kontór modellek segítsegevel. In Proc. model. This described the behaviour of only one band KEPAF, Debrecen, Hungary, January 2007. of the three available bands in the CIR images which we are using provided by the French Forest Inventory [6] P. Horváath, I. H. Jermyn, J. Zerubia, and Z. Kato. (IFN). The model was Gaussian, with the values at Higher-Order Active Contour Model of a ‘Gas of different pixels independent, and with different means Circles’ and its Application to Tree Detection. Re­ and variances for tree crowns and the background. search Report 6026, INRIA, France, November While successful, this model, even with the strong re­ 2006. gion prior, was not capable of extracting accurately the borders of all trees. Some trees were simply too IX. PARAMETRIC ESTIMATIONS OF 2D similar to the background. The purpose of [1], is to re­ AFFINE TRANSFORMATIONS ON place the likelihood model in [ 2- 6] by one that makes BINARY IMAGES use of all three bands in the CIR images. We studied We consider the problem of planar object registration the improvement or otherwise of the extraction results on binary images. The purpose is to find an unknown produced by modelling the three bands as indepen­ transformation between a given known object (tem­ dent or as correlated. As we shown, even at the level plate) and a distorted observation of the template. of maximum likelihood, the inclusion of ‘colour’ infor­ We only consider affine transformations (translation, mation, and in particular, interband correlations, can scaling, rotation and shearing). The direct approach

26 Figure 7. Sequences of curve evolution using E g itself, from left to right: from the initialization to stable state.

Figure 8. Results on real aerial images, first column: original, second: results with [2,3,6] model, last column: results using [4,5]. IFN ©

Figure 9. Results on real CIR aerial images, first column: original images, second: results using only the infrared channel, last column: results using [1] model. IFN ©

27 is to apply each of the allowed affine deformations to be invertible. The first step is to find the determi­ the template and search for the one that matches the nant of A , i.e. the measure of the transformation. observation. While the object is known, the tremen­ A simple approach is to integrate t(x) by substitu­ dous number of possible transformations makes this tion using Eq. (2). Note that we always use Lebesgue approach unfeasible. Therefore classical registration integrals. The Jacobian |A| can then be evaluated algorithms reformulate the task as a non-linear opti­ through the identity relation mization problem. Our approach adopts a novel idea where the exact transformation is obtained as a so­ o'(A x) == \A - i\ o(y) (3) lution of a set of polynomial equations. These equa­ J r 2 tions are constructed in a simple way using some basic _ fit2 o(y) geometric information of the binary image. Another |A | (4) t(x) advantage of the proposed solution is that it is fast, Jr 2 unique and exact regardless of the magnitude of trans­ The equality in Eq. (2) remains valid if we multiply formation. by the same non-zero constant or take the integral of INTRODUCTION both sides. Hence for k = 1, 2, we have Image registration is a crucial step in almost all image processing tasks 1[ ,8] where images of different / xk t(x) = IA qki yt o(y) (5) Jm2 t=1 J r 2 views or sensors of an object need to be compared or combined. In a general setting, one is looking for a Since the characteristic functions take only values transformation which aligns two images such that one from {0, 1 }, we can further simplify the above inte­ image (called the observation ) becomes similar to the grals: second one (called the template). Due to the large number of possible transformations, there is a huge variability of the object signature. In fact, each ob­ where the domain F consists of the foreground re­ servation is an element of the orbit of the transfor­ gions: F = {x e R2| (x) = 1}. Therefore evaluating mations applied to the template. Hence the problem the integrals in Eq. (6) yields the area of the fore­ is inherently ill-defined unless this variability is taken ground regions. From this point of view, the measure into account. Recently, a novel approach has been pro­ of the transformation |A| corresponds to the ratio of posed by Hagege and Francos [4-6] which provides an the observation and template objects’ area. In the re­ accurate and computationally simple solution to the maining part of this paper, we will always integrate problem avoiding both the correspondence problem as over the respective domain F unless otherwise noted. well as the need for optimization. The fundamental Therefore we obtain from Eq. (19) and Eq. ( 6) novelty is that it reformulates the original problem as an equivalent linear parameter estimation one having a unique and exact solution. qki yi + qk2 y2 - I A I xk = 0, k = 1,2 (7)

ESTIMATION OF 2D AFFINE TRANSFOR­ Let us notice that these equations are based on the MATIONS first order moments of the object on the observation The parametric estimation of two-dimensional and template . Similarly, we can obtain another two affine transformations between two gray-level images equations by matching the second order moments of has been addressed by Hagege and Francos in [ 6]: The the object: observation and template is regarded as two bounded, Lebesgue measurable two-dimensional functions g and q h y 2 + 2qkiqk 2 y iy 2 + q h v 2 — \A\ 0 h (both mapping R2 ^ R) such that h(x) = g(Ax), (8) where A is the unknown affine transformation that where k = 1, 2. The system (7),(8) provides 4 equa­ we want to recover. The proposed solution yields to tions which is enough to solve for the four unknowns. a system of linear equations employing only zero and We may get up to two possible solutions for each un­ first order constraints while higher order moments are known qkt due to the quadratic polynomial equations avoided. In this project, we have addressed an impor­ in Eq. (8). Out of these potential solutions, we have to tant special case: the registration of binary images. chose the transformation whose elements are real and Binary images do not contain radiometric informa­ the determinant equals the Jacobian |A - 1 | computed tion hence they can be represented by the characteris­ in Eq. (4). The sign ambiguity of the determinant can tic function : R2 ^ {0,1}, where 0 and 1 correspond be easily eliminated: A negative Jacobian would mean to the background and foreground respectively. Let us that the transformation is not orientation-preserving denote the template by t and the observation by o. (i.e. flipping of coordinates is allowed). In practice, We will also use the following notations: however, physical constraints will usually prevent such x = [xi ,x 2\T and y = [yi ,y 2]T , where x,y e R2 a transformation hence we can assume that |A | is al­ ways positive. The uniqueness of the solution is then a ii qi 2 A ai2 ^ and A 1 qii guaranteed as long as the observation and template is a2i a22 q2i q22 not affine symmetric (see [4] for the proof). i Let us now examine the existence of the solution. y = Ax, x = A y (1) For that purpose, rewrite Eq. (7) and Eq. (8) for a If A is the transformation which aligns the observation fixed k in the following simplified form, where we and template , then the following equality holds: omit the k index and replace the coefficients of the unknowns by a,b, ...,g: i (x) = o(A x) (2) Now we will construct a solution for A. Note aqi + bq 2 — c = 0 that it is also possible to solve for A -1 since A must dqf + eqiq 2 + fq2 — g = 0 (9)

28 We will show that an algebraic solution of the system an exact solution. These equations are defined in the exists if the resultant [2] has a real solution: Assuming continuum while in practice we are working on dig­ a = 0, let us rewrite the system Eq. (9) in terms of qj.: ital (i.e. discrete) images. This means that an in­ tegral over the domain F can only be approximated aqi + (bq 2 — c) = 0 by a discrete sum over the foreground pixels intro­ dql + (eq2)qi + f - g) = 0 (10) ducing an inherent, although negligible error into our computation. A more important issue is the numeri­ Since d > 0, a sufficient condition for the existence cal error caused by unnormalized image coordinates. of common roots of the system Eq. (9) is th at the This can be especially severe in our case since we are resultant of the system must have real roots: working with squares and third powers of the coordi­ nates. A standard technique to minimize this error is (a2 f + b2 d — abe)q2 + (ace — 2bcd)q2 + (c2d — a 2g) = 0 to transform the whole image into [—1 , 1] x [—1 , 1] (see (11) Fig. 10): Fist we apply H to the template image T Obviously, the above quadratic polynomial has real and G to the observed image O. Then the normalized roots if its discriminant D is non-negative: images O' and T ' are registrated. D = (ace — 2bcd)2 — 4(a2f + b2d — abe)(c2d — a 2g) > 0

Note th a t D can always be computed hence our algo­ rithm can always tell whether a solution exists or not.

ESTIMATION IN THE PRESENCE OF TRANSLATION In the following we extend the presented solu­ tion and show how to obtain the parameters when Figure 10. Normalization of the template T and ob­ the transformation also includes an unknown transla­ servation O . The origin is translated to the center of tion [4]: the image and then it is scaled into [— 1 , 1] x [—1 , 1].

y = Ax + c, x = A 1y — A 1 c, and Of course, we have to take into account the effect of normalization in our calculations since it affects the t (x) = 0(A x + c) (12) measures. Therefore the Jacobian of the transforma­ where c is a two-dimensional real vector representing tion is com puted as the translation along the two axis. We can put all parameters in a single matrix by using homogeneous \ G \ j o(y) |G | (15) coordinates. More specifically let — A - 1c = [q10,q20]T H \ / t(x) H | and y = [1,y1,y 2]T . Eq. (12) becomes where A' is the transformation aligning the normal­ ized images. Furthermore, the left and right hand x = T y w ith T = q10 q11 q12 (13) q20 q21 q22 sides of equations has to be multiplied by |G | and |H | respectively. Finally, the transformation aligning The first column of T contains the translational pa­ the original, unnormalized images is obtained as rameters. The Jacobian of the transformation can be computed by Eq. (4) since the translation has no ef­ A = G -1 A ' H (16) fect on the measure of the transformation. Further­ more, 0(y) = o(y) by definition, hence Eq. (19) and Eq. (7) can be rew ritten as follows: EXPERIMENTS

xk t(x) = I T k y o(Ax + c) The proposed algorithm has been tested on syn­ thetic as well as on real images. In Fig. 11, we have applied a known affine transformation A to the tem­ y2 = \A\ x k , k = 1, 2 plate and measured the error of the estimated trans­ formation matrix A as A - 1A — I : (14) The second order moment equations can be similarly 4 2 100 « A rewritten. In the translational case, however, we have 1 3 50 two more variables, therefore we have to add two more equations. This is achieved by matching the third 4.0007 1.9983 95.0785 order moments. 0.9843 2.9997 50.9082 Now the system of equations contains six polyno­ ) 0.0034 —0.0004 —1.6581 mial equations up to order three. Therefore we may A -1 A — I get up to six possible values for each unknown qki. —0.0063 0.0001 0.8554 Out of these solutions, we can select the right one by The small errors are mainly caused by the discretiza­ following the procedure described in the previous sec­ tion and rounding when we applied A to the template. tion (i.e. drop the complex roots and select the trans­ Due to these errors, there is no perfect mapping be­ formation whose determinant matches the Jacobian tween the template and observation. Nevertheless, the computed by Eq. (4)). alignment of the images is almost perfect in spite of the relatively large size (~ 2000x3000) and fine details NUMERICAL IMPLEMENTATION of the foreground object (see Fig. 11). We had simi­ In the previous section, we have constructed a sys­ lar findings on real images, where a printed template tem of polynomial equations and shown how to obtain has been scanned and registrated. Registration error

29 is typically below 5% independently of the strength of COLLABORATION the transformation. This work is a joint research between the Depart­ In Fig. 12, we can see a comparison between our ment of Electrical and Computer Engineering, Ben- method and the one proposed by Thevenaz et al. [7]. Gurion University of the Negev, Israel and Institute Our algorithm performs clearly better. of Informatics, University of Szeged. Finally we remark that the CPU time of our Mat­ lab implementation has been around 1 sec. on images ACKNOWLEDGEMENT of size 3000 x 4000. Csaba Domokos was having his scholarship through the Doctoral School of the University of Szeged.

REFERENCES

[1] B row n , L. G. A survey of image registration techniques. ACM Computing Surveys 24 (1992), 325-376. (a) (b) (c) [2] C ohen , H. A Course in Computational Algebraic Figure 11. Synthetic example: (a) template (b) ob­ Number Theory. Springer, 1993. servation (c) registrated image [3] D omokos , C., K ato , Z., and F rancos , J. M. Parametric estimation of two-dimensional affine transformations of binary images. 6th Confer­ ence of Hungarian Association for Image Process­ ing and Pattern Recognition (2007), 257-265. [4] Ha g eg e , R., and F rancos , J. M. Parametric estimation of multi-dimensional affine transforma­ tions: Solving a group-theory as a linear problem. IEEE Trans. Signal Process.. [5] Ha g eg e , R., and F rancos , J. M. Parametric (a) (b) estimation of two dimensional affine transforma­ tions. Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP 2004) 3 (2004), 305­ 308. [6] Ha g eg e , R., and F rancos , J. M. Paramet­ ric estimation of multi-dimensional affine trans­ formations: An exact linear solution. Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP ’05) 2 (2005), 861-864. [7] T h Evenaz , P., R uttim a n n , U. E., and U nser , (c) (d) M. A pyramid approach to subpixel registration based on intensity. IEEE Transactions on Image Processing 7 (January 1998), 27-43. [8] Zito v A, B., and F lusser , J. Image registration methods: A survey. Image and Vision Computing 21 (2003), 977-1000.

MARKOV RANDOM FIELDS AND MCMC SAMPLING IN IMAGE SEGMENTATION Markov Random Field (MRF) modeling and Markov (e) (f) Chain Monte Carlo (MCMC) sampling methods are Figure 12. Result of registrations: (a) template successfully used in different areas of image process­ (337x400) (b) difference image of our method, error ing [20]. Herein, we will consider two topics: The first = 1.69% (c) the result of our method (d) observa­ one is dealing with automatic segmentation of color tion (2248x1587) (e) difference image with [7], error images in a probabilistic framework. In particular, = 29.52% (f) result of registration [7] we address the problem of automatic identification of Gaussian mixture components either with known [9] or unknown [6,7] number of components. The second CONCLUSION one deals with a multilayer MRF model applied to the We have presented a novel approach for binary segmentation of color video objects [ 8, 10]. image registration. The fundamental difference com­ SEGMENTETION OF COLOR IMAGES VIA pared to classical image registration algorithms is that REVERSIBLE JUMP MCMC SAMPLING our model works without any landmark, feature de­ tection or optimization. It uses all the information The simplest statistical model for an image con­ available in the input images, but there is no need for sists of the probabilities of pixel classes. The knowl­ an established correspondence between them. edge of the dependencies between nearby pixels can be modeled by a MRF. Such models are quite pow­ erful even if it is not easy to determine the values of

30 the parameters which specify a MRF. If each pixel w must posses regardless the image data. These are class is represented by a different model then the ob­ described by P (w), the prior, which tells us how well served image may be viewed as a sample from a real­ any occurrence w satisfies these properties. For that ization of an underlying label field. Unsupervised seg­ purpose, ws is modeled as a discrete random variable mentation can therefore be treated as an incomplete taking values in the set of labels A = {1, 2,...,L}. data problem where the color values are observed, the The set of these labels w = {ws,s e 5} is a ran­ label field is missing and the associated class model dom field, called the label process . Furthermore, the parameters, including the number of classes, need to observed color features are supposed to be a realiza­ be estimated. Such problems are often solved using tion F from another random field, which is a func­ MCMC procedures. Although the general theory and tion of the label process w. Basically, the image pro­ methodology of these algorithms are fairly standard, cess F represents the manifestation of the underly­ they have their limitations in case of problems with ing label process. The multivariate Normal density parameters of varying dimension. Recently, a novel is typically an appropriate model for such classifica­ method, called Reversible Jump MCMC (RJMCMC), tion problems where the feature vectors f s for a given has been proposed by Green [4]. This method makes class A are mildly corrupted versions of a single mean it possible to construct reversible Markov chain sam­ vector fi\. Applying these ideas, the image process plers that jump between parameter subspaces of dif­ F can be formalized as follows: P (fs | ws) follows ferent dimensionality. a three-variate Gaussian distribution N(p, S ), each Due to the difficulty of estimating the number of pixel class A e A = {1, 2,...,L} is represented by its pixel classes (or clusters), unsupervised algorithms of­ mean vector p A and covariance matrix S a. As for the ten assume that this parameter is known a priori [10]. label process w, a M RF model is adopted [10,11] over When the number of pixel classes is also being esti­ a nearest neighborhood system. The prior P (w) will mated, the unsupervised segmentation problem may represent the simple fact that segmentations should be treated as a model selection problem over a com­ be locally homogeneous. Factoring the above distri­ bined model space. Our approach [ 6, 7] consists of butions and applying the Bayes theorem gives us the building a Bayesian color image model using a first posterior distribution P (w |F)

31 3. sampling the mixture weightspx(A e A); moment equations and the random numbers u1, u 2 , 4. sampling the MRF hyperparameter ¡3; and u3: 5. sampling the number of classes L (splitting one p+i = p xu l (21) mixture component into two, or combining two p x(1 - u l) (22) into one). p +2 = L l - ul The only randomness in scanning these move types is T+i ,i = (¿\,i “h -y (23) the random choice between splitting and merging in move (5). One iteration of the hybrid sampler, also (24) called a sweep, consists of a complete pass over these T+2 ,i = moves. The first four move types are conventional in the sense that they do not alter the dimension of the (^1 — u2i2^) if i = j v+ = j (25) parameter space. Hereafter, we will focus on move (5), — u“2i2) which requires the use of the reversible jump mecha­ , x x / (1 — m2 j 2) u 3 itiu 3 jtj if i = j nism. This move type involves changing L by 1 and making necessary corresponding changes to w, © and (1 - u3i,i) (1 - u2i2) P. X i i — if i = j v+ = u l ^X2,i,j < (1 — u S ij) X) a ,i,j (26) V X\/(l — u‘2i2) (1 - u 23__ j2) d+r dimensional subspace X X \/( l- (1 - u3j,j ) if i = j The random variables u are chosen from the inter­ d dimensional subspace X V val (0,1]. In order to favor splitting a class into roughly equal portions, beta(1 .1 , 1 .1) distributions are used. To guarantee numerical stability in inverting Figure 13. ^ is a diffeomorphism which transforms S+ and S+ , one can use some regularization like back and forth between parameter subspaces of differ­ in [2], or one can use the well-known Wishart dis­ ent dimensionality. Dimension matching can be im­ tribution [15]. However, we did not experience such plemented by generating a random vector u such that problems, mainly because the obtained covariance ma­ the dimensions of (X , u) and X ' are equal. trices are also reestimated from the image data in sub­ sequent move types. Therefore as long as our input The split proposal begins by randomly choosing a image can be described by a mixture of Gaussians, we class A with a uniform probability PlPiTct(^) = 1/L. can expect that the estimated covariance matrices are Then L is increased by 1 and A is split into Ai and correct. The next step is the reallocation of those sites A2. In doing so, a new set of parameters need to be s e S \ where ws = A. This reallocation is based on generated. Altering L changes the dimensionality of the new parameters and has to be completed in such the variables © and P. Thus we shall define a deter­ a way as to ensure the resulting labeling w+ is drawn ministic function ^ as a function of these Gaussian from the posterior distribution with © = ©+, p = p+ mixture parameters: and L = L + 1 .

(© +,p+) = ^ (© ,p ,u ) (17) where the superscript + denotes parameter vectors af­ ter incrementing L . u is a set of random variables hav­ ing as many elements as the degree of freedom of joint variation of the current parameters (©,p) and the pro­ posal (©+,p+). Note that this definition satisfies the dimension matching constraint [4] (see Fig. 13), which Original image Segmentation (3 labels) guarantees that one can jump back and forth between different parameter sub-spaces. This is needed to en­ sure the convergence of simulated annealing towards a global optimum. The new parameters of A1 and A 2 are assigned by matching the 0th, 1th, 2th moments of the component being split to those of a combination of the two new components [6,7]: Initial Gaussians Final (3 classes) px = P + + P+2 (18) Figure 14. Segmentation of image rose^l. p xp x = P+1 T+i + P+2 P+2 (19)

p x (PxPx + ^X ) = p +i K t +T + ) Table 2. F-measure and CPU time comparison M ethod F-measure CPU time (20) + p X2 (Ta 2 p-x2 + S >2) Human segmentation 0.79 — There are 10 degrees of freedom in splitting A since co­ RJMCMC 0.57 15 min variance matrices are symmetric. Therefore, we need JSEG 0.56 2 min to generate a random variable u 1 , a random vector u2 and a symmetric random matrix u3. We can now Merging of a pair (A1,A2) is basically the inverse define the diffeomorphism ^ which transforms the old of the split operation. parameters (©,p) to the new (©+,p+) using the above Finally, the split or merge proposal is accepted with a probability relative to the probability ratio of

32 the current and the proposed states. The segmenta­ different image features has to be handled in a parallel tion and parameter estimation is then obtained as a fashion. In this project, we attempt to develop such a MAP estimation implemented via simulated anneal­ model in a Markovian framework based on our earlier ing: work on color-texture segmentation [12]. We propose a new MRF image segmentation model which aims at Algorithm 1 (RJMCMC Segmentation) combining color and motion features for video object segmentation. The model has a multi-layer structure: (3 Set k = 0. Initialize ¡3°, L °, p°, ©°, and the initial Each feature has its own layer, called feature layer , temperature T°. where an MRF model is defined using only the cor­ (3 A sample (tok,Lk,pk,3k, ©k) is drawn from the responding feature. A special layer is assigned to the posterior distribution using the hybrid sampler combined MRF model. This layer interacts with each outlined earlier. Each sub-chain is sampled via the feature layer and provides the segmentation based on corresponding move-type while all the other param­ the combination of different features. Unlike previous eter values are set to their current estimate. methods, our approach doesn’t assume motion bound­ (3 Goto Step (3 with k = k + 1 and Tk+1 until k < K. aries being part of spatial ones. The uniqueness of the proposed method is the ability to detect boundaries As usual, an exponential annealing schedule that are visible only in the motion feature as well as (Tk+1 = 0.98Tk, T° = 6.0) was chosen so that those visible only in the color one. the algorithm would converge after a reasonable We use perceptually uniform CIE-L*u*v* color number of iterations. In our experiments, the al­ values; and optical flow data obtained via the algo­ gorithm was stopped after 200 iterations (T 200 ~ rithm proposed in [18]. We have chosen this method 0.1). because it provides smooth optic flow fields neces­ sary for our MRF model. Our model consists of 3 layers. At each layer, we use a first order neighbor­ hood system and extra inter-layer cliques (Fig. 17). The image features are represented by multi-variate Gaussian distributions. For example, on the color layer, the observed image F c = {fs|s £ Sc} consists of three spectral component values (L*u*v*) at each pixel s denoted by the vector fs. We assume that P (fS | t s) follows a Gaussian distribution, the classes A £ Ac = {1, 2, ...,Lc} are represented by the mean vectors pcx and the covariance matrices S cx. The class label assigned to a site s on the color layer is denoted by Gs. The energy function U(G, F c) of the so defined MRF layer has the following form:

X Gc(fcs,P s)+ ¡3 X 5(Gs,Gr ) + X V c (Ps,nc) sESc {s,r}EC sESc

where Gc(fcs,Gs) denotes the Gaussian energy term while S(Gs,Gr ) = 1 if Gs and Gr are different and — 1 otherwise. 3 > 0 is a parameter controlling the homo­ Figure 16. Precision-recall curve for JSEG and RJM­ geneity of the regions. As 3 increases, the resulting CMC. regions become more homogeneous. The last term (Vc(Gs,n's)) is the inter-layer clique potential. The EXPERIMENTAL RESULT motion layer adopts a similar energy function with some obvious substitutions. The proposed algorithm has been tested on a va­ The combined layer only uses the motion and color riety of real color images and results have also been features indirectly, through inter-layer cliques. A label compared to those produced by JSEG [3], a recent consists of a pair of color and motion labels such that unsupervised color image segmentation algorithm. In n = {nc,Vm ), where nc £ A c and nm £ Am. The set of Fig. 15, we show a couple of results obtained on the labels is denoted by A x = Ac x Am and the number of Berkeley Segmentation D ataset [16], and in Fig. 16, we classes L x = L cL m. Obviously, not all of these labels plot the corresponding precision-recall curves. Note are valid for a given image. Therefore the combined that RJMCMC has a slightly higherF-measure (see layer model also estimates the number of classes and Table 2) which ranks it over JSEG. However, it is fair chose those pairs of motion and color labels which are to say that both method perform equally well but be­ actually present in a given image. The energy function have differently: while JSEG tends to smooth out fine U (n) is of the following form: details (hence it has a higher precision but lower re­ call value), RJMCMC prefers to keep fine details at X (Vs(ns) + v c(Gs,nSc) + v m (Gs,nT)) the price of producing more edges (i.e. its recall values se sx are higher at a lower precision value). + a X S(nsinr) MULTILAYER MRF MODELIZATION {s,r }GC The human visual system is not treating differ­ where Vs (ns) denotes singleton energies, V c(Gs ,ns) ent features sequentially. Instead, as pointed out by (resp. V m (4>s,n 7) denotes inter-layer clique poten­ K ersten etal. [13], multiple cues are perceived simul­ tials. The last term corresponds to second order intra­ taneously and then they are integrated by our visual layer cliques which ensures homogeneity of the com­ system in order to explain the observations. Therefore bined layer. a has the same role as 3 in the color layer

33 Hum an Original image JSEG RJMCMC segmentation Figure 15. Benchmark results on images from the Berkeley Segmentation Dataset

34 model and S(ns ,nr ) = — 1 if ns = Vr, 0 if ns = Vr and 1 if nC = rfc and nT = nr™ or nC = n'C and nT = nT. The idea is that region boundaries present at both color and motion layers are preferred over edges that are found only at one of the feature layers. At any site s, we have 5 inter-layer interactions between two layers: Site s interacts with the corresponding site on the other layer as well as with the 4 neighboring sites Original frame Optic flow two steps away (see Fig- 17). This potential is based on the difference of the first order potentials at the corresponding feature layers. Clearly, the difference is 0 if and only if both the feature layer and the com­ bined layer has the same label- If the labels are dif­ ferent then it is proportional to the energy difference between the two labels. Finally, the singleton energy controls the number of classes at the combined layer by penalizing small classes. Color only Motion only EXPERIMENTS The proposed algorithm has been tested on real video sequences. Herein we present two of these re­ sults. The computing time was around 3 minutes on a Pentium4 3GHz on 320 x 240 frames. We also compare the results to motion only and color only segmenta­ tion (basically a monogrid model similar to the one defined for the feature layers but without inter-layer cliques). The mean vectors and covariance matrices were computed over representative regions selected by the user. The number of motion and color classes is known a priori but classes on the combined layer are Multilayer estimated during the segmentation process. Fig. 18 shows some segmentation results. Note that the head Figure 18. Segmentation results. of the men on this image can only be separated from the background using motion features. Clearly, the multi-layer model provides significantly better results fellowship of the Hungarian Academy of Sciences; compared to color only and motion only segmenta­ and the Hungarian Scientific Research Fund - OTKA tions. See Fig. 19 to compare the performance of the T046805. proposed method with the one from [14] on the Mother and Daughter standard sequence. Clearly, some of the REFERENCES contours are lost by [14] (the sofa, for example) while our method successfully identifies region boundaries. [1] B a r k er , S. A., and R ayner , P. J. W. Unsu­ In particular, our method is able to separate the hand pervised image segmentation using Markov ran­ of the mother from the face of the daughter in spite of dom field models. Pattern Recognition 33, 4 (Apr their similar color. This demonstrates again that the 2000) , 587-602. proposed method is quite powerful at combining mo­ tion and color features in order to detect boundaries [2] C rem ers, D., T ischhauser , F., W eic k er t , j ., visible only in one of the features. and Schnorr , C. Diffusion snakes: Introducing statistical shape knowledge into the Mumford- OOOOOOOOO Shah functional. International Journal of Com­ oooodoooo Intra-layer Cliques puter Vision 50, 3 (2002), 295-313. O 0 - 0 o o o o jfb o o o [3] D en g , Y., , and M anjunath , B. S. Unsuper­ Color oooooaooo vised segmentation of color-texture regions in im­ ages and video. IEEE Transactions on Pattern oo oooo Inter-layer Cliques ooo oooo Analysis and Machine Intelligence 23, 8 (Aug. ooo ooo 2001) , 800-810. oooo ooo Combined [4] G r e e n , P. J. Reversible jump Markov chain oooo oo Monte Carlo computation and Bayesian model OOp/pQOOOO determination. Biom etrika 82, 4 (1995), 711-731. oopoppooo [5] Hastings , W. K. Monte Carlo sampling meth­ o o o q¥ o o o o Motion ods using Markov chains and their application. OOOOOOOOO Biometrika 57 (1970), 97-109. Figure 17. Multi-layer MRF model. [6] K ato , Z. Reversible jump Markov chain Monte Carlo for unsupervised MRF color image seg­ mentation. In Proceedings of Brithish Machine ACKNOWLEDGEMENTS Vision Conference (Kingston, UK, Sept. 2004), This research was partially supported by an A. Hoppe, S. Barman, and T. Ellis, Eds., vol. 1, ERCIM postdoctoral fellowship during the author’s BMVA, pp. 37-46. stay at CWI, Amsterdam; the Janos Bolyai research

35 [16] M a rtin , D., F ow lkes , C., Tal , D., and M a ­ lik , J. A database of human segmented natu­ ral images and its application to evaluating seg­ mentation algorithms and measuring ecological statistics. In Proceedings of International Con­ ference on Computer Vision (July 2001), vol. 2, IEEE, pp. 416-423. [17] M um ford , D. Pattern theory: a unifying per­ Original frame Optic flow spective. In Perception as Bayesian Inference, D. Knill and W. Richards, Eds. Cambridge Uni­ versity Press, 1996, pp. 25-62. [18] P roesmans , M., G ool , L. V., P auw els , E., and O osterlinck , A. Determination of optical flow and its discontinuities using non-linear diffu­ sion. In Proceedings of Eurpoean Conference on Computer Vision (1994), vol. 2, pp. 295-304. Multilayer Khan & Shah [14] [19] R ichardson , S., and G r een , P. J. On Bayesian analysis of mixtures with an unknown Figure 19. Comparison of the segmentation results number of components. Journal of the Royal Sta­ obtained by the proposed method and those produced tistical Society, series B 59, 4 (1997), 731-792. by the algorithm of Khan & Shah [14]. [20] Zerubia , J., J alobeanu , A., and K ato , Z. Markov random fields in image processing, appli­ cation to remote sensing and astrophysics. Jour­ [7] K ato , Z. Segmentation of color images via re­ nal de Physique, EDP Sciences IV, 12 (2002), versible jump MCMC sampling. Image and Vi­ 117-136. sion Computing (2007). to appear. [8] K ato , Z., and P o ng , T. C. Video object seg­ X. COMPUTER ASSISTED SURGERY mentation using a multicue Markovian model. In AND BIOMECHANICAL ANALYSIS Joint Hungarian-Austrian Conference on Image INTRODUCTION Processing and Pattern Recognition (Veszprem, Hungary, May 2005), D. Chetverikov, L. Czuni, The surgical repair of fractured bones is often a and M. Vincze, Eds., KEPAF, OAGM/AAPR, difficult task, and the fixation of these bones has to be Austrian Computer Society, pp. 111-118. planned very carefully. This is why trauma surgeons [9] K ato , Z., and P ong , T. C. A Markov ran­ may use a Computer Aided Surgery (CAS) system to dom field image segmentation model for color improve surgical accuracy. textured images. Image and Vision Computing Our goal here is to develop a suitable CAS pack­ 24, 10 (Oct. 2006), 1103-1114. age that is also capable of performing biomechanical tests. The program can simulate the biomechanical [10] K ato , Z., and P o ng , T. C. A multi-layer MRF behavior of possible surgical solutions and calculate model for video object segmentation. In Proceed­ its deformations and material stresses. These calcu­ ings of Asian Conference on Computer Vision lations are based on Finite Element Analysis (FEA). (Hyderabad, India, Jan. 2006), P. J. Narayanan, Using these results the surgeon is able to see the week S. K. Nayar, and H.-Y. Shum, Eds., vol. 3852 points of the fixation before the surgery. He can even of Lecture Notes in Computer Science, Springer, try several surgical plans to pick the most promising pp. 953-962. one. [11] K ato , Z., P ong , T. C., and Le e , J. C. M. Color image segmentation and parameter estima­ DESCRIPTION OF THE SYSTEM tion in a Markovian framework. Pattern Recog­ The system gets its data from CT images. The nition Letters 22, 3-4 (Mar. 2001), 309-321. first step is the segmentation [1] where the differenti­ [12] K ato , Z., P ong , T. C., and Song , G. Q. Un­ ation is done between various bone fragments and the supervised segmentation of color textured images background. Next, the segmented surface is approx­ using a multi-layer MRF model. In Proceedings imated [3,4] the with a triangle mesh (see Fig. 20), of International Conference on Image Process­ followed by a surface simplification [ 2] which reduces ing (Barcelona, Spain, Sept. 2003), vol. I, IEEE, the number of triangles in the mesh. pp. 961-964. This surface mesh contains all the geometrical in­ formation needed by the surgical planning module. In [13] K e r ste n , D., M amassian , P., and Y u ille , A. this module the user can move and rotate the various Object perception as Bayesian inference. Annual Review of Psychology 55 (2004), 271-304. bone fragments with the mouse. The planning mod­ ule is also the place where virtual implants (screw and [14] K han , S., and Shah , M. Object based segmen­ fixation plate) are inserted. tation of video using color, motion and spatial To simulate the biomechanical behavior of the sur­ information. In Proceedings ofInternational Con­ gical plan the geometrical model has to be converted ference on Computer Vision and, Pattern Recog­ into a mechanical model. The FEA mesh is generated nition (Kauai, Hawaii, Dec. 2001), vol. II, IEEE, from the triangle mesh used for rendering. The ad­ pp. 746-751. dition of load and boundary conditions is handled by [15] M ardia , K. V ., K e n t , J. T ., and B ibby , J. M. the user interface of the planning module. On Fig. 21. Multivariate Analysis. Academic Press, Duluth, arrows indicate the area and direction of the applied London, 1979. load.

36 [3] Lorensen WE, Cline HE. Marching Cubes: A High Resolution 3D Surface Construction Algo­ rithm. ACM SIGGRAPH; 1987 [4] Visualization Toolkit: www.vtk.org

XI. SKELETONIZATION BY THINNING IN 3D

Skeleton is a region-based shape feature to represent the general form of an object. Skeletonization (i.e., skeleton extraction from binary objects) in 3D has become a very challenging task in various medical Figure 20. Combined 3D view of a CT slice and the and engineering applications. Thinning is a frequently triangle mesh. used technique for producing a reasoable approxima­ tion to the skeleton or extracting skeleton-like features (i.e., centerline or topological kernel). SKELETON AS A SHAPE FEATURE Shape is a fundamental concept in computer vi­ sion. It can be regarded as the basis for high-level image processing stages concentrating on scene analy­ sis and interpretation. There are basically two differ­ ent approaches for describing the shape of an object: • using the boundary that surrounds it and • using the occupied region. Boundary-based techniques are widely used but Figure 21. The surgical plan of a broken jaw. The there are some deficiencies which limit their useful­ fracture is stabilized with two fixation plates and ten ness in practical applications especially in 3D. There­ screws. Arrows show the direction of the applied load. fore, the importance of the region-based shape fea­ tures shows upward tendency. The local object sym­ metries represented by the skeleton certainly cannot The finite element analysis is performed by an ex­ replace boundary-based shape descriptors, but com­ ternal software. The results of the analysis, namely plement and support them. the deformation under the load and the material stress The skeleton is a region-based shape feature that are presented in our system, see Fig. 22. has been proposed by Blum as the result of the Medial Axis Transform. A very illustrative definition of the skeleton is given using the prairie-fire analogy: the ob­ ject boundary is set on fire and the skeleton is formed by the loci where the fire fronts meet and quench each others. The formal definition of the skeleton has been stated by Calabi: the skeleton of an object is the lo­ cus of the centers of all the maximal inscribed hyper­ spheres. The continuous skeleton of a solid 3D box is illustrated in Fig. 23. □□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□□

Figure 22. The result of the finite element analysis. Dark colors indicate high material stress.

CONCLUSION A novel system was presented to help the surgeon in planning orthopedic operations. With this system a virtual biomechanical lab was created and various FEA studies of jaw, pelvis, hip, knee, and wrist were carried out. The tool can be used by the surgeon to Figure 23. Example of 3D skeleton. The original ob­ create surgical plans for fractured bone fixation and to ject was a solid box. Note, a skeleton in 3D generally predict the biomechanical stability of the plan before contains surface pathes (i.e., branched 2D manifolds). the operation takes place.

REFERENCES SKELETONIZATION TECHNIQUES IN DISCRETE SPACES [1] Nyul LG, Falcao AX, Udupa JK. Fuzzy- Con­ nected 3D Image Segmentation at Interactive During the last two decades skeletonization in the Speeds. SPIE Medical Imaging 2000. digital image raster has been an important research field. There are two major requirements to be com­ [2] Garland M, Heckbert PS. Surface simplification plied with. The first one is geometrical. It means that using quadric error metrics. ACM SIGGRAPH; the “skeleton” must be in the “middle” of the object 1997

37 and invariant under geometrical transformations. The second one is topological requiring that the “skeleton” must be topologically equivalent to the original object. There are three major discrete skeletonization methods: • based on distance transformation, • thinning, and • based on Voronoi-diagram. The first method is to find the maximal inscribed hyperspheres. It requires the following 3-step process: 1. The original binary picture is converted into another one consisting feature and nonfeature original object after 15 iterations elements. The feature elements belong to the boundary of the discrete object. 2. The distance map is generated where each ele­ ment has a value that approximates the distance to the nearest feature element. 3. The detection of ridges (local extremas) as the centers of maximal inscribed hyperspheres. Unfortunately, the result of the distance transfor­ mation depends on the selected distance and the ridge extraction is a rather difficult task. The distance map based method fulfils the geometrical requirement if a good approximation to the Euclidean distance is ap­ plied, but the topological correctness is not guaran­ teed. The thinning process is to simulate the fire-front propagation: a layer by layer erosion is executed until the “skeleton” is left. The iterative process is shown in Fig. 24. The topological aspect is taken care by thin­ ning. On the other hand the geometrical requirement correctness (i.e., invariance under arbitrary rotations) is not guaranteed. The Voronoi diagram of a discrete set of points (called generating points) is the partition of the given space into cells so that each cell contains exactly one generating point and the locus of all points which are after 60 iterations final “skeleton” superim­ nearer to this generating point than to other generat­ posed on the original ob­ ing points. It is shown that the skeleton of an object ject which is described by a set of boundary points can be Figure 24. Example of thinning in 2D. The size of the approximated by a subgraph of the Voronoi diagram test image is 430 x 460 of that generating points. Both requirements can be fulfilled by the skele­ tonization based on Voronoi diagrams but it is re­ ones) or completely deleted, if any cavity in the in­ garded as an expensive process, especially for large put picture is merged with the background or another and complex objects. hole, or if a cavity is created where there was none We prefer thinning, since it: in the input picture. There is an additional concept • preserves topology, called hole in 3D pictures. A hole (that doughnuts • makes easy implementation possible (as a se­ have) is formed by 0’s, but it is not a cavity. Topol­ quence of local Boolean operations), ogy preservation implies that eliminating or creating • can produce different types of skeleton-like any hole is not allowed. shape features (see fig. 25), Thinning must be a topology-preserving reduc­ • takes the least computational costs, and tion. Existing 3D thinning algorithms can be clas­ • can be executed in parallel. sified from several points of view. One of them is the classification on the produced skeletons: surface­ THINNING METHODOLOGIES thinning algorithms result in medial surfaces, curve­ A 3D binary picture is a mapping that assigns thinning ones can produce medial lines, and shrinking value of 0 or 1 to each point with integer coordinates algorihms extract topological kernels. in the 3D digital space denoted by Z 3. Points hav­ Since the fire front propagation is by nature paral­ ing the value of 1 are called black points, while 0’s lel, most of the existing thinning algorithms are par­ are called white ones. Black points form objects of allel (i.e., all border points satisfying the deletion con­ the picture. White points form the background and dition of the actual phase of the process are deleted the cavities of the picture. Both the input and the simultaneously) [1-9]. Despite of this fact, we have output of a picture operation are pictures. An oper­ proposed two sequential thinning algorithms [ 10, 11]. ation is reduction if it can delete some black points APPLICATIONS (i.e., changes them to white) but white points remain the same. There is a fairly general agreement that a Thinning is a common preprocessing operation in reduction operation is not topology preserving if any raster-to-vector conversion or in pattern recognition. object in the input picture is split (into two or more Its goal is to reduce the volume of elongated objects.

38 [7] K. Palaagyi: A 3D parallel shrinking algorithm, Acta Cybernetica 15, 2001, 201-211. [8] K. Palaagyi: A 3-subiteration 3D thinning al­ gorithm for extracting medial surfaces, Pattern Recognition Letters 23, 2002, 663-675. [9] K. Palagyi: A 2-Subfield 3D Thinning Algo­ rithm for Extracting Medial Curves, in Proc. Joint Hungarian-Austrian Conference on Image Processing and Pattern Recognition HACIPPR 2005, Austrian Computer Society, 2005, 135-142.

J 40^ IK taiPalagyiita]Etal^ orantin ta]E miSmloShtaiAmi™^mlna i Cs. Halmai, B. Erdohelyi, K. Hausegger: A se­ quential 3D thinning algorithm and its medical applications, in Proc. 17th Int. Conf. Informa­ tion Processing in Medical Imaging, IPMI 2001, Davis, USA, Lecture Notes in Computer Science 2082, Springer, 2001, 409-415. [11] K. Palagyi, J. Tschirren, E.A. Hoffman, M. Sonka: Quantitative analysis of pulmonary air­ way tree structures, Computers in Biology and Medicine 36, 2006, 974-996. [12] K. Palagyi, E. Sorantin, Cs. Halmai, A. Kuba: 3D thinning and its applications to medical image processing, TASK Quarterly 3, 1999, 397-408. Figure 25. Different types of 3D “skeletons”. The original elongated object (upper left), its medial sur­ [13] E. Sorantin, E. Balogh, A. Vilanova i Bartroli, K. face produced by a surface thinning algorithm (upper Palagyi, L.G. Nyul, S. Loncaric, M. Subasic, D. right), its medial line (bottom left) extracted by a Kovacevic: Virtual Dissection of the Colon, in D. curve thinning algorithm, and its topological kernel Caramella, C. Bartolozzi (eds.) 3D Image Pro­ (i.e., a minimal structure being topologically equiva­ cessing - Techniques and Clinical Applications, lent to the original object) created by a shrinking al- Springer, 2002, 197-209. gorithm(bottom right). (Each small cube represents [14] J. Tschirren, K. Palagyi, J.M. Reinhardt, E.A. an object voxel.) Hoffman, M. Sonka: Segmentation, skeletoniza­ tion, and branchpoint matching - A fully au­ tomated quantitative evaluation of human in­ Some important applications have been appeared in trathoratic airway trees, in Proc. 5th Int. medical image processing, too [1-7,19-22]. Conf. Medical Image Computing and Computer- Assisted Intervention, MICCAI 2002, Part II, REFERENCES Tokyo, Japan, Lecture Notes in Computer Sci­ [1] K. Palagyi, A. Kuba: A thinning algorithm to ence 2489, Springer, 2002, 12-19. extract medial lines from 3D medical images, in [15] E. Sorantin, Cs. Halmai, B. Erdohelyi, K. Proc. 15th Int. Conf. Information Processing in Palagyi, L.G. Nyul, K. Olle, B. Geiger, F. Lind- Medical Imaging, IPMI’97, Poultney, USA, Lec­ bichler, G. Friedrich, K. Kiesler: Spiral-CT- ture Notes in Computer Science 1230, Springer, based assessment of tracheal stenoses using 3­ 1997, 411-416. D-skeletonization, IEEE Transactions on Medical [2] K. Palagyi, A. Kuba: A parallel 12-subiteration Imaging 21, 2002, 263-273. 3D thinning algorithm to extract medial lines, in [16] K. Palagyi, J. Tschirren, M. Sonka: Quantitative Proc. 7th Int. Conf. Computer Analysis of Images analysis of intrathoracic airway trees: methods and Patterns, CAIP’97, Kiel, Germany, Lecture and validation, in Proc. 18th Int. Conf. Informa­ Notes in Com puter Science 1296, Springer, 1997, tion Processing in Medical Imaging, IPMI 2003, 400-407. Ambleside, UK, Lecture Notes in Computer Sci­ [3] K. Palagyi, A. Kuba: A 3D 6-subiteration thin­ ence 2732, Springer, 2003, 222-233. ning algorithm for extracting medial lines, Pat­ [17] E.A. Hoffman, J.M. Reinhardt, M. Sonka, B.A. tern Recognition Letters 19, 1998, 613-627. Simon, J. Guo, O. Saba, D. Chon, S. Samrah, H. [4] K. Palagyi, A. Kuba: A hybrid thinning algo­ Shikata, J. Tschirren, K. Palagyi, K.C. Beck, G. rithm for 3D medical images, J. Computing and McLennan: Characterization of the Interstitial Information Technology 6, 1998, 149-164. Lung Diseases via Density-Based and Texture- Based Analysis of Computed Tomography Im­ [5] K. Palagyi, A. Kuba: A parallel 8-subiteration ages of Lung Structure and Function, Academic 3D thinning algorithm, in Proc. 8th Int. Conf. on Discrete Geometry for Computer Imagery, Radiology 10, 2003, 1104-1118. DGCI’99, Marne-la-Valle, France, Lecture Notes [18] K. Palagyi, J. Tschirren, M. Sonka: Quantitative in Computer Science 1568, Springer, 1999, 325­ analysis of three-dimensional tubular tree struc­ 336. tures, in Medical Imaging 2003: Image Process­ [6] K. Palagyi, A. Kuba: A parallel 3D 12- ing, San Diego, USA, in Proceedings of SPIE Vol. subiteration thinning algorithm, Graphical Mod­ 5032, 2003, 277-287. els and Image Processing 61, 1999, 199-221.

39 [19] K. Palagyi, J. Tschirren, E.A. Hoffman, M. scanning, rotational angiography, or other volumetric Sonka: Assessment of Intrathoracic Airway imaging means. Trees: Methods and In Vivo Validation, in Proc. There are many reasons why identifying tree Computer Vision and Mathematical Methods in skeletons is important. Skeletons can serve as one­ Medical and Biomedical Image Analysis: ECCV dimensional structures allowing guidance for orderly 2004 Workshops CVAMIA and MMBIA, Prague, exploration of the entire tree, they can serve as view­ Czech Republic, Lecture Notes in Computer Sci­ point trajectory for navigation purposes in virtual ence 3117, Springer, 2004, 341-352. bronchoscopy or angioscopy. To facilitate quantita­ [20] R. Beichel, T. Pock, Ch. Janko, B. Zotter, B. Re- tive analysis of the vascular or bronchial tree, e.g., itinger, A. Bornik, H. Bischof, K. Palagyi, E. So- luminal area or wall thickness, measurements must be rantin, G. Werkgartner, M. Sonka: Liver segment obtained in cross-sections perpendicular to the long approximation in CT data for surgical resection axis of the tree segments. Clearly, planes normal to planning, in Medical Imaging 2004: Image Pro­ the tree skeletons must be identified and skeleton cor­ cessing, San Diego, USA, in Proceedings of SPIE rectness is of paramount importance. As such, quan­ Vol. 5370, 2005, 1435-1446. titative assessment of asthma or cystic fibrosis from pulmonary CT images depends on the performance [21] J. Tschirren, G. McLennan, K. Palagyi, E.A. of the tree skeletonization method. Similarly, accu­ Hoffman, M. Sonka: Matching and anatomical la­ racy and reproducibility of arterial plaque thickness beling of human airway tree, IEEE Transactions measurements from coronary CT or intravascular ul­ on Medical Imaging 24, 2005, 1540-1547. trasound depends on the ability to skeletonize tubular [22] E. Sorantin, D. Mohadjer, L.G. Nyul, K. Palagyi, structures. F. Lindbichler, B. Geiger: New advances for METHOD imaging of laryngotracheal stenosis by post pro­ cessing of spiral-CT data, in W. Hruby (ed.) Dig­ The input of the proposed method is a 3D binary ital (R)Evolution in Radiology - Bridging the Fu­ image representing a segmented voxel-level tree ob­ ture of Health Care, Springer, 2006, pp. 297-308. ject. All main components of our method were specif­ ically developed to deal with imaging artifacts typi­ XII. QUANTITAVIVE ANALYSIS OF cally present in volumetric medical image data. As TUBULAR TREE STRUCTURES such, the method consists of the following main steps:

The developed approach is specifically targeting skele­ 1 . correction of the segmented tree - hole and cav­ ity filling, tonization of vascular and airway tree structures in medical images but it is general and applicable 2. extraction of the 3D centerline - skeletoniza­ to many other skeletonization tasks. It builds on tion, the following concepts and properties: fast curve­ 3. tree pruning, thinning algorithm to increase computational speed, endpoint re-checking to avoid generation of spuri­ 4. generation of a formal tree structure (see Fig. ous side branches, depth-and-length sensitive pruning, 26), and exact tree-branch partitioning allowing branch 5. tree partitioning (see Fig. 27), and volume and surface measurements. The method was 6. quantitative analysis. validated in computer and physical phantoms and in in vivo CT scans of human lungs. The validation stud­ For each partition/branch of the tree, the follow­ ies demonstrated sub-voxel accuracy of branch point ing measures/indices are calculated: branch length positioning, insensitivity to changes of object orienta­ (defined as a Euclidean distance between the parent tion, high reproducibility of derived quantitative in­ and child branch-points), branch volume (defined as a dices of the tubular structures. volume of all voxels belonging to the branch), branch surface area (defined as a surface area of all boundary INTRODUCTION voxels belonging to the branch), and branch radius Tubular structures are frequently found in living (derived from the branch length and the branch vol­ organisms. The tubes - e.g., arteries or veins are orga­ ume). nized into more complex structures. Trees consisting The automated method for skeletonization, of tubular segments form the arterial and venous sys­ branch-point identification and quantitative analysis tems, intrathoracic airways form bronchial trees, and of tubular tree structures is robust, efficient, and other examples can be found. Computed tomography highly reproducible. It facilitates calculation of a (CT) or magnetic resonance (MR) imaging provides number of morphologic indices described above [1-7]. volumetric image data allowing identification of such tree structures. Frequently, the trees represented as REFERENCES contiguous sets of voxels must be quantitatively an­ [1] J. Tschirren, K. Palagyi, J.M. Reinhardt, E.A. alyzed. The analysis may be substantially simplified Hoffman, M. Sonka: Segmentation, skeletoniza­ if the voxel-level tree is represented in a formal tree tion, and branchpoint matching - A fully au­ structure consisting of a set of nodes and connect­ tomated quantitative evaluation of human in­ ing arcs. To build such formal trees, the voxel-level trathoratic airway trees, in Proc. 5th Int. tree object must be transformed into a set of inter­ Conf. Medical Image Computing and Computer- connected single-voxel centerlines representing indi­ Assisted Intervention, MICCAI 2002, Part II, vidual tree branches. Therefore, the aim of our work Tokyo, Japan, Lecture Notes in Computer Sci­ was to develop a robust method for identification of ence 2489, Springer, 2002, 12-19. centerlines and bifurcation (trifurcation, etc.) points in segmented tubular tree structures acquired in vivo [2] K. Palagyi, J. Tschirren, M. Sonka: Quantitative from humans and animals using volumetric CT or MR analysis of intrathoracic airway trees: methods

40 Figure 27. The aim of the partitioning procedure Figure 26. A human airway tree and its centerlines is to partition all voxels of the segmented tree into (up). The corresponding formal tree structure, in branches - each voxel is assigned a branch-specific la­ which a path between two branch-points is replaced bel. The segmented volume and the partitioned skele­ by a single edge (down). tal tree (up) and the partitioned volume after label­ propagation (down). (Note, that we used only 9 colors in displaying these trees, therefore, the same color was and validation, in Proc. 18th Int. Conf. Informa­ assigned to multiple branches.) tion Processing in Medical Imaging, IPMI 2003, Ambleside, UK, Lecture Notes in Computer Sci­ ence 2732, Springer, 2003, 222-233. [6] J. Tschirren, G. McLennan, K. Palágyi, E.A. [3] E.A. Hoffman, J.M. Reinhardt, M. Sonka, B.A. Hoffman, M. Sonka: Matching and anatomical la­ Simon, J. Guo, O. Saba, D. Chon, S. Samrah, H. beling of human airway tree, IEEE Transactions Shikata, J. Tschirren, K. Paiagyi, K.C. Beck, G. on Medical Imaging 24, 2005, 1540-1547. McLennan: Characterization of the Interstitial [7] K. Palagyi, J. Tschirren, E.A. Hoffman, M. Lung Diseases via Density-Based and Texture- Sonka: Quantitative analysis of pulmonary air­ Based Analysis of Computed Tomography Im­ way tree structures, Computers in Biology and ages of Lung Structure and Function, Academic Medicine 36, 2006, 974-996. Radiology 10, 2003, 1104-1118. [4] K. Palagyi, J. Tschirren, M. Sonka: Quantitative analysis of three-dimensional tubular tree struc­ tures, in Medical Imaging 2003: Image Process­ ing, San Diego, USA, in Proceedings of SPIE Vol. 5032, 2003, 277-287. [5] K. Palagyi, J. Tschirren, E.A. Hoffman, M. Sonka: Assessment of Intrathoracic Airway Trees: Methods and In Vivo Validation, in Proc. Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis: ECCV 2004 Workshops CVAMIA and MMBIA, Prague, Czech Republic, Lecture Notes in Computer Sci­ ence 3117, Springer, 2004, 341-352.

41 Department of Software Engineering

I. AD-HOC MOBILE AND MULTIMEDIA “Triple Play” services are the place where the tra­ NETWORKS ditional telecommunication companies meet with ca­ ble TV operators and with Internet Service providers. WIRELESS MESH NETWORKS WITH MO­ The IP layer will be the commons basis for these ser­ BILITY SUPPORT vices. Real-time services demand new services and For geographical and demographic reasons the In­ strict quality features from the network layer. The ternet penetration in rural areas is far from that in multicast data communication paradigm is not a new larger cities. It seems that current business models innovation and is actually as old as the World Wide and technologies cannot achieve a breakthrough in Web. Due to the technical challenges and the lack this area. So new business models which are closer of a “killer” application, it is still not widely used. to real life situations in rural areas and villages are It seems that the IPTV will change this. The unicast needed. For example, in a small community people data communication paradigm is not suitable for serv­ know each other and they try to solve any arising ing a huge number of online TV watchers. We have not found a software solution for the testing and mon­ problems in much closer cooperation than in larger itoring of a multicast network. Our network testing towns and cities. From the aspect of technology and business models the Wireless Mesh Network (WMN) and monitoring software solution tries to fill this gap. solution seems to fit the bill. Utilizing this solution a In the Network Testing section we will describe this community can achieve wireless network coverage for tool and our result in the field of network testing and a small town or village. The network infrastructure is monitoring. managed by volunteer citizens. As the whole system is The Video-On-Demand is another promising area. Here cheap and scalable data storage capable of serv­ adaptive and self-tuning, the system can be expanded in a plug-and-play manner without any special knowl­ ing a high number of concurrent streams is the biggest edge being needed. The WMN can be used to extend issue that needs to be addressed. Our LanStore frame­ the range and the services of an already existing WiFi work is unique among the distributed storage solutions based ISP (W-ISP) or multiple WISP’s. In the case because it uses the unused storage capacity of desktop of multiple WISPs the WMN can be used as a com­ machines. In the Distributed Storage section we will describe our results in the field of distributed consis­ mon access network. With a adaptive and volunteer run WMN the cost of the network maintenance will tency and storage. be significantly cheaper. As the cost of the network NETWORK TESTING maintenance can be as high as 80% of the total cost using the WMN as an access network could be signif­ Testing an already deployed network can provide icantly cheaper compared to current solutions. valuable information about future situations and ser­ The limitations and the capabilities of the Wireless vices. System administrators need a framework that Mesh Network has been studied by numerous articles. can also supply them with traffic orchestration and Despite numerous WMN implementations and large measurement data. In the Campus 6 EU and Hungar­ WMN projects we have not found a solution that ad­ ian state-funded research and development project, dresses the following issues: the NetSpotter framework is a general purpose net­ work testing package that has been designed and de­ • Efficient resource scheduling veloped. With this framework the user has the free­ • Network wide QoS guaranties dom to create arbitrary packets and arbitrary mes­ • Mobility support sage sequences. The message sequences can defined by a user-friendly GUI or by an XML format of the As a participants in the C@R EU-Funded project, our official MSC representation. With our powerful tem­ goal is to design and develop a WiFi-based WMN so­ plate solution one can easily create complex test sce­ lution for rural communities. One novelty of our solu­ narios. Current test scenarios (RFC 3918) define only tion is the new metric for the link selection. With this point to multipoint measurements. We think that to metric we will be able to minimalize the interference be able to correctly measure a network, we need mul­ in the network and hence we will be able to maxi- tipoint to multipoint measurements. With this ap­ malize the global throughput. Another novelty of our proach we can probably model the real traffic prop­ solution lies in the scheduling structure. The nodes erties more precisely. Our framework provides this with uplinks are the clusterheads in our topology. The capability with the help of software agents. There is a member nodes in a cluster report the measured/tested central server cluster and there can be arbitrary num­ link properties to the clusterhead. Based on this data ber of agents. One can define the message sequences this node will be able to optimize the frequency reuse among the agents with the previously mentioned MSC inside and outside the cluster. As we have a strict engine. scheduling, a fine grained QoS control will be possi­ We measured the channel-handling capabilities of the ble. As a unique feature our mobility handling is an MRD6 multicast routing daemon for Linux. In the lit­ integrated part of our solution. For further details, erature we have not seen results like that for MRD 6 or read article [ 1]. IPv 6 multicast routing solutions. In our experiments MULTIMEDIA NETWORKS it turned out that the multicast network can be an easy target of a DoS attack. With a relatively small There is an ongoing integration process in the field packet number a multicast network can be shut down. of communication and broadcasting. The so called

42 In a real world scenario some rate limiting solution [5] V. Bilicki, D. J. Dombi: Paxos with multiple should be used. Further details about the framework leaders, In Fifth Conference of PhD Students in and the results can be found in articles [2-4]. Computer Science (CSCS 2006) DISTRIBUTED STORAGE [6] V. Bilicki, D. J. Dombi: Building a framework for the consistency management of the distributed LanStore is a highly reliable, fully decentralized applications. In Proceedings of the 4th Interna­ storage system which can be constructed from already tional Conference on .NET Technologies, Pilsen, existing desktop machines. Our software utilizes the Czech Republic, May-June 2006, Proceedings otherwise wasted storage capacity of these machines. ISBN 80-86943-10-0, page(s): 55-63 Reliability is achieved with the help of a traditional [7] V. Bilicki: LanStore: a highly distributed reli­ erasure coding algorithm called the Reed-Solomon al­ able file storage system. In Proceedings of the 3rd gorithm which generates n error correcting code items International Conference on .NET Technologies, for each m data item. The distributed behavior is Pilsen, Czech Republic, May-June 2005 controlled by a voting-based quorum algorithm. This algorithm is an optimized version of the classic Paxos II. OPEN SOURCE DEVELOPMENT FOR algorithm. Further details about the algorithm can EMBEDDED SYSTEMS be found in the article [5] and presentation [5]. With this solution we can tolerate up to n simultaneously INTRODUCTION failing machines. As LanStore is intended to be used Nowadays, and according to the trends, in the in LAN environments, instead of employing an over­ future embedded systems and devices get more and lay multicast solution we used an IP-level multicast more widespread - their market is about 100 times service. To use the bandwidth effectively, we designed the size of the desktop market, and will also grow ex­ a special UDP-based multicast flow control protocol. ponentially in the next decade. For the implementation platform we chose the Win­ Embedded systems are omnipresent nowadays and dows family and the .NET framework as they are the make possible the creation of systems with a function­ most popular platforms in offices and university de­ ality that cannot be provided by human beings. Ex­ partments. So far we have implemented a prototype ample application areas are consumer electronic prod­ version of this solution. We measured its performance ucts (e.g. CD players, microwave ovens), telecommu­ and the results indicate that this solution can pro­ nication (e.g. mobile phones), medical systems (e.g. vide a throughput comparable to the currently used pacemakers), traffic control (e.g. intelligent traffic network file systems, its performance depending on lights), driving and car control (e.g. ABS), airborne the selected error correcting capability, the number equipment (e.g. fly-by-wire), and plant control (e.g. of failing machines and the performance of the client packaging machines, wafer steppers). machine. In special cases like video-on-demand with Due to their importance, the researchers of the a high client number our solution can outperform the department are working on several embedded system- traditional single server solutions. Further details can related research areas. These research topics were sug­ be found in article [ 6] gested by industrial partners, and most of the results CONNECTIONS OF RESEARCH TO EDU­ are immediately utilized in real products. CATION OPTIMIZING FOR ENERGY Students can take part in the R&D projects as One of the big design challenges for mobile devices part time participants or they can do their graduate is the optimal usage of the typically very limited en­ work on a selected part of an R&D project. E.g: The ergy resources. Within the framework of the Bilateral LanStore software was developed by more than fifteen German-Hungarian Collaboration Project on Ambi­ graduating students. As we are involved in the Cisco ent Intelligence Systems (BelAmI), we have been con­ academy network, the students can use the latest net­ ducting research on the possibilities of reducing the work devices for their studies. energy consumption of software with the help of com­ pilers since late 2005. The evaluation of software opti­ REFERENCES misation techniques requires the ability to accurately measure the power consumption of a system. The [1] V. Bilicki, T. Kllai, M. Kasza: Wireless Mesh most trivial solution is to perform measurements on a Network For Rural Communities. IST-Africa real hardware. However, in some scenarios, e.g., where 2007 Conference & Exhibition (IST-Africa 2007) automatic collection and evaluation of large amount [2] V. Bilicki, M. Bohus, M. Kasza: Netspotter: a of results is required, hardware measurements can be framework for network testing. In 7th Interna­ overly expensive or impractical. In these situations tional Conference on Applied Informatics (ICAI an accurate simulation tool can be used. Thus, we 2007) have created a cycle-accurate energy simulator tool [3] V. Bilicki: Testing and Verifying an IPv 6 Based for the ARM v5TE architecture-based XScale proces­ Multicast Network. In Proceedings of the In­ sor cores. The power dissipation graphs showing the ternational Conference on Wireless and Mobile accuracy of the created simulator compared to real Communications and the International Multi­ measurement are shown in Figure 28. Conference on Computing in the Global Infor­ Currently, the simulator is used to assess the effect mation Technology (ICWMC/ICCGI 2006, Pub­ of various optimisation methods on energy consump­ lication Date: 01-03 Aug. 2006, On page(s): 3­ tion. Our focus is on static and dynamic voltage and 3, ISBN: 0-7695-2629-2) frequency scaling techniques. [4] V. Bilicki: Network topology discovery, In Fifth OPTIMIZING FOR SIZE Conference of PhD Students in Computer Science In the resource constrained domain of embedded (CSCS 2006) systems the program size is an important aspect as

43 Figure 29. Blackdog, a small Linux server utilizing JFFS2

Figure 28. Measured and simulated power dissipation. well. However, since the majority of compiler develop­ ers are interested in the performance of the generated code, this objective is often neglected. Several bench­ marks exist that measure the performance of the gen­ erated code on a daily basis, however benchmark for code size have not existed previously. We have devel­ Figure 30. The Nokia770-based mobile ECG applica­ oped a benchmark called CSiBE (Code Size Bench­ tion. mark) [1], which regularly measures the size of the code generated by GCC. We continuously maintain the benchmark and look for irregular changes in the the JFFS2 filesystem and the Linux kernel, and part of result and act if required. Thanks to the existence many industrial products such as Nokia 770 and N800 of the benchmark, the compiler has been improved and small Linux server of Realm called Blackdog (see several times to generate a smaller code. Now it is Figure 29). considered as the standard GCC benchmark for size, Unfortunately JFFS2 has reached its limit: it was which is used on a daily basis by several developers. designed more then 5 years ago, and it cannot be The website gets more than 100 hits daily on average, tuned for larger flash than 512M. The problems are and the offline version was downloaded by more than in the design level of the filesystem, so the develop­ 500 times. We presented our work related to the mea­ ment of a new generation of this filesystem (JFFS3) surement of the code size generated by GCC in two was necessary. This development is partially spon­ talks at the GCC Developers Summit, which gathered sored by Nokia, and is still in the designing phase. the key participants of this open source project [4,5]. Besides the measuring, we worked on algorithms for code size reduction as well. We implemented code ECG APPLICATION DEVELOPMENT factoring algorithms in GCC and developed an en­ The above developments are close to the system hanced procedural abstraction technique, which pro­ level. To validate their effectiveness, we started an vides superior results compared to the existing solu­ application development project on Nokia 770 in 2006, tions [7]. which was based on open source techniques. FLASH FILE SYSTEM IMPROVEMENTS We cooperated with Meditech Ltd., an ECG man­ ufacturer company, and improved the functionality Embedded systems mostly use flash memory as of their mobile ECG device (called CardioBlue) with storage device. The embedded systems which are some useful features using a Nokia 770 device: it dis­ complex enough to run a real operating system (in plays ECG diagrams, extends the capacity of Car- open source environment it is Linux), need a special dioBlue, configures CardioBlue, etc. The created ap­ flash file system to store their base (root) file system. plication [3] is capable of transfering real-time ECG Using an ordinary file system would wear out the flash data to a remote PC as well, thus it makes remote prematurely. medical consultation possible. The most effective and most popular open-source The application was introduced at the Medica in­ flash file system is JFFS2. To make it more power­ ternational workshop in November, 2006. Figure 30 ful we improved its compression performance [ 6], and shows an example setup of the application. speed (speeded up its mount/boot time 5-10 times). Our improvements [2] were partially sponsored by REFERENCES Nokia Finland, and the results were approved by the open-source community. Now it is the official part of [1] Homepage of CSiBE. http://www.csibe.org.

44 [2] Homepage of JFFS2/3 Improvements. We also experimented with several methods on http://www.inf.u-szeged.hu/jffs 2. how to reduce the size of static slices. In [ 6], we de­ [3] Homepage of SmartECG. scribed how superfluous edges can be removed from http://www.sed.hu/smartecg. the statically computed call graph with the help of dynamically gathered information. The evaluation of [4] A. Beszedes, R. Ferenc, T. Gergely, T. Gyimothy, this method demonstrated that the slice size could be G. Loki, and L. Vidács. CSiBE benchmark: One dramatically reduced if the application being analysed year perspective and plans. In Proceedings of the made extensive use of indirect function calls. 2004 GCC Developers’ Summit, pages 7-15, June 2004. THEORY OF SLICING [5] A. Beszedes, T. Gergely, T. Gyimothy, G. Loki, Previously, a large number of different slicing tech­ and L. Vidacs. Optimizing for space : Mea­ niques have been introduced. Each preserves some as­ surements and possibilities for improvement. In pect of a programs behaviour and simplifies the pro­ Proceedings of the 2003 GCC Developers’ Summit gram to focus exclusively upon this behaviour. Their (GCC 2003), pages 7-20, Ottawa, Canada, May definitions, when given, have been operational, and 2003. their descriptions have been algorithmic. However, in order to understand the similarities and differences [6] T. Gergely, F. Havasi, and T. Gyimothy. Binary between slicing techniques, a formal mechanism is re­ code compression based on decision trees. Pro­ quired. ceedings of the Estonian Academy of Sciences - We used a projection theory of slicing to provide Engineering, 11(4):269-285, Dec. 2005. a declarative formulation of the definition of the dif­ [7] G. Loki, A. Kiss, J. Jász, and A. Beszedes. ferent forms of slicing [5]. W ith the help of the theory Code factoring in GCC. In Proceedings of the we uncovered the precise relationship between various 2004 GCC & GNU Toolchain Developers’ Sum­ forms of dynamic slicing and static slicing and pro­ mit (GCC 2004), pages 79-84, Ottawa, Canada, duced formal and executable definitions of forward June 2-4, 2004. slicing. Our analysis of dynamic slicing introduced by Korel and Laski revealed that the subsumes rela­ III. STATIC AND DYNAMIC PROGRAM tionship between static and dynamic slicing is more ANALYSIS intricate that previous authors have claimed. In all applications of slicing, the size of slices is cru­ INTRODUCTION cial: the smaller the better. Based on the projection Program slicing is a powerful program analysis theory we established a formal mechanism for com­ technique. It can be used for debugging, maintenance, paring sets of minimal slices, which form the ideal for reverse engineering and testing of programs. A slice any slicing algorithm, to reveal the ordering relation­ ship between various static and dynamic slicing tech­ consists of all statements and predicates that might niques [2]. This allows us to determine whether one affect a set of variables at a certain program point. A slice may be an executable program or a subset of definition of slicing leads to inherently smaller slices the program code. Static slicing methods compute than another. This puts statements such as “dynamic those statements which influence the value of a vari­ slices are smaller than static slices” on a firm theoret­ able occurrence for all possible program inputs, while ical footing. The extended versions of the theoretical results dynamic slicing methods take only one specific input into account. have been published in journals [3,4]. The Department of Software Engineering of the EFFICIENT DYNAMIC SLICING Institute of Informatics performs significant research activity in the field of program analysis and specifi­ Dynamic Dependence Graph-based methods for cally program slicing, both in theoretical and practical dynamic program slicing are well understood but in­ aspects. In the period 2003-2006 the following results appropriate for practical use due to their inefficiency have been achieved. in terms of space requirements. Namely, many tradi­ tional methods for computing dynamic program slices SLICING BINARY PROGRAMS are based on this graph representation, which cap­ The original slicing algorithms were developed for tures the dynamically occurring dependences among high-level structured programs and comparatively lit­ program elements. The problem is that, being depen­ tle attention has been paid to the slicing of binary ex­ dent on the size of the execution history, this approach ecutable programs. However, the application domain produces data structures of unbounded size. We proposed a common framework and different for slicing binaries is similar to that for slicing high- level languages. Furthermore, there are special appli­ algorithms within it, which compute dynamic slices cations of the slicing of programs without source code based on the same dynamic dependences that the like assembly programs, legacy software, and viruses. DDG is built on, but without requiring the DDG it­ E.g., the slicing of binary executables can be a useful self to be used. Rather, specialized data structures method for source code recovery or for helping extract are applied depending on the slicing scenario. Al­ though some researchers mention similar algorithms, security critical code fragments. To address the above needs we gave a method we are not aware of any other such comprehensive for the interprocedural static slicing of binary exe­ overview of the basic dependence-based dynamic slic­ cutables [7]. We presented a conservative dependence ing algorithms. These algorithms have been presented graph based approach and also improvements. We in a conference paper with the discussion about their evaluated both approaches on programs compiled for complexities and application scenarios [1]. The sce­ narios are categorized along three dimensions: for- ARM architecture. ward/backward slicing, demand driven/global, and

45 forward/backward trace processing. Of the eight pos­ analysis front end, and the implementation of block- sibilities, two are unfeasible while the others vary in level program instrumentation method, which is used their complexity. by the regression testing method. This work has been selected for publication in a ACKNOWLEDGEMENTS special issue of the Journal of Software Maintenance and Evolution: Research and Practice published by This work was supported, in part, by national John Wiley & Sons, Ltd. expectedly in 2008. grants NKFP-2004 2/013/04 (CREG++), GVOP- 3.1.1.-2004-05-0049/3.0 (JARTA) and grant no. RET- ONGOING RESEARCH 07/2005 of the Peter Pazmany Program of the Hun­ There are two topics in the field of program analy­ garian National Office of Research and Technology. sis in which we produced the first results only recently. The concept of union slices - the union of dynamic REFERENCES slices corresponding to different executions - proved to be useful as a replacement to static slices, which are in [1] A. Beszedes, T. Gergely, and T. Gyimothy. Graph­ many cases overly conservative and hence imprecise. less dynamic dependence-based dynamic slicing al­ We continued the verification of our previous results in gorithms. In Proceedings of the Sixth IEEE In­ this field on Java programs, which was presented by a ternational Workshop on Source Code Analysis 5th year student at the Student Research Competition and Manipulation (SCAM’06), pages 21-30, Sept. in 2006. 2006. The second topic deals with approximate algo­ [2] D. Binkley, S. Danicic, T. Gyimothy, M. Harman, rithms for program analysis. Although there are well A. Kiss, and B. Korel. Minimal slicing and the elaborated methods (to which we also contributed relationships between forms of slicing. In Proceed- significantly) that compute program dependences at mgs of the 5th IEEE International Workshop on the lowest instruction level, the computational cost Source Code Analysis and Manipulation (SCAM of these algorithms is inappropriate in many appli­ 2005), pages 45-54, Budapest, Hungary, Sept. 30 - cations. Therefore, more efficient though less precise Oct. 1, 2005. IEEE Computer Society. Best paper methods are welcome. An approximate method for award. the computation of dynamic dependences among func­ tions (without requiring instruction level analysis) has [3] D. Binkley, S. Danicic, T. Gyimothy, M. Harman, been elaborated with applications to impact analysis, Ao . Kiss, and B. Korel. A formalisation of the rela­ debugging and program testing. The first publication tionship between forms of program slicing. Science of this algorithm was made by a 5th year student at of Computer Programming, 62(3):228-252, Oct. the Student Research Competition winning the first 2006. prize in 2006. [4] D. Binkley, S. Danicic, T. Gyimothy, M. Harman, Also, both of these results are accepted for presen­ Ao . Kiss, and B. Korel. Theoretical foundations of tation at the 2007 European Conference on Software dynamic program slicing. Theoretical Computer Maintenance and Reengineering. Science, 360(1-3):23-41, Aug. 2006. CONFERENCE ORGANIZATION [5] D. Binkley, S. Danicic, T. Gyimothy, M. Harman, The 21st event of the most significant software Ao . Kiss, and L. Ouarbya. Formalizing executable maintenance conference, the International Conference dynamic and forward slicing. In Proceedings of the on Software Maintenance (ICSM 2005) was organized 4th IEEE International Workshop on Source Code by the Department of Software Engineering in 2005. Analysis and Manipulation (SCAM 2004), pages The local organization issues of the Fifth Workshop on 43-52, Chicago, Illinois, USA, Sept. 15-16, 2004. Source Code Analysis and Manipulation (SCAM 2005) IEEE Computer Society. held in Budapest were coordinated by Akos Kiss. [6] A. Kiss, J. Jasz, and T. Gyimothy. Using dynamic information in the interprocedural static slicing R&D PROJECTS of binary executables. Software Quality Journal, Static and dynamic program analysis techniques 13(3):227-245, Sept. 2005. can be utilized in many practical problems related [7] A. Kiss, J. Jasz, G. Lehotai, and T. Gyimothy. to the maintenance of large software systems. The Interprocedural static slicing of binary executa­ application of different techniques, including program bles. In Proceedings of the 3rd IEEE International slicing, to industrial software systems was verified in Workshop on Source Code Analysis and Manipu­ the scope of R&D projects partly financed by na­ lation (SCAM 2003), pages 118-127, Amsterdam, tional grants and performed with partners from in­ The Netherlands, Sept. 26-27, 2003. IEEE Com­ dustry. The purpose of the JARTA (Java regression puter Society. testing and analysis) project (duration: 2005-6, our share of the grant: 4 MFt) was to produce a pro­ totype tool that integrates various program analysis techniques for program understanding and regression testing, most notably instruction level program slic­ ing. Similarly, in the CREG++ (C++ regression testing and analysis) project (duration: 2005-6, our share of the grant: 31.5 MFt) efficient methods were implemented for the analysis of large C++ software systems. In both projects, the role of the Institute of Informatics was the development of the program

46 Research Group on Artificial Intelligence

I. MACHINE LEARNING ALGORITHMS loping syntax rules and an effective syntactic IN NATURAL LANGUAGE PROCESS­ parser for Hungarian [7], [8], [9], [5], [11]. ING The corpus is available in XML and was encoded using the TEIXLITE3 P2 or the P4 DTD scheme. The application of ML (Machine Learning) to practi­ Texts were collected from six different areas of re­ cal problems is an emerging field of research and de­ cent Hungarian written sources (fiction, newspapers, velopment. In many cases only machine learning can legal texts, computer-oriented texts, teenage composi­ provide feasible approaches to algorithms, testing, and tions, short business news). The HLT group maintain validation. Researchers at the Institute of Informatics a software environment that supports the annotation are studying a number of areas related to NLP (Natu­ works [4]. The different versions of the Szeged Cor­ ral Language Processing) and extensively use machine pus and the Treebank can be freely obtained for re­ learning algorithms for solving various problems [16]. search and education purposes after registration [3], see http://www.inf.u-szeged.hu/hlt .

THE NATURAL LANGUAGE PROCESS­ THE HUNGARIAN EUROWORNET ING DATABASE Investigating characteristic features of Hungarian Semantic analysis of natural language texts re­ language by means of information technology is a tra­ quires a comprehensive database containing possi­ dition at the Institute of Informatics. The history of ble meanings of concepts, so-called senses. Such it goes back to László Kalmar’s work in the seventies. databases have already been available for foreign lan­ The intensity of research into this area substantially guages and they are called wordnets. The EuroWord- increased in 1998 when the institute, as a participant net 4 family of wordnets provides not only a mean to of the ESPRIT LTR20237 ”ILP2” project, began to establish interconnections between senses in different deal with the application of machine learning algo­ European languages (by making use of the ILI, the rithms to NLP (Natural Language Processing). International Language Index) but also for represent­ The Institute of Informatics initiated a Hungar­ ing different kinds of feature hierarchies. In 2005 the ian NLP consortium in 1999 consisting of Research Hungarian NLP consortium began to build a Hungar­ Institute for Linguistics at the Hungarian Academy of ian EuroWordnet database starting from the English Sciences and MorphoLogic Ltd. Budapest, and the wordnet by translating about 30 000 general terms Institute of Informatics at the University of Szeged. and adding 10 000 new ones [1]. This project was fi­ The institute is a founding member of the inter­ nanced by the Ministry of Economy in the framework national TEI (Text Encoding Initiative) Consortium of GVOP AKF 2004/0191 grant. (http://www.tei-c.org) as well. PROCESSING NATURAL LANGUAGE The Hungarian NLP consortium successfully ap­ TEXTS plied for R&D grants from the Hungarian Ministry of Education and Ministry of Economy. These grants Researchers at the institute are studying the ap­ provided financial support which enabled them doing plication of formal techniques at different stages of the research described below. NLP. Besides the preprocessing of texts, three partic­ ular tasks are mentioned below where the application THE SZEGED CORPUS AND ITS SUCCES­ of formal approaches seems to be promising, as re­ SOR - THE SZEGED TREEBANK ported in the publications. Development work of the manually annotated PART-OF-SPEECH TAGGING Hungarian corpus began in 2000. At that time there was no sufficiently large morpho-syntactically anno­ The task of a POS tagger is, for a given text, tated and disambiguated corpus for Hungarian. The to provide for each text word its contextually dis­ Hungarian NLP consortium won the support of the ambiguated part-of-speech tag. In the first experi­ Ministry of Education (grant OM IKTA 27/2000) ments in 1999, the annotated Hungarian TELRI cor­ with a project aiming the creation of a 1 million- pus from the MULTEXT-East5 project was used. In words-long disambiguated corpus. The project ended [2], authors presented a preliminary study designed in 2002. to illustrate the capabilities and limitations of cur­ Later, during the NKFP 2/017/2001 project 20% rent ILP and non-ILP algorithms on the Hungarian more text was added as well as every hierarchic NP POS-tagging task. The popular C4.5 and Progol sys­ (noun phrase) annotation. This database was a pre­ tems as propositional and ILP representatives were se­ liminary 1.0 version of the Szeged Treebank. The lected, adding experiments with methods AGLEARN, word treebank means a syntactically analyzed and an­ a C4.5 preprocessor based on attribute grammars, and notated corpus. The recent, Szeged Treebank 2.0 two ILP approaches PHM and RIBL. Each algorithm has been finalized by 2005 in the framework of the produced disambiguation rules and, by applying these OM IKTA 37/2002 project when all ADVPs (adver­ rules in a working tagger, a 96-97% per-word accuracy bial phrases), ADJPs (adjectival phrases), PPs (post­ noun phrases), CLs (clausal phrases), and VPs (verb 3http://www.tei-c.org 4http://www.illc.uva.nl/EuroWordNet/ phrases) were annotated. Using this corpus as a train­ 5 http://nl.ijs.si/M E/ ing and validation database the consortium are deve-

47 could be attained. The work was done in coopera­ dataset with 2000 short business news items as a basis tion with researchers from the Fraunhofer Institute in for further investigation. Studying the applicability of Bonn. ML in learning semantic frames is investigated in [16]. When the Szeged Corpus was ready for use re­ In the framework of the GVOP AKF 2004/0119 searchers studied several different learning algorithms grant of the Ministry of Economy the consortium part­ for making a real-world POS-tagger program for ners developed a prototype of an IE system, that pro­ Hungarian. After several attempts at using first­ cesses abstracts of biomedical publications can be re­ order (ILP) learning methods, a cascade of a TnT trieved from the PubMed 7 database. It collects infor­ (http://www.coli.uni-sb.de/ thorsten/tnt) and a mation on gene interactions from the sentences, i.e. Brill tagger http://www.cs.jhu.edu/ ( brill) cur­ after reading an abstract it predicts whether the re­ rently gives the best results trained on a larger part ferred publication deals with interactions of two or of the 1.2 million-word corpus [18], [19]. more genes, it tries to determine the type of the inter­ actions between the genes as well [ 6]. An experiment LEARNING SYNTAX RULES FOR HUN­ with different realizations of an IE system for En­ GARIAN glish language medical discharge records can be found Similar to many other languages, Hungarian also in [ 20]. relies heavily on the use and interrelation of ele­ The Institute of Informatics together with its con­ mentary word structures (syntagmas). NPs (Noun sortium partners is developing a tool-chain of NLP Phrases) are the most distinctive units of Hungarian modules necessary for building experimental IE sys­ sentences, hence shallow parsing primarily focuses on tems. An example prototype system is able to extract NP recognition. information from short business news related to cer­ Named entities, like person names, geographic tain types of events in business life, such as acquisi­ names, organizations’ names etc. play special role tions, balance reports, mid-term reports, contracts, or among noun phrases. Correct recognition of them, fusion. especially of those that have multiple words before Formal specification of semantic-frames can be for­ syntactic parsing may have strong influence on the mulated at a higher level of abstraction after the Hun­ accuracy of further parsing. Researchers developed a garian EuroWordnet database will be finished in 2007. method for Hungarian that made use of only lexical Semantic frame definitions then can refer not only to features of text words [12]. Later it has been success­ lexical words, but to concepts with synonyms, and fully applied in an international environment [ 22]. restrictions on senses can also be applied. The de­ Sometimes, there are cases when the task is not to velopment works are supported by the grant GVOP collect the recognized named entities, but to remove AKF 2004/0191. them from the text. In some medical research elec­ OTHER APPLICATIONS OF LANGUAGE tronic health records are processed by computers but TECHNOLOGY before that the texts have to be anonymized in order to protect privacy of the patients. In the named entity The researchers at the institute began to assem­ removal task the above mentioned method attained an ble a Hungarian named entity corpus. Its name is exceptionally good result for English [21]. NER (Named Entity Recognition) corpus and con­ For producing a recognizer for general NP struc­ tains named entities collected by members of the tures researchers used parse trees collected from the NLP consortium and other stakeholders during the Szeged Treebank as input. They produced NP syntax past years. A smaller sense annotated corpus is cur­ rule sets from frequent tree patterns occurred. Since rently being built in connection with the EuroWordnet the number of such tree patterns were high, they made project, the so-called wsd corpus. This can later be experiments on generalization of rules and in such a used as a test database for word sense disambiguation way unite the similar ones [15]. algorithms. When in 2005 the complete syntax annotation for RESEARCH CONNECTIONS IN EDUCA­ the Szeged Treebank was ready, they applied the pre­ TION viously developed methods to produce rules for the full syntax [13]. Later, attempts were made to investigate This research activities relate to the following on how to compress the initially large rule sets, and fields in Computer Science: Artificial Intelligence, on how this compression can be aided by statistical or Machine Learning, Knowledge Discovery, Computa­ machine learning algorithms [5], [14]. tional Linguistics, Information Extraction, Formal Languages, Theory of Compiling and Parsing. INFORMATION EXTRACTION Unsolved problems are being studied by several The aim of the IE (Information Extraction) is to PhD students and investigated in students’ scien­ provide a structured, queriable dataset from the con­ tific projects, in masters and bachelor theses. The tent of natural language texts. This does not require a homepage of Human Language Technology group program to fully understand the text. The approach is: http://www.inf.u-szeged.hu/hlt . The web to IE investigated at the institute is to set up tem­ site contains up-to-date information about R & D plates (frames) with slots to be filled with information projects, consortium partners, researchers, publica­ - so-called semantic frames -, then try to match sen­ tions, and downloadables provided by the group. tences to these templates. This approach is similar to THE MSZNY CONFERENCE SERIES the one that has been introduced by C. J. Fillmore in the FrameNet project 6. In 2003 the Institute of Informatics organized the Machine learning algorithms have been success­ First Hungarian Conference on Computational Lin­ fully used in learning semantic frames from training guistics, MSZNY 2003 in Szeged. About hundred par­ data. Researchers at the institute created a learning ticipants from all over Hungary came and presented

6 http://framenet.icsi.berkeley.edu/ 7http://www.pubmed.gov

48 an overview of their work. A special issue of the inter­ [8] Csendes, D., Csirik, J., Gyimothy, T.: The national journal Acta Cybernetica has been published Szeged Corpus, in Proc. of the 5th International in 2004 containing the best papers of the conference. Workshop on Linguistically Interpreted Corpora Since then this tradition was going on and in each (LINC 2004) at The 20th International Con­ year from 2003 the Institute of Informatics organized ference on Computational Linguistics (COLING the MSZNY 2004, MSZNY 2005 and MSZNY 2006 2004), Geneva, Switzerland 23-29 August, pp. conferences. An issue of Acta Cybernetica containing 19-23 (2004) the best papers of MSZNY 2004 has been published [9] Csendes, D., Csirik, J., Gyimothy, T.: The in the Spring of 2006. See the conference homepage Szeged Corpus: A POS Tagged and Syntactically at the http://www.inf.u-szeged.hu/mszny2006 . Annotated Hungarian Natural Language Corpus, ACKNOWLEDGEMENTS in Proc. of the Seventh International Confer­ ence on Text, Speech and Dialogue (TSD 2004), The above-mentioned research were partially sup­ Brno, Czech Republic 8-11 September, pp. 41-49 ported by the following grants: OM IKTA 27/2000, (2004) NKFP 2/017/2001, OM IKTA 37/2002, NKFP [10] Csendes, D., Csirik, J., Kocsor, A.: The Szeged 2/008/2004, NKFP 2/042/2004, GVOP-3.1.1-2004- Treebank Project, in Proc. of the Corpus Lin­ 05-119/3.0 AKF, GVOP-3.1.1-2004-05-191/3.0 AKF, guistics Conference, Birmingham, UK 14-17 and NKFP 6/074/2005. July, Conference series Vol. 1, No. 1, e-journal: www.corpus.bham.ac.uk/PCLC , ISSN 1747-9398 REFERENCES [11] Csendes D., Csirik J., Gyimothy T., Kocsor A.: [1] Alexin, Z., Csirik, J., Kocsor, A., Miháltz, M., The Szeged Treebank, in Proc. of the Eighth In­ Szarvas, Gy.: Construction of the Hungarian Eu- ternational Conference on Text, Speech and Dia­ roWordNet Ontology and its Application to In­ logue (TSD 2005), Karlovy Vary, Czech Republic formation Extraction, Project Report, in Proc. of 12-16 September, and LNAI series Vol. 3658, pp. the Third International Global WordNet Confer­ 123-131 (2005) ence (GWC-06), Jeju Island, Korea, 22-26 Jan­ [12] Farkas, R., Szarvas, Gy., Kocsor, A.: Named uary, pp. 291-292 (2006) Entity Recognition for Hungarian Using Various Machine Learning Algorithms, Acta Cybernet­ [2] Alexin Z., Csirik J., Gyimothy T.: Pro­ ica, Vol. 17, No. 3, pp. 633-646, Szeged, Hungary gramcsomag informaáciáokinyeráesi kutataások támogatasara, II. Magyar Számítógepes (2006) Nyelváeszeti Konferencia (MSZNY 2004) ki- [13] Hoocza, A.: Learning Tree Patterns for Syntactic advanya, Szeged, december 9-10., pp. 41-49 Parsing Acta Cybernetica, Vol. 17, No. 3, pp. (2004) 616-622, Szeged, Hungary (2006) [3] Alexin, Z., Csirik, J., Gyimáthy, T., Bibok K., [14] Hocza A., Felfoldi L., Kocsor A.: Learning Syn­ Hatvani, Cs., Prászeky, G., Tihanyi, L.: Man­ tactic Patterns Using Boosting and Other Classi­ ually Annotated Hungarian Corpus in Proceed­ fier Combination Schemas, in Proc. of the Eighth ings of the Research Note Sessions of the 10th International Conference on Text, Speech and Di­ Conference of the European Chapter of the Asso­ alogue (TSD 2005), Karlovy Vary, Czech Repub­ ciation for Computational Linguistics EACL’03, lic 12-16 September, and LNAI series Vol. 3658, Budapest, Hungary 15-17 April, pp. 53-56 (2003) pp. 69-76 (2005) [15] Hocza, A.: Noun Phrase Recognition with Tree [4] Alexin, Z., Leipold, P., Csirik, J., Bibok, K., Patterns, A cta Cybernetica, Vol. 16, No. 3, pp. Gyimáthy, T.: A rule-based tagger develop­ 611-623, Szeged, Hungary (2004) ment framework in Proc. of the Third Workshop on Learning Language in Logic LLL’2001 Eds: [16] Hocza, A., Alexin, Z., Csendes, D., Csirik, J., Lubos Popelásky, Strasbourg, France, pp. 1-10, Gyimothy, T.: Application of ILP methods in (2001) different natural language processing phases for information extraction from Hungarian texts, in [5] Barta, Cs., Csendes, D., Csirik, J., Hocza, A., Proceedings of the Kalmar Workshop on Logic Kocsor, A., Kovács, K.: Learning Syntactic Tree and Computer Science, Szeged, Hungary, 1-2 Oc­ Patterns from a Balanced Hungarian Natural tober, pp. 107-116, (2003) Language Database, The Szeged Treebank, in [17] Horvath, T., Alexin, Z., and Gyimothy, T, Wro- Proc. of IEEE International Conference on Nat­ bel, S.: Application of Different Learning Meth­ ural Language Processing and Knowledge Engi­ ods to Hungarian Part-of-Speech Tagging, in neering (IEEE NLP-KE 2005), Wuhan, China 30 Proc. of the 9th International Workshop on In­ October - 1 November, pp. 225-231 (2005) ductive Logic Programming, Eds: Saso Dzeroski [6] Csendes, D., Alexin, Z., Busa-Fekete, R., Kovacs, and Peter Flach, LNAI, 1634, pp. 128-139, K.: New, Linguistics-based, Ontology-enabled Springer Verlag, ISBN: 3-540-66109-3, (1999) Approaches in Biological Information Manage­ [18] Kuba, A., Bakota, T., Hocza, A., Oravecz, Cs.: ment, in the Proceedings of the e-Challenges Comparing different POS-tagging techniques for 2006 Conference, October 25-27, pp. 1352-1359, Hungarian, in Proceedings of the MSZNY 2003 Barcelona, Spain (2006). (Hungarian Computational Linguistics) Confer­ [7] Csendes D., Alexin Z., Csirik J., Kocsor A.: A ence, Szeged, Hungary, 10-11 December, pp. 16­ Szeged Korpusz s Treebank verziáinak t ’ortenete, 24, (2003) III. Magyar Számltogepes Nyelveszeti Konferen­ [19] Kuba, A., Hocza, A., Csirik, J.: POS Tagging of cia (MSZNY 2005) kiadványa, Szeged, december Hungarian with Combined Statistical and Rule- 8-9., pp. 409-412 (2005) based Methods in Proc. of the Seventh Interna­ tional Conference on Text, Speech and Dialogue

49 (TSD 2004), Brno, Czech Republic 8-11 Septem­ and executes two different threads. The active one ber, pp. 113-121 (2004) periodically initiates an information exchange w ith a [20] György Szarvas, Szilárd Iván, András Bánhalmi, peer node selected randomly, by sending a message János Csirik: Automatic Extraction of Seman­ containing the local state and waits for a response tic Content from Medical Discharge Records, 5th from the selected node. The passive thread waits for International Conference on System Science and messages sent by an initiator and replies with its local Simulation in Engineering, WSEAS Transactions state. on Systems and Control, Issue 2, Vol 1, Decem­ Method UPDATE builds a new local state based on ber 2006, ISSN: 1991-8763 pp. 312-317, (2006) the previous local state and the state received dur­ ing the information exchange. The output of UPDATE [21] György Szarvas, Richard Farkas, Szilard Iván, depends on the specific function implemented by the András Kocsor, and Robert Busa-Fekete: An it­ protocol. The local states at the two peers after an erative method for the de-identification of struc­ information exchange are not necessarily the same, tured medical text Workshop on Challenges in since UPDATE may be non-deterministic or may pro­ Natural Language Processing for Clinical Data duce different outputs depending on which node is the (2006) initiator. [22] Gyöorgy Szarvas, Richaárd Farkas, Andráas Koc- In the following we describe example instantia­ sor: A Multilingual Named Entity Recognition tions we have developed, indicated by the gray com­ System Using Boosting and C4.5 Decision Tree ponents in Figure 32, that illustrates the dependence Learning Algorithms, in Proceedings of the Ninth relations between these and various other existing or International Conference on Discovery Science, planned components. LNAI 4265, pp. 267-278, (2006) NEWSCAST

II. PEER-TO-PEER ALGORITHMS AND In NEWSCAST [ 8], the state of a node is given by SYSTEMS a partial view, which is a set of peer descriptors with a fixed size c. A peer descriptor contains the address INTRODUCTION of the peer, along with a timestamp corresponding to During the past decade the Internet has under­ the time when the descriptor was created. gone an impressive growth and has reached very high M ethod GETPEER returns an address selected levels of penetration into homes and businesses. This randomly among those in the current partial view. has lead to a radical shift in the possibilities it offers Method UPDATE merges the partial views of the two and new applications such as (illegal) file sharing and nodes involved in an exchange and keeps the c fresh­ collective computation have appeared. Many of these est descriptors, thereby creating a new partial view. applications, mostly due to legal pressure, have ob­ New information enters the system when a node sends tained a truely peer-to-peer (P2P) character, in that its partial view to a peer. In this step, the node al­ they are fully decentralized, extremely fault tolerant ways inserts its own, newly created descriptor into the and scalable. partial view. Old information is gradually and auto­ These systems and their success have contributed matically removed from the system and gets replaced to revitalizing the interest of the scientific community by newer information. This feature allows the proto­ in fully decentralized, scalable, robust distributed sys­ col to “repair” the overlay topology by forgetting dead tems, since they have many legitimate applications as links, which by definition do not get updated because well, such as content distribution networks, sensor net­ their owner is no longer active. works, network monitoring, distributed data mining, In NEWSCAST, the overlay topology is defined by and so on. the content of partial views. We have shown in [ 8] that In the past years, we have worked in this area the resulting topology has small diameter and is very developing several P2P algorithms for data aggrega­ close to a random graph with out-degree c. According tion [9,10,12,14,16], overlay network topology man­ to our experimental results, choosing c = 20 is already agement [6,7,13,15,17], peer sampling [8,19] and load sufficient for very stable and robust connectivity. We balancing [11]. have also shown that, within a single cycle, the num­ We have also worked on an integrated framework ber of exchanges per node can be modeled through a where these components can be combined together in random variable with the distribution 1 + Poisson(l). a natural way [3,4,11]. Finally, we have attempted The implication of this property is that no node is to distill some of the main design ideas we applied in more important (or overloaded) than others. the form of design patterns [ 1 , 2], that capture basic T-MAN approaches to achieve certain functionalities based on fully decentralized and local communication models. Another instantiation of the gossip skeleton we de- In the following we briefly discuss some examples to illustrate our approach to P2P protocol design. do fo re v er EXAMPLE ALGORITHMS do fo re v er wait(T time units) sp ^ receive(*) Our algorithms are based on the gossip-based p ^ GETP e e r Q send s to sender(sp) paradigm. Gossip-style protocols are attractive since send s to p s ^ UPDATE( s , sp) they are extremely robust to both computation and sp ^ receive(p) communication failures. They are also extremely re­ s ^ UPDATE( s , Sp) sponsive and can adapt rapidly to changes in the un­ (a) active thread (b) passive thread derlying communication structure without any addi­ tional measures. Figure 31. The skeleton of a gossip-based protocol. The skeleton of a generic gossip-based protocol is Notation: s is the local state, sp is the state of the shown in Figure 31. Each node possesses a local state peer p.

50 In addition to being fast, our aggregation protocol is also very robust. Node failures may perturb the final result, as the values stored in crashed nodes are lost; but both analytical and empirical studies have shown that this effect is generally marginal [16]. As long as the overlay network remains connected, link failures do not modify the final value, they only slow down the aggregation process. NOTES ON COMBINING THE BUILDING BLOCKS The combination of the building blocks is done in the traditional way: a building block has a local inter­ face (within one node) towards the other components, Figure 32. Dependence relations between compo­ and it has a protocol and an implementation asso­ nents. ciated with it. The implementation can differ over different nodes, just like the local interface. For this reason, we have focused on protocols in the above dis­ veloped is T-M an [7], a protocol for creating a large class of topologies. The idea behind the protocol is cussion. Nodes using the same protocol (for example, very similar to that of NEWSCAST. The difference is aggregation) form a “layer” in the system. This, how­ that instead of using the creation date (freshness) of ever, is not a layer in the usual sense: we allow for arbitrary dependency relations between the building descriptors, T-M an applies a ranking function that blocks. In general, the directed graph that describes ranks any set of nodes according to increasing dis­ the dependencies (such as the example shown in Fig­ tance from a base node. M ethod GETPEER returns neighbors with a bias towards closer ones, and, sim­ ure 32) will not contain cycles, however, this is not ilarly, UPDATE keeps peers that are closer, according strictly required. Two “layers” can mutually depend to the ranking. on each other’s services; for instance, in a bootstrap­ ping phase when they can catalyze each other’s per­ Figure 33 illustrates the protocol, as it constructs formance. a torus topology. In [7] it was experimentally shown Having said that, we need to mention one excep­ that the protocol converges in logarithmic time even tion. There is a “lowest layer” in our framework, for networks of 106 nodes and for other topologies in­ cluding rings and binary trees. With the appropriate which in a sense represents the group abstraction: the set of nodes that form the domain of the other com­ ranking function, T-M an can also be used to sort a ponents. This layer is the random network compo­ set of numbers. nent, which provides the peer sampling service (see T-M an relies on another component for generat­ Section II. and [ 8]). The main requirement for this ing an initial random topology which is later evolved into the desired one. In our case this service is pro­ service is that it must return all nodes with equal vided by NEWSCAST. probability, in particular, no nodes are to be excluded forever. The peer sampling service is used to support GOSSIP-BASED AGGREGATION and bootstrap other services like aggregation or struc­ In the case of gossip-based aggregation [10,12,16], tured topologies. the state of a node is a numeric value. In a practical Finally, the aspect of time-scale should also be setting, this value can be any attribute of the environ­ noted. While all of the protocols are based on the ment, such as the load or the storage capacity. The scheme given in Figure 31, the waiting time T can be task of the protocol is to calculate an aggregate value different for different building blocks. This degree of over the set of all numbers stored at nodes. Although freedom allows for certain architectures that otherwise several aggregate functions may be computed by our would not be possible. For example, if an up-to-date protocol, in this paper we provide only the details for aggregate value is needed “instantly” according to the the average function. timescale of a relatively slow layer, like load balancing, In order to work, this protocol needs an overlay then we can simply apply aggregation at a relatively protocol that provides an implementation of method faster timescale. GETPEER. Here, we assume th a t this service is pro­ OPEN SOURCE SOFTWARE vided by NEWSCAST, but any other overlay could be used. We did project administrating and developing To compute the average, method UPDATE (a, b) (with Alberto Montresor) for the PeerSim open source must return (a + b)/2. After one state exchange, the project that develops a simulator for large scale peer- sum of the values maintained by the two nodes does to-peer algorithms and networks [18]. The number not change, since they have just balanced their values. of times the simulator has been downloaded now ap­ So the operation does not change the global average proaches 5000. either; it only decreases the variance over all the esti­ CONFERENCE ORGANIZATION AND mates in the system. EDITING In [ 10] it was shown that if the communication topology is not only connected but also sufficiently We involved in organizing the invitation-only random, at each cycle the empirical variance com­ workshop “International Workshop on Self-* Prop­ puted over the set of values maintained by nodes is re­ erties in Complex Information Systems”, in Berti- duced by a factor whose expected value is '2yie. Most noro, Italy, in 2004, with Ozalp Babaoglu, Alberto importantly, this result is independent of the network Montresor, Christof Fetzer, Aad van Moorsel, Stefano size, confirming the extreme scalability of the proto­ Leonardi and Maarten van Steen. After the workshop col. we edited a post-proceedings [5].

51 after 2 cycles after 3 cycles after 4 cycles after 7 cycles

Figure 33. Illustrative example of constructing a torus over 50 x 50 = 2500 nodes, starting from a uniform random graph: 20 random entries in each view, with m = 20, ^ = 10 and K = 4.

We also took part in organizing the “The 15. Socially Inspired Computing Symposium at the Fourth International Workshop on Engineering Self­ AISB convention on Social Intelligence and Organizing Applications (ESOA’06)” togeather with Interaction in Animals, Robots And Agents Sven Brueckner, Salima Hassas and Dan Yamins. The (AISB SIC) 2005 workshop was a satellite workshop of the “2006 Inter­ national Conference on Autonomous Agents and Mul­ REFERENCES tiagent Systems” in Hakodate, Japan. With Ozalp Babaoglu and Robert Laddaga, we [1] Ozalp Babaoglu, Geoffrey Canright, Andreas edited a special issue of “IEEE Intelligent Systems”, Deutsch, Gianni Di Caro, Frederick Ducatelle, published as volume 21, number 2, in 2006. The Luca Gambardella, Niloy Ganguly, Márk Jela- theme of the issue was “Self-Management through sity, Roberto Montemanni, and Alberto Montre- Self-Organization in Information Systems”. sor. Design patterns from biology for distributed computing. In Proceedings of the European Con­ PROGRAM COMMITTEE MEMBER ference on Complex Systems (ECCS’05), Paris, France, November 2005. on CD-ROM. 1. IEEE Conference on Peer-to-Peer Computing [2] Ozalp Babaoglu, Geoffrey Canright, Andreas (P2P) 2006 and 2007 Deutsch, Gianni A. Di Caro, Frederick Ducatelle, 2. IEEE Congress on Evolutionary Computation Luca M. Gambardella, Niloy Ganguly, Mark Je- (CEC) 2007 special session on EC for decen­ lasity, Roberto Montemanni, Alberto Montresor, tralized systems and Tore Urnes. Design patterns from biology 3. International Conference on Parallel Processing for distributed computing. ACM Transactions (ICPP) 2007, P2P track on Autonomous and Adaptive Systems, 1(1):26- 66, September 2006. 4. International Conference on Computer Com­ munications and Networks (ICCCN) 2006 and [3] Ozalp Babaoglu, Márk Jelasity, Anne-Marie Ker- 2007, P2P track marrec, Alberto Montresor, and Maarten van Steen. Managing clouds: A case for a fresh 5. Workshop on Data Processing in Ubiquitous In­ look at large unreliable dynamic networks. ACM formation System (DPUbiq) 2007 SIGOPS Operating Systems Review, 40(3):9-13, 6. Workshop on Modeling, Simulation and 2006. Optimization of Peer-to-peer environments [4] Ozalp Babaoglu, Maárk Jelasity, and Alberto (M SOP2P) 2007 Montresor. Grassroots approach to self­ 7. Workshop on Multi-Agents for modeling Com­ management in large-scale distributed systems. plex Systems (MA4CS) 2006 In Jean-Pierre Banátre, Pascal Fradet, Jean­ Louis Giavitto, and Olivier Michel, editors, 8. International Conference on Bio inspired Mod­ Unconventional Programming Paradigms (UPP els of Network, Information and Computing 2004), volume 3566 of Lecture Notes in Computer Systems (BIONETICS) 2006 Science, pages 286-296. Springer-Verlag, 2005. 9. European Conference on Parallel Computing [5] Ozalp Babaoglu, Maárk Jelasity, Alberto Montre- (Euro-Par) 2005 and 2006, vice chair of topic: sor, Christof Fetzer, Stefano Leonardi, Aad van Peer-to-Peer and Web Computing Moorsel, and Maarten van Steen, editors. Self­ 10. IEEE International Workshop on Self-Managed Star Properties in Complex Information Systems , Networks, Systems and Services(SelfMan) 2006 volume 3460 of Lecture Notes in Computer Sci­ 11. International Conference on Distributed Com­ ence, Hot Topics. Springer-Verlag, May 2005. puting Systems (ICDCS) 2006, P2P track [6] Marco A. Boschetti, Márk Jelasity, and Vittorio 12. International Workshop on Security and Trust Maniezzo. A fully distributed Lagrangean meta­ in Decentralized/Distributed Data Structures heuristic for a P2P overlay network design prob­ (STD3S) 2006 lem. In Proceedings of the Sixth Metaheuristics International Conference (MIC2005), 2005. ex­ 13. IEEE Workshop on Stochasticity in Distributed tended abstract, on CD-ROM. Systems (StoDiS) 2005 [7] Mark Jelasity and Ozalp Babaoglu. T-Man: 14. Engineering Self-Organising Applications Gossip-based overlay topology management. In (ESOA) 2005

52 Sven A. Brueckner, Giovanna Di Marzo Seru- large-scale overlay networks. In Proceedings of gendo, David Hales, and Franco Zambonelli, edi­ The 2004 International Conference on Depend­ tors, Engineering Self-Organising Systems: Third able Systems and Networks (DSN), pages 19-28, International Workshop (ESOA 2005), Revised Florence, Italy, 2004. IEEE Computer Society. Selected Papers, volume 3910 of Lecture Notes in [17] Alberto Montresor, Máark Jelasity, and Ozalp Computer Science, pages 1-15. Springer-Verlag, Babaoglu. Chord on demand. In Proceedings 2006. of the Fifth IEEE International Conference on [8] Márk Jelasity, Rachid Guerraoui, Anne-Marie Peer-to-Peer Computing (P2P 2005) , pages 87­ Kermarrec, and Maarten van Steen. The peer 94, Konstanz, Germany, August 2005. IEEE sampling service: Experimental evaluation of Computer Society. unstructured gossip-based implementations. In [18] PeerSim. http://peersim.sourceforge.net/. Hans-Arno Jacobsen, editor, Middleware 2004, [19] Spyros Voulgaris, Maárk Jelasity, and Maarten volume 3231 of Lecture Notes in Computer Sci­ van Steen. A robust and scalable peer-to-peer ence, pages 79-98. Springer-Verlag, 2004. gossiping protocol. In Gianluca Moro, Claudio [9] Márk Jelasity, Wojtek Kowalczyk, and Maarten Sartori, and Munindar P. Singh, editors, Agents van Steen. An approach to massively distributed and Peer-to-Peer Computing: Second Interna­ aggregate computing on peer-to-peer networks. tional Workshop, AP2PC 2003, volume 2872 of In Proceedings of the 12th Euromicro Confer­ Lecture Notes in Artificial Intelligence, pages 47­ ence on Parallel, Distributed and Network-Based 58. Springer, 2004. Processing (PDP’04), pages 200-207, A Coruna, Spain, 2004. IEEE Computer Society. III. SPEECH TECHNOLOGY [10] Mark Jelasity and Alberto Montresor. Epidemic- style proactive aggregation in large overlay net­ During the period 2003-2006 our speech technology works. In Proceedings of The 24th International team achieved many new results both in inventing Conference on Distributed Computing Systems novel speech recognition related algorithms and in (ICDCS 2004), pages 102-109, Tokyo, Japan, constructing working speech recognition systems for 2004. IEEE Com puter Society. Hungarian. Two of our colleagues obtained their Ph.D. degree from the results of this research [10,48]. [11] Mark Jelasity, Alberto Montresor, and Ozalp The most recent and probably most important devel­ Babaoglu. A modular paradigm for building opment was a 3-year IKTA -6 project for the design self-organizing peer-to-peer applications. In Gio- and implementation of a medical dictation system. vanna Di Marzo Serugendo, Anthony Karageor- gos, Omer F. Rana, and Franco Zambonelli, ed­ SPEECH IMPEDIMENT THERAPY itors, Engineering Self-Organising Systems, vol­ In 2004 the IKTA-4 project for the development of ume 2977 of Lecture Notes in Artificial Intelli­ the ”SpeechMaster” speech impediment therapy sys­ gence, pages 265-282. Springer, 2004. invited pa­ tem ended, and the software was made available to per. many elementary schools and speech therapy insti­ [12] Márk Jelasity, Alberto Montresor, and Ozalp tutes for testing. Since then we have received a lot Babaoglu. Gossip-based aggregation in large dy­ of feedback, and teachers seem to be very satisfied namic networks. ACM Transactions on Com­ with the results achieved thanks to the application of puter Systems, 23(3):219-252, August 2005. the software in both reading teaching and speech im­ [13] Mark Jelasity, Alberto Montresor, and Ozalp pediment therapy. We published numerous papers on Babaoglu. The bootstrapping service. In Proceed- the pedagogical, linguistic and technological aspects ins of the 26th International Conference on Dis­ of ”SpeechMaster” [6,8,14,16,17,20,21,23,24,26-28, tributed Computing Systems Workshops (ICDCS 30,31,40,41,43,46]. WORKSHOPS), Lisboa, Portugal, 2006. IEEE SPEECH RECOGNITION RESEARCH Computer Society. International Workshop on Dynamic Distributed Systems (IWDDS). We have continued the development of our mod­ ular speech recognition system ”OASIS”. Most im­ [14] Wojtek Kowalczyk, Márk Jelasity, and A. E. portantly, it was extended with a statistical language Eiben. Towards data mining in large and fully model, so we are now able to conduct experiments on distributed peer-to-peer overlay networks. In realistic continuous speech recognition tasks. Besides Tom Heskes, Peter Lucas, Louis Vuurpijl, and its original segment-based acoustic model, the system Wim Wiegerinck, editors, Proceedings of The was adapted to be able to work following the conven­ 15th Belgian-Dutch Conference on Artificial In­ tional frame-based scheme as well. Huge efforts were telligence (BNAIC’03), pages 203-210. Univer­ made to investigate and understand the similarities sity of Nijmegen, 2003. and differences between the segment-based and the [15] Vittorio Maniezzo, Marco A. Boschetti, and frame-based acoustic modelling technique [29]. Quite Máark Jelasity. An ant approach to mem­ recently we experimented with the hybrid HMM/ANN bership overlay design. In Marco Dorigo, technology in acoustic modelling, and compared its Mauro Birattari, Christian Blum, Luca M. behavior with our conventional ANN-based segmen­ Gambardella, Francesco Mondada, and Thomas tal modelling scheme [32, 34, 49]. We investigated Stützle, editors, Ant Colony Optimization and several search space pruning techniques in order to Swarm Intelligence, 4th International Workshop obtain a faster and more efficient decoding perfor­ (ANTS 2004), volume 3172 of Lecture Notes in mance [2, 5, 19, 22, 25, 36, 47]. O ur colleagues ex­ Computer Science, pages 37-48. Springer-Verlag, perimented with novel types of machine learning al­ 2004. gorithms [12, 35] and knowledge source combination [16] Alberto Montresor, Márk Jelasity, and Ozalp techniques [1,3,9,15,26] to achieve the highest possi­ Babaoglu. Robust aggregation protocols for ble phone recognition performance. On the acoustic

53 side the so-called modulation or 2D-cepstum features Artificial Neural Networks (ANNs) instead of the con­ were introduced to our system, and were shown to ventional Gaussian mixtures (GMM). As ANNs seem yield a noticeable improvement [42]. to be more capable of modelling the observation con­ text than GMMs, hybrid models are usually trained DATABASE CONSTRUCTION over longer time windows. Knowing that the modu­ In 2004 the Department of Informatics at the Uni­ lation components play an important role in human versity of Szeged and the Laboratory of Speech Acous­ speech perception, a frequency analysis over the fea­ tics of the Budapest University of Technology and ture trajectories seems to be a reasonable representa­ Economics began a project with the aim of collect­ tion technique. We apply this analysis to the cepstral ing and/or creating the basic resources needed for the coefficients, that produces the so-called 2D-cepstrum. construction of a continuous dictation system for Hun­ In order to construct the domain-specific language garian. The project lasted for three years (2004-2006), models we got 9231 medical reports from the Depart­ and was financially supported by the national fund ment of Nuclear Medicine of the University of Szeged. IKTA-056/2003. To support the training of dictation These thyroid scintigraphy reports were written us­ systems, the project included the creation of a large ing various software packages during 1998 to 2004, so speech corpus of phonetically rich sentences that al­ first of all we had to convert them to a common for­ lows the training of general-purpose dictation systems. mat, followed by several steps of routine error correc­ Hence in the first phase of the project we designed, tion. After this the corpus contained approximately assembled and annotated a speech database called 2500 different word forms, so we were confronted with the MRBA (’’Hungarian Reference Speech Database”) a medium-sized vocabulary dictation task. Thanks corpus [18]. The contents of the database were de­ to this limited vocabulary we could avoid the use of signed by the Laboratory of Speech Acoustics, based a morphological model. Although 2500 words could on the phone and diphone statistics of a phonetically be easily managed even by a simple list (‘linear lexi­ transcribed large text corpus. From this corpus 1992 con’), we organized the words into a lexical tree where sentences and 1992 words were selected, and then they the common prefixes of the lexical entries are shared. were recorded from 332 speakers, each reading 12 sen­ Apart from storage reduction advantages, the prefix tences and 12 words. Both teams participated in the tree representation also speeds up decoding, as it elim­ collection of the recordings, which was carried out in inates redundant acoustic evaluations. four big cities. The sound files were cleaned up and an­ The limited size of the vocabulary and the highly notated at the Laboratory of Speech Acoustics, while restricted (i.e. low-perplexity) nature of the sentences the Research Group on Artificial Intelligence manu­ used in the reports allowed us to create very efficient ally segmented and labelled one third of the files at n-grams. The system applies 3-grams by default, but the phone level. This part of the corpus is intended it is able to ‘back off’ to smaller n-grams (in the worst to support the initialization of phone models. case to a small e constant) when necessary. During the evaluation of the n-grams the system applies a CONSTRUCTION OF A MEDICAL DICTA­ language model lookahead technique.For this reason TION SYSTEM the lexical trees are stored in a factored form, which Besides the collection of a speech corpus, the allows a more efficient pruning of the search space. IKTA project also contained the creation of a proto­ Besides word n-grams we also tried construct­ type dictation system. To make the task more man­ ing class n-grams. For this purpose the words were ageable, especially the language modelling part, we re­ grouped into classes according to their parts-of-speech stricted the target domain of the dictation to a specific category. The words were categorized based on their type of medical report. Although this task is clearly MSD code, and we constructed the class n-grams over easier than general dictation, we chose this applica­ these codes. In previous experiments we found that tion area with the intent of assessing the capabilities the application of the language model lookahead tech­ of our technologies. Depending on the findings, we nique and class n-grams brought about a 30% decrease later hope to extend the system to more general dic­ in the word error rate when it was applied in combi­ tation domains. As our team focused on the task of nation with our HMM-based fast decoder [39]. the dictation of thyroid scintigraphy medical reports, For testing purposes we recorded 20-20 medical we summarize these results in the following [37-39,42]. reports from 2 male and 2 female speakers. The At the level of acoustic modelling we have been language model applied in the tests was constructed experimenting with two quite different technologies. based on just 500 reports instead of all the 8546 we One of these is a quite conventional Hidden Markov had collected. This subset contained almost all possi­ Model (HMM) decoder that works with the usual mel- ble sentence types, so this restriction just reduced the frequency cepstral coefficient (MFCC) features.The dictionary by removing rarely occurring words (e.g. phone models applied have the usual 3-state left-to- dates and disease names). Besides the HMM decoder right topology and are monophone models, that is no we tested the HMM/ANN hybrid system with the con­ context-dependent models were tested in the system. ventional features and the 2D-cepstrum features as The decoder built on these HMM phone models per­ well. The results are listed in Table 3 below. As can forms a combination of Viterbi and multi-stack decod­ be seen, each configuration performed well above 90%, ing. For speed efficiency it contains several built-in but for some reason the HMM system did not like the pruning criteria. With the proper choice of param­ set of female voices. In the next part we plan to ex­ eters the decoder on a typical PC runs faster than tend the language model to cover all the available data real-time on the medical dictation task. and to test the system over other dictation domains Our alternative, experimental acoustic model em­ as well. We also intend to implement speaker adapta­ ploys the HMM/ANN hybrid technology. The ba­ tion and context-dependent models within the HMM sic difference between this and the standard HMM system and to continue our research on observation scheme is that here the probabilities are modelled by context modelling in the HMM/ANN system.

54 Model Type Feature Set Male 1 Male 2 Female 1 Female 2 HMM MFCC + A + AA 97.75% 98.22% 93.40% 93.39% HMM/ANN MFCC + A + AA 97.65% 97.37% 96.78% 96.91% HMM/ANN 2D-cepstrum 97.88% 97.83% 96.86% 96.42% Table 3. Word recognition accuracies of the various models and feature sets.

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[33] Banhalmi, A., Kovócs, K., Kocsor, A., Tóth, Machine learning and computational learning the­ L.: Fundam ental Frequency Estim ation by Least- ory deal with the automatic acquisition of knowledge Squares Harmonic Model Fitting, Proc. Eu­ from data, for example, in the form of classification rospeech 2005, pp. 305-308. or regression rules. The field developed rapidly in the past decade, in terms of the construction of new, [34] Toth, L., Kocsor, A.: Explicit Duration Mod­ efficient learning algorithms, the theoretical under­ elling in HMM/ANN Hybrids, Proc. TSD 2005, standing of the possibilities and limitations of efficient LNAI 3658, pp. 310-317, Springer Verlag, 2005. learning methods, and also in terms of the scope of ap­ [35] Kocsor, A.: On Kernel Discriminant Analyses plication areas. applied to Phoneme Classification, Proc. ISNN Results achieved at the Research Group on Arti­ 2005, LNCS 3497, pp. 357-362, 2005. ficial Intelligence (RGAI) in the area of learning dur­ [36] Gosztolya, G., Kocsor, A.: Speeding Up Dy­ ing 2003-2007 involved work in all these directions: namic Search Methods in Speech Recognition, the development of SpeechMaster, a successful soft­ Proc. IEA/AIE 2005, LNCS 3533, pp. 98-100, ware product which uses machine learning technol­ Springer Verlag, 2005. ogy, research on the development of machine learning algorithms such as kernel and support vector meth­ [37] Sejtes, Gy., Kocsor, A., Zsigri, Gy., Paczolay, D., ods, and theoretical results in various formal models (in Hungarian) Medical ’’scrivener”. Latin Words of computational learning theory, such as theory revi­ and Collocations in a Dictation System, Proc. sion in query and mistake-bounded models. MANYE 2005, p. 119. [38] Kocsor, A., Bónhalmi, A., Paczolay, D., Csirik, SPEECHMASTER, APLLICATIONS OF J., Pavics, L.: The OASIS Speech Recogni­ MACHINE LEARNING IN SPEECH tion System for Dictating Medical Reports, Proc. RECOGNITION EANM ’05, 2005. The software package SpeechMaster was devel­ [39] Kocsor, A., Banhalmi, A., Paczolay, D., (in Hun­ oped for speech impediment therapy and the teaching garian) Technical Background of a System for of reading. It is freely available at Dictating Thyroid Gland Medical Reports, Acta Agraria Kaposvariensis, 10(1):113-128, 2006. www.inf.u-szeged.hu/beszedmester [40] Andraós Kocsor, Dóenes Paczolay: Speech Tech­ The system uses machine learning methods as part nologies in a Computer-Aided Speech Therapy of speech recognition technology. The objective in System. Proc. ICCHP 2006: 615-622 the two tasks is to provide visual phonetic feedback [41] Csendes, D., Kocsor, A., Paczolay, D., Banhalmi, and to reinforce the correct association between the A.: Advanced Technology and Interface for In­ phoneme/grapheme pairs. A brief overview of the var­ teractive Speech Impediment Therapy in Proc. ious functionalities of the system is given in [ 6]. of e-Challenges 2006, pp. 1531-1538, 2006. Research completed in the course of the develop­ [42] Bónhalmi, A., Paczolay, D., Tóth, L., Kocsor, A.: ment of the system includes a comprehensive evalu­ First Results of a Hungarian Medical Dictation ation of several recent machine learning algorithms, Project, Proc. of IS-LTC 2006, pp. 23-26. such as kernelized versions of principal component analysis (KPCA), independent component analysis [43] Kocsor, A., Bócsi, J., Mihalovics, J.: (in Hun­ (KICA), linear discriminant analysis (KLDA) and garian) Speechmaster: computer-aided reading springy discriminant analysis (KSDA) in the context teaching and speech impediment therapy, Uj of speech recognition tasks [7], several of which has pedagóogiai szemle, 2006/3, pp. 108-113. been developed earlier at the research group. A com­ [44] Bónhalmi, A., Kocsor, A., Kovacs, K., Tóth, L.: parison of several learning methods for the particu­ Fundamental Frequency Estimation by Combina­ lar task of phoneme classification is given in [ 8]. Be­ tions of Various Methods, Proc. NORSIG 2006. sides kernel methods, another important recent de­ velopment in machine learning is the construction of [45] Banhalmi, A., Paczolay, D., Kocsor, A.: An On­ efficient techniques for combining classifiers, such as line Speaker Adaptation Method for HMM-based boosting. The paper [1] gives a detailed computa­ ASRs , Proc. CSCS 2006, pp 21-22 tional study of the different combination methods for [46] Paczolay, D., Bónhalmi, A., Kocsor, A.: Ro­ speech recognition tasks, and [4] compares the combi­ bust Recognition of Vowels In Speech Impedi­ nation methods for natural language processing tasks. ment Therapy Systems, Proc. CSCS 2006, pp 82­ [17] discusses a sampling scheme handling the impor­ 83. tant practical problem of imbalances in training data. [47] Kocsor, A., Gosztolya, G.: Application of Full The paper [18] gives a general algorithmic framework Reinforcement Aggregation Operators in Speech to provide experimental evidence and explanation for Recognition, Proc. RASC 2006, pp. 109-116. the success of Hidden Markov Model techniques in

56 speech recognition, in spite of the simplistic indepen­ [2] J. Goldsmith, R. H. Sloan, B. Szörényi, Gy. dence assumptions inherent in the model. Turan: Theory revision with queries: Horn, read- once and parity formulas, Artificial Intelligence MACHINE LEARNING ALGORITHMS Journal 156 (2004), 139-176. Convex Networks (CN), a new learning method [3] M. Grohe, Gy. Turán: Learnability and defin­ combining certain attractive features of neural net­ ability in trees and similar structures, Theory of works and support vector machines (SVM), is intro­ Computing Systems 37 (2004), 193-220. duced in [10] and developed further in [11]. Clas­ sification techniques leading to simpler optimization [4] A. Hácza, L. Felföldi, A. Kocsor: Learning syn­ problems than SVM techniques have been developed tactic patterns using boosting and other classifier in [9]. These techniques are computationally more combination schemes, Proceedings of the 8. Int. efficient than SVM, but produce classifiers competi­ Conf. on Text, Speech and Dialogue (TSD 2005), tive with SVM and other methods, when compared Springer LNAI 3658 (2005), 69-76. on standard benchmark data sets. Margin Maximiz­ [5] A. Kocsor, K. Kovaács, Cs. Szepesvaári: Margin ing Discriminant Analysis (MMDA), a new feature ex­ maximizing discriminant analysis, Proceedings of traction method, is developed in [5]. It has linear and the 15. European Conference on Machine Learn­ non-linear (kernelized) versions, has attractive com­ ing (ECML 2004), 227-238. Springer LNAI 3201, putational features and it is competitive with other 2004. related methods. The method is applied for the devel­ [6] A. Kocsor, D. Paczolay: Machine learning and its opment of feature extraction algorithms for regression novel application in speech impediment therapy, problems in [16]. The MMD approach is integrated Lexikográfia (2005). (In Hungarian.) with the CVM (Core Vector Machine) method in [19]. CVM is a recent approach to classification and regres­ [7] A. Kocsor, L. Táoth: Kernel-based feature extrac­ sion, which is significantly faster than SVM (Support tion with a speech technology application, IEEE Vector Machines) and competitive with it in learning Transactions on Signal Processing 52 (2004), quality. 2250-2263. [8] A. Kocsor, L. Táoth: Application of kernel-based COMPUTATIONAL LEARNING THEORY feature space transformations and learning meth­ Theory revision provides efficient concept learning ods to phoneme classification, Applied Intelli­ algorithms given an initial theory which is an approx­ gence 21 (2004), 129-142. imation of the target. Several theory revision algo­ [9] K. Kovacs, A. Kocsor: Various hyperplane classi­ rithms are presented in query models [2,14] and mis­ fiers using kernel feature spaces, Acta Cybernetica take bounded models [13,15]. [12] considers the effect 16 (2003), 271-278. on the size of a DNF formula, of incorporating excep­ tions into the formula. This problem is motivated by [10] K. Kovaács, A. Kocsor: Classification using a applications in computational learning theory. The sparse combination of basis functions, Acta Cy- paper [3] studies learnability consequences of restric­ bernetica, 17 (2005). tions on the tree width and clique width of first-order [11] K. Kovács, A. Kocsor: Improving a basis func­ logic structures, by studying combinatorial parame­ tion based classification method using feature se­ ters such as the Vapnik-Chervonenkis dimension and lection algorithms, IEEE Int. Workshop on Soft the strong consistency dimension. Computing Applications (SOFA 2005). CONFERENCES ORGANIZED [12] D. Mubayi, Gy. Turan, Y. Zhao: The DNF ex­ ception problem, Theoretical Computer Science 13th International Conference on Inductive Logic 352 (2006), 85-96. Programming (ILP 2003), September 29 - October 1, 2003, Szeged. [13] R. H. Sloan, B. Szörényi: Revising projective DNF in the presence of noise, Acta Cybernetica , Kalmár Workshop on Logic and Computer Sci­ accepted for publication. ence, October 1 - 2, 2003, Szeged. [14] R. H. Sloan, B. Szörényi, Gy. Turan: Revising ACKNOWLEDGEMENTS threshold functions, Theoretical Computer Sci­ ence, to appear. The mentioned research tasks were supported by the following grants. [15] R. H. Sloan, B. Szörényi, Gy. Turán: Projective 2005-2007: NKFP 2/008/2004, Hungarian- DNF formulas and their revision, Discrete Ap­ English Machine Translator System. plied Mathematics, to appear. 2004-2006: IKTA-056/2003, The Establishment of [16] Cs. Szepesvari, A. Kocsor, K. Kovacs: Kernel a Speech Corpus for General Purposes and the Devel­ machine based feature extraction algorithms for opment of a Speech Recognition System for Medical regression problems, 16. European Conference on Reports. Artificial Intelligence (ECAI 2004), 1091-1092. 2002-2004: IKTA-055/2001, Machine Learning [17] L. Táoth, A. Kocsor: Training HM M /ANN hybrid and Its Application to Speech Impediment Therapy. speech recognizers by probabilistic sampling, In ­ REFERENCES ternational Conference on Artificial Neural Net­ works (ICANN 2005), 597-603. Springer LNCS [1] L. Felföldi, A. Kocsor, L. Toth: Classifier combi­ 3696. nation in speech recognition, Periodica Polytech- [18] L. Toáth, A. Kocsor, J. Csirik: On Naive Bayes nica, Electrical Engineering 47 (2003), 125-140. in speech recognition, Applied Mathematics and Computer Science 15 (2005), 101-108.

57 [19] I. W. Tsang, A. Kocsor, J. T. Kwok: Diversified SVM ensembles for large data sets, Proceedings of the 17. European Conference on Machine Learn­ ing (ECML 2006), pp.792-800, Berlin, Germany, September 2006.

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