DOCSLIB.ORG

Mathematica and Matlab Scripts

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mathematica and Matlab Scripts Appendix A Mathematica and Matlab Scripts This Appendix contains Mathematica and Matlab scripts referenced in the chapters. Wolfram Mathematica® 10 is used to write the MScripts (Math scripts) and Matlab® 7.10.0 (R2010a) is also used to write the Matlab scripts. A.1 Scripts from Chap. 1 Mscript 16 Convex 2D region centroid. (* 2D Region centroid *) R = ConvexHullMesh[RandomReal[1, {8, 2}]]; c = RegionCentroid[R] Show[HighlightMesh[R, Style[{2, Black}, Opacity[0.2]]], Graphics[{Red, PointSize[0.02], Point[RegionCentroid[R]]}]] © Springer International Publishing Switzerland 2016 355 J.F. Peters, Computational Proximity, Intelligent Systems Reference Library 102, DOI 10.1007/978-3-319-30262-1 356 Appendix A: Mathematica and Matlab Scripts A.1.1: Corner A.1.2: Intensity A.1.3: Keypoint Fig. A.1 Three Dirichlet tessellations Mscript 17 StanfordBunny centroid. (* 3D Region centroids *) gr = ExampleData[{“Geometry3D”, “StanfordBunny”}]; gm = DiscretizeGraphics[gr]; c2 = RegionCentroid[gm] Show[Graphics3D[Prepend[First[gr], Opacity[0.5]]], Graphics3D[{Red, PointSize[0.03], Point@c2}]] Mscript 18 UNISA coin centroid. (* Digital Image Region Centroid *) img =; c = ComponentMeasurements[img, “Centroid”][[All, 2]][[1]]; Show[img, Graphics[{Black, PointSize[0.02], Point[c]}]] See, e.g., (Fig. A.1) for three types tessellations obtained using Mscript 19. Mscript 19 Tessellations from Three Different Types of Seed Points. (*Corner, intensity, keypoint − based Dirichlet Tessellations*) img =; ImageDimensions[img]; corncoords = ImageCorners[img, MaxFeatures → 50]; HighlightImage[img, corncoords] ListPlot[corncoords, PlotStyle →{Red, PointSize[.01]}, PlotLegends →{“corner”}, AxesLabel →{wpixels, ht(pixels)}, LabelStyle → Directive[Blue, Bold]] (* Give the Voronoï mesh and display on the image *) Appendix A: Mathematica and Matlab Scripts 357 vm = VoronoiMesh[corncoords]; t12 = Graphics[{Red, {PointSize[0.02], Point[corncoords]}, Blue, MeshPrimitives[vm, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] Show[img, t12] (*p = ImageValue[img, {300, 200}]*) pts = ImageValuePositions[img, White, 0.45]; vm2 = VoronoiMesh[pts]; t13 = Graphics[{Red, {PointSize[0.02], Point[pts]}, Blue, MeshPrimitives[vm2, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] Show[img, t13] corncoords2 = ImageKeypoints[img, MaxFeatures → 60]; vm3 = VoronoiMesh[corncoords2]; t15 = Graphics[{Red, {PointSize[Large], Point[corncoords2]}, Blue, MeshPrimitives[vm3, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] Show[img, t15] Mscript 20 Conventional near sets. (*Conventional near sets : Cech, Efremovich, Lodato, ...*) Plot[1/x, {x, −10, 10}, AxesLabel →{x, 1/x}, PlotRange → {{−10, 10}, {−1, 1}}, LabelStyle → Directive[Blue, Bold]] 358 Appendix A: Mathematica and Matlab Scripts Mscript 21 Strongly near sets. (*Strongly near sets : intersection of A, B > 1*) Plot[Sin[8/x], {x, 0.1, 10}, AxesLabel →{x, Sin[8/x]}, PlotRange →{{0, 2}, {−1.1, 1.1}}, LabelStyle → Directive[Blue, Bold]] Mscript 22 Mesh on a Hooke Needle Point Image. (* Mesh Containing Multiple Nearves *) img = ; corncoords = ImageCorners[img, MaxFeatures → 60]; HighlightImage[img, corncoords] (* Give the Voronoï mesh and display on the image *) vm = VoronoiMesh[corncoords]; t11 = Graphics[{Blue, {PointSize[Large], Point[corncoords]}, Black, MeshPrimitives[vm, 1]}] t12 = Graphics[{Red, {PointSize[Large], Point[corncoords]}, Green, MeshPrimitives[vm, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] Show[img, t12] Mscript 23 Image Raster Mesh. (* Nearness of image pixel keypoint mesh parts *) img = ; Rasterize[img, RasterSize → 32](*32pixelwiderasterization.*) x1 = ImageKeypoints[img]; HighlightImage[img, x1, “HighlightColor” → White]; P1 = ImageKeypoints[img, {“Position”, “Scale”, “Orientation”, “ContrastSign”}, MaxFeatures → 100]; Show[img, Graphics[ Table[{{If[p[[4]] == 1, Red, Green], Circle[p[[1]], p[[2]] ∗ 3.5], Line[{p[[1]], p[[1]] + p[[2]] ∗ 1.5 ∗{Cos[p[[3]]], Sin[p[[3]]]}}]}}, {p, P1}]]] Mscript 24 Image Keypoint Mesh Nerves. (* Mesh Containing Multiple Keypoint Nearves *) img = ; Appendix A: Mathematica and Matlab Scripts 359 corncoords = ImageKeypoints[img, MaxFeatures → 60]; HighlightImage[img, corncoords] (* Give the Voronoï mesh and display on the image *) vm = VoronoiMesh[corncoords]; t11 = Graphics[{Blue, {PointSize[Large], Point[corncoords]}, Black, MeshPrimitives[vm, 1]}] t12 = Graphics[{Red, {PointSize[Large], Point[corncoords]}, Green, MeshPrimitives[vm, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] Show[img, t12] Mscript 25 Mesh on an Annulus. (*Set up a boundedness that is amesh circular region. Each inner circular region is aproximal nerve.*) annulus[x_, y_]:=(9/10)∧2 ≤ x∧2 + y∧2 ≤ 1∧2 holes[{x0_, y0_}, r_]:=((x + x0)∧2 + (y + y0)∧2 ≤ (r)∧2) crds = {{−1/2, 0}, {1/2, 0}, {0, −1/2}, {0, 1/2}, {2/5, 2/5}, {−2/5, −2/5}, {2/5, −2/5}, {−2/5, 2/5}}; sd = Or@@(holes[#, 1/64]&/@crds); Ω2 = ImplicitRegion[Or[annulus[x, y], sd], {x, y}]; ToElementMesh[Ω2, “BoundaryMeshGenerator” →{“Continuation”}, “RegionHoles” → crds][ “Wireframe”[“MeshElementStyle” →{Directive[FaceForm[Green], EdgeForm[{Red}]]}]] Mscript 26 Four-Dimensional Array of Cubes. (*Four − dimensional array of cubes.*) Graphics3D[Raster3D[RandomReal[1, {8, 5, 5, 3}], ColorFunction → (RGBColor[#[[1]], #[[2]], #[[3]], 0.299#[[1]] + 0.587#[[2]] + 0.114#[[3]]]&)]] 360 Appendix A: Mathematica and Matlab Scripts A.2 Scripts from Chap. 2 Mscript 27 Delaunay and Voronoï Mesh on Hand Image CornerDelaunay.nb. (*Corner − based Delaunay triangulation*) img = ; ImageDimensions[img] corncoords = ImageCorners[img, MaxFeatures → 50] HighlightImage[img, corncoords] ListPlot[corncoords, PlotStyle →{Black, PointSize[.01]}, PlotLegends →{“corner”}, AxesLabel →{wpixels, ht(pixels)}, LabelStyle → Directive[Blue, Bold]] (* Give the Delaunay mesh and display on the image *) vm = DelaunayMesh[corncoords]; dm = VoronoiMesh[corncoords]; t11 = Graphics[{Blue, {PointSize[0.02], Point[corncoords]}, Black, MeshPrimitives[vm, 1]}] t12 = Graphics[{Red, {PointSize[0.02], Point[corncoords]}, Blue, MeshPrimitives[vm, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] t13 = Graphics[{Red, {PointSize[0.02], Point[corncoords]}, Yellow, MeshPrimitives[dm, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] t14 = Graphics[{Red, {PointSize[0.02], Point[corncoords]}, Blue, MeshPrimitives[dm, 1], {Opacity[0.1], EdgeForm[{Thick, Yellow}], FaceForm[Yellow]}}] Show[img, t12] Show[img, t13] Show[img, t12, t13] Appendix A: Mathematica and Matlab Scripts 361 % centroid−based image Delaunay and Voronoi mesh clc, clear all, close all im = imread(’redcarFrame.jpg’ ); % if size(im,3)==3 % g=rgb2gray(im) ; %end [m,n]=size(im); bw = im2bw(im,0.5); % threshold at 50% bw = bwareaopen(bw,2); % remove objects less 2 than pixels stats = regionprops(bw,’Centroid’ ); % centroid coordinates centroids = cat(1,stats.Centroid); fc=[1 1;n 1; 1 m; nm]; % identify image corners centroids=[centroids;fc]; imshow(im),hold on plot(centroids(:,1) ,centroids(:,2) ,’y+’ ) hold on; X=centroids(:,1); Y=centroids(:,2); %find delaunay triangulation TRI = delaunay(X,Y); triplot(TRI,X,Y,’y’ ); %find Voronoi tessellation [vx,vy]=voronoi(X,Y); plot(vx,vy,’g-’); Listing A.1 Matlab script in findCentroidalMesh.m to construct a centroidal-based mesh. Mscript 28 Centroid-based Voronoï mesh: ch2centroidalMesh.nb. (*Mesh experiment with centroids.*) pts = RandomReal[1, {100, 2}]; R = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; 362 Appendix A: Mathematica and Matlab Scripts vcf[pts_]:= RegionCentroid/@MeshPrimitives[VoronoiMesh[pts, {{0, 1}, {0, 1}}], “Faces”]; centroids = NestList[vcf, pts, 3]; vm = VoronoiMesh[#, {{0, 1}, {0, 1}}]&/@centroids MapThread[Show[#1, Graphics[{Black, Point[#2], Red, Point[vcf[#2]]}]]&, {vm, centroids}] Show[R, Graphics[{Red, Point[pts]}]] Mscript 29 Centroid-based Voronoï mesh: centroidCornerVoronoiMesh.nb. (*Centroids N.B. position of PointSize[0.01]*) Im1 = ; im1corners = ImageCorners[Im1, 3, 0.01, 5]; im1vm = VoronoiMesh[im1corners]; im1centroids = RegionCentroid/@MeshPrimitives[im1vm, “Faces”]; centroids = Graphics[{PointSize[0.01], Red, Point[im1centroids]}]; corners = Graphics[{PointSize[0.01], Yellow, Point[im1corners]}]; ptsCorners = MeshCells[im1vm, 1]; mesh = VoronoiMesh[im1centroids]; mesh2 = VoronoiMesh[centroids]; pts = MeshCoordinates[mesh]; lines = MeshCells[mesh, 1]; vm = MeshRegion[pts, lines] mesh3 = HighlightMesh[vm, Style[1, Green]] Show[Im1, vm] Show[Im1, centroids] Show[Im1, vm, centroids] Show[Im1, mesh3, centroids] Show[Im1, mesh3, centroids, corners] Appendix A: Mathematica and Matlab Scripts 363 A.3 Scripts from Chap. 3 Mscript 30 Unbounded descriptive Nbd: UnboundedDescriptiveNbd.nb. (* Unbounded Descriptive Neighbourhood of a Point *) x = ; ImageDimensions[x] p = ImageValue[x, {300, 190}] im = Show[x, Frame → True] pts = ImageValuePositions[im, p, 0.022]; HighlightImage[im, pts, “HighlightColor” → Red] Note The following picture neighbourhood GUI is a minor revision of a script written by Binglin Li. A sample bounded descriptive nhdb using the neigbourhood GUI is shown in Fig.A.2. function varargout = Nbds(varargin) % NBDS MATLAB c o d e f o r Nbds. fig % NBDS, by itself , creates a newNBDSor raises the existing % singleton∗. % % H = NBDS returns the handle to a new NBDS or the handle to Fig. A.2 Bounded descriptive Nbd at (347,320), r = 100, ε = 50 364 Appendix A: Mathematica and Matlab Scripts % the existing singleton∗. % % NBDS(’CALLBACK’,hObject,eventData,handles
Load more

Recommended publications
  • Snakes in the Plane
    Snakes in the Plane by Paul Church A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Mathematics in Computer Science Waterloo, Ontario, Canada, 2008 c 2008 Paul Church I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract Recent developments in tiling theory, primarily in the study of anisohedral shapes, have been the product of exhaustive computer searches through various classes of poly- gons. I present a brief background of tiling theory and past work, with particular empha- sis on isohedral numbers, aperiodicity, Heesch numbers, criteria to characterize isohedral tilings, and various details that have arisen in past computer searches. I then develop and implement a new “boundary-based” technique, characterizing shapes as a sequence of characters representing unit length steps taken from a finite lan- guage of directions, to replace the “area-based” approaches of past work, which treated the Euclidean plane as a regular lattice of cells manipulated like a bitmap. The new technique allows me to reproduce and verify past results on polyforms (edge-to-edge as- semblies of unit squares, regular hexagons, or equilateral triangles) and then generalize to a new class of shapes dubbed polysnakes, which past approaches could not describe. My implementation enumerates polyforms using Redelmeier’s recursive generation algo- rithm, and enumerates polysnakes using a novel approach.
    [Show full text]
  • Open Problem Collection
    Open problem collection Peter Kagey May 14, 2021 This is a catalog of open problems that I began in late 2017 to keep tabs on different problems and ideas I had been thinking about. Each problem consists of an introduction, a figure which illustrates an example, a question, and a list related questions. Some problems also have references which refer to other problems, to the OEIS, or to other web references. 1 Rating Each problem is rated both in terms of how difficult and how interesting I think the problem is. 1.1 Difficulty The difficulty score follows the convention of ski trail difficulty ratings. Easiest The problem should be solvable with a modest amount of effort. Moderate Significant progress should be possible with moderate effort. Difficult Significant progress will be difficult or take substantial insight. Most difficult The problem may be intractable, but special cases may be solvable. 1.2 Interest The interest rating follows a four-point scale. Each roughly describes what quartile I think it belongs in with respect to my interest in it. Least interesting Problems have an interesting idea, but may feel contrived. More interesting Either a somewhat complicated or superficial question. Very interesting Problems that are particularly natural or simple or cute. Most interesting These are the problems that I care the most about. Open problem collection Peter Kagey Problem 1. Suppose you are given an n × m grid, and I then think of a rectangle with its corners on grid points. I then ask you to \black out" as many of the gridpoints as possible, in such a way that you can still guess my rectangle after I tell you all of the non-blacked out vertices that its corners lie on.
    [Show full text]
  • Gemblo and Polyhex Blokus
    with John Gough < [email protected]> Gemblo and Polyhex Blokus Blokus joined together whole-edge to whole-edge. Gemblo is one of the possible polyhex Blokus is an abstract strategy board game games that might be invented. Why for 2 to 4 players. It uses polyominoes obvious? Because both Blokus and Blokus WHicH are plane geometric lgures formed Trigon used families of shapes made from by joining one or more equal squares edge regular polygons that tessellate. How many to edge refer &igure . 0olyominoes HaVe are there? been described as being “a polyform whose cells are squaresv and they are classiled Gemblo according to how many cells they have. ie. number of cells. Wikipedia, 2017 March In 2005, Gemblo was created by Justin Oh 19). Polyominoes and other mathematically in Korea. It is an abstract strategy board patterned families of shapes were invented game with translucent, coloured pieces, by Solomon Golomb, and popularised by each of which is made up of one to lve hex- Martin Gardner. agons. The six colours are clear, red, yellow, green, blue, and purple. Despite the obvious similarities to Blokus, Oh has stated that when he was inventing Gemblo he did not know about Blokus. The name is based on the word ‘gem’, alluding to the gem-like colours used for the play- ing pieces and ‘blocking’—a central feature of playing. The size of the playing board depends on the number of people playing. Figure 1: Examples of polyominoes With players using a hexagonal shaped board that has sides of 8 unit-hexagons. Blokus—using squares—has a sister- game called Blokus Trigon that uses poly- Playing Gemblo iamonds, those families of shapes made s Gemblo can be played as a one- from unit-sided equilateral triangles joined person puzzle or solitaire, or by whole-edge to whole-edge.
    [Show full text]
  • Edgy Puzzles Karl Schaffer Karl [email protected]
    Edgy Puzzles Karl Schaffer [email protected] Countless puzzles involve decomposing areas or volumes of two or three-dimensional figures into smaller figures. “Polyform” puzzles include such well-known examples as pentominoes, tangrams, and soma cubes. This paper will examine puzzles in which the edge sets, or "skeletons," of various symmetric figures like polyhedra are decomposed into multiple copies of smaller graphs, and note their relationship to representations by props or body parts in dance performance. The edges of the tetrahedron in Figure 1 are composed of a folded 9-gon, while the cube and octahedron are each composed of six folded paths of length 2. These constructions have been used in dances created by the author and his collaborators. The photo from the author’s 1997 dance “Pipe Dreams” shows an octahedron in which each dancer wields three lengths of PVC pipe held together by cord at the two internal vertices labeled a in the diagram on the right. The shapes created by the dancers, which might include whimsical designs reminiscent of animals or other objects as well as mathematical forms, seem to appear and dissolve in fluid patterns, usually in time to a musical score. L R a R L a L R Figure 1. PVC pipe polyhedral skeletons used in dances The desire in the dance company co-directed by the author to incorporate polyhedra into dance works led to these constructions, and to similar designs with loops of rope, fingers and hands, and the bodies of dancers. Just as mathematical concepts often suggest artistic explorations for those involved in the interplay between these fields, performance problems may suggest mathematical questions, in this case involving finding efficient and symmetrical ways to construct the skeletons, or edge sets, of the Platonic solids.
    [Show full text]
  • Treb All De Fide Gra U
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by UPCommons. Portal del coneixement obert de la UPC Grau en Matematiques` T´ıtol:Tilings and the Aztec Diamond Theorem Autor: David Pardo Simon´ Director: Anna de Mier Departament: Mathematics Any academic:` 2015-2016 TREBALL DE FI DE GRAU Facultat de Matemàtiques i Estadística David Pardo 2 Tilings and the Aztec Diamond Theorem A dissertation submitted to the Polytechnic University of Catalonia in accordance with the requirements of the Bachelor's degree in Mathematics in the School of Mathematics and Statistics. David Pardo Sim´on Supervised by Dr. Anna de Mier School of Mathematics and Statistics June 28, 2016 Abstract Tilings over the plane R2 are analysed in this work, making a special focus on the Aztec Diamond Theorem. A review of the most relevant results about monohedral tilings is made to continue later by introducing domino tilings over subsets of R2. Based on previous work made by other mathematicians, a proof of the Aztec Dia- mond Theorem is presented in full detail by completing the description of a bijection that was not made explicit in the original work. MSC2010: 05B45, 52C20, 05A19. iii Contents 1 Tilings and basic notions1 1.1 Monohedral tilings............................3 1.2 The case of the heptiamonds.......................8 1.2.1 Domino Tilings.......................... 13 2 The Aztec Diamond Theorem 15 2.1 Schr¨odernumbers and Hankel matrices................. 16 2.2 Bijection between tilings and paths................... 19 2.3 Hankel matrices and n-tuples of Schr¨oderpaths............ 27 v Chapter 1 Tilings and basic notions The history of tilings and patterns goes back thousands of years in time.
    [Show full text]
  • Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity∗
    Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity∗ Erik D. Demaine, Martin L. Demaine MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA, {edemaine,mdemaine}@mit.edu Dedicated to Jin Akiyama in honor of his 60th birthday. Abstract. We show that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete. Furthermore, we show direct equivalences between these three types of puzzles: any puzzle of one type can be converted into an equivalent puzzle of any other type. 1. Introduction Jigsaw puzzles [37,38] are perhaps the most popular form of puzzle. The original jigsaw puzzles of the 1760s were cut from wood sheets using a hand woodworking tool called a jig saw, which is where the puzzles get their name. The images on the puzzles were European maps, and the jigsaw puzzles were used as educational toys, an idea still used in some schools today. Handmade wooden jigsaw puzzles for adults took off around 1900. Today, jigsaw puzzles are usually cut from cardboard with a die, a technology that became practical in the 1930s. Nonetheless, true addicts can still find craftsmen who hand-make wooden jigsaw puzzles. Most jigsaw puzzles have a guiding image and each side of a piece has only one “mate”, although a few harder variations have blank pieces and/or pieces with ambiguous mates. Edge-matching puzzles [21] are another popular puzzle with a similar spirit to jigsaw puzzles, first appearing in the 1890s. In an edge-matching puzzle, the goal is to arrange a given collection of several identically shaped but differently patterned tiles (typically squares) so that the patterns match up along the edges of adjacent tiles.
    [Show full text]
  • Formulae and Growth Rates of Animals on Cubical and Triangular Lattices
    Formulae and Growth Rates of Animals on Cubical and Triangular Lattices Mira Shalah Technion - Computer Science Department - Ph.D. Thesis PHD-2017-18 - 2017 Technion - Computer Science Department - Ph.D. Thesis PHD-2017-18 - 2017 Formulae and Growth Rates of Animals on Cubical and Triangular Lattices Research Thesis Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Mira Shalah Submitted to the Senate of the Technion | Israel Institute of Technology Elul 5777 Haifa September 2017 Technion - Computer Science Department - Ph.D. Thesis PHD-2017-18 - 2017 Technion - Computer Science Department - Ph.D. Thesis PHD-2017-18 - 2017 This research was carried out under the supervision of Prof. Gill Barequet, at the Faculty of Computer Science. Some results in this thesis have been published as articles by the author and research collaborators in conferences and journals during the course of the author's doctoral research period, the most up-to-date versions of which being: • Gill Barequet and Mira Shalah. Polyominoes on Twisted Cylinders. Video Review at the 29th Symposium on Computational Geometry, 339{340, 2013. https://youtu.be/MZcd1Uy4iv8. • Gill Barequet and Mira Shalah. Automatic Proofs for Formulae Enu- merating Proper Polycubes. In Proceedings of the 8th European Conference on Combinatorics, Graph Theory and Applications, 145{151, 2015. Also in Video Review at the 31st Symposium on Computational Geometry, 19{22, 2015. https://youtu.be/ojNDm8qKr9A. Full version: Gill Barequet and Mira Shalah. Counting n-cell Polycubes Proper in n − k Dimensions. European Journal of Combinatorics, 63 (2017), 146{163. • Gill Barequet, Gunter¨ Rote and Mira Shalah.
    [Show full text]
  • Embedded System Security: Prevention Against Physical Access Threats Using Pufs
    International Journal of Innovative Research in Science, Engineering and Technology (IJIRSET) | e-ISSN: 2319-8753, p-ISSN: 2320-6710| www.ijirset.com | Impact Factor: 7.512| || Volume 9, Issue 8, August 2020 || Embedded System Security: Prevention Against Physical Access Threats Using PUFs 1 2 3 4 AP Deepak , A Krishna Murthy , Ansari Mohammad Abdul Umair , Krathi Todalbagi , Dr.Supriya VG5 B.E. Students, Department of Electronics and Communication Engineering, Sir M. Visvesvaraya Institute of Technology, Bengaluru, India1,2,3,4 Professor, Department of Electronics and Communication Engineering, Sir M. Visvesvaraya Institute of Technology, Bengaluru, India5 ABSTRACT: Embedded systems are the driving force in the development of technology and innovation. It is used in plethora of fields ranging from healthcare to industrial sectors. As more and more devices come into picture, security becomes an important issue for critical application with sensitive data being used. In this paper we discuss about various vulnerabilities and threats identified in embedded system. Major part of this paper pertains to physical attacks carried out where the attacker has physical access to the device. A Physical Unclonable Function (PUF) is an integrated circuit that is elementary to any hardware security due to its complexity and unpredictability. This paper presents a new low-cost CMOS image sensor and nano PUF based on PUF targeting security and privacy. PUFs holds the future to safer and reliable method of deploying embedded systems in the coming years. KEYWORDS:Physically Unclonable Function (PUF), Challenge Response Pair (CRP), Linear Feedback Shift Register (LFSR), CMOS Image Sensor, Polyomino Partition Strategy, Memristor. I. INTRODUCTION The need for security is universal and has become a major concern in about 1976, when the first initial public key primitives and protocols were established.
    [Show full text]
  • An Investigation Into Three Dimensional Probabilistic Polyforms Danielle Marie Vander Schaaf Olivet Nazarene University, [email protected]
    Olivet Nazarene University Digital Commons @ Olivet Honors Program Projects Honors Program 5-2012 An Investigation into Three Dimensional Probabilistic Polyforms Danielle Marie Vander Schaaf Olivet Nazarene University, [email protected] Follow this and additional works at: https://digitalcommons.olivet.edu/honr_proj Part of the Algebraic Geometry Commons, and the Geometry and Topology Commons Recommended Citation Vander Schaaf, Danielle Marie, "An Investigation into Three Dimensional Probabilistic Polyforms" (2012). Honors Program Projects. 27. https://digitalcommons.olivet.edu/honr_proj/27 This Article is brought to you for free and open access by the Honors Program at Digital Commons @ Olivet. It has been accepted for inclusion in Honors Program Projects by an authorized administrator of Digital Commons @ Olivet. For more information, please contact [email protected]. An Investigation into Three Dimensional Probabilistic Polyforms Danielle Vander Schaaf Olivet Nazarene University 1 Abstract Polyforms are created by taking squares, equilateral triangles, and regular hexagons and placing them side by side to generate larger shapes. This project addressed three-dimensional polyforms and focused on cubes. I investigated the probabilities of certain shape outcomes to discover what these probabilities could tell us about the polyforms’ characteristics and vice versa. From my findings, I was able to derive a formula for the probability of two different polyform patterns which add to a third formula found prior to my research. In addition, I found the probability that 8 cubes randomly attached together one by one would form a 2x2x2 cube. Finally, I discovered a strong correlation between the probability of a polyform and its number of exposed edges, and I noticed a possible relationship between a polyform’s probability and its graph representation.
    [Show full text]
  • Some Open Problems in Polyomino Tilings
    Some Open Problems in Polyomino Tilings Andrew Winslow1 University of Texas Rio Grande Valley, Edinburg, TX, USA [email protected] Abstract. The author surveys 15 open problems regarding the algorith- mic, structural, and existential properties of polyomino tilings. 1 Introduction In this work, we consider a variety of open problems related to polyomino tilings. For further reference on polyominoes and tilings, the original book on the topic by Golomb [15] (on polyominoes) and more recent book of Gr¨unbaum and Shep- hard [23] (on tilings) are essential. Also see [2,26] and [19,21] for open problems in polyominoes and tiling more broadly, respectively. We begin by introducing the definitions used throughout; other definitions are introduced as necessary in later sections. Definitions. A polyomino is a subset of R2 formed by a strongly connected union of axis-aligned unit squares centered at locations on the square lattice Z2. Let T = fT1;T2;::: g be an infinite set of finite simply connected closed sets of R2. Provided the elements of T have pairwise disjoint interiors and cover the Euclidean plane, then T is a tiling and the elements of T are called tiles. Provided every Ti 2 T is congruent to a common shape T , then T is mono- hedral, T is the prototile of T , and the elements of T are called copies of T . In this case, T is said to have a tiling. 2 Isohedral Tilings We begin with monohedral tilings of the plane where the prototile is a polyomino. If a tiling T has the property that for all Ti;Tj 2 T , there exists a symmetry of T mapping Ti to Tj, then T is isohedral; otherwise the tiling is non-isohedral (see Figure 1).
    [Show full text]
  • Biased Weak Polyform Achievement Games Ian Norris, Nándor Sieben
    Biased weak polyform achievement games Ian Norris, Nándor Sieben To cite this version: Ian Norris, Nándor Sieben. Biased weak polyform achievement games. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.147–172. hal- 01188912 HAL Id: hal-01188912 https://hal.inria.fr/hal-01188912 Submitted on 31 Aug 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Discrete Mathematics and Theoretical Computer Science DMTCS vol. 16:3, 2014, 147–172 Biased Weak Polyform Achievement Games Ian Norris∗ Nándor Siebeny Northern Arizona University, Department of Mathematics and Statistics, Flagstaff, AZ, USA received 21st July 2011, revised 20th May 2014, accepted 6th July 2014. In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker’s goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker.
    [Show full text]
  • Teacher's Guide to Shape by Shape
    Using Puzzles to Teach Problem Solving TEACHER’S GUIDE TO SHAPE BY SHAPE Also includes Brick by Brick, Block by Block, and That-A-Way BENEFITS Shape by Shape vs. Tangrams Shape by Shape is an assembly puzzle that is an exciting way to teach elements of Shape by Shape is closely related to Tangrams, a classic — problem solving puzzle invented in China that became a world wide — visual and thinking craze in the early 18th century. The seven simple — geometry and measurement Tangram shapes can be arranged to create thousands — combinatorial reasoning of different silhouettes, such as people, animals, letters, The game is self-directed, with 60 challenge cards that and everyday objects. Tangrams are used in schools to include hints. The activities in this guide will help your stu- teach problem solving, geometry and fractions. dents get more out of Shape by Shape. ABOUT THE GAME Equipment. Shape by Shape includes 14 puzzle pieces (6 orange and 8 yellow), 60 challenge cards with answers on the backs, and a tray that doubles as storage for the cards. Shape by Shape and Tangrams are both based on the same triangular grid. They are similar enough that most Tangram activities work with Shape by Shape. Shape by Shape, however, is bigger and more complex. We recommend that you introduce math concepts with Tangrams first, then use Shape by Shape as a fol- low-up activity to explore concepts in more depth. Shape by Shape is different enough fromTangrams that both are worth owning. The main differences are: In a frame .
    [Show full text]