ULF GRENANDER
L. Herbert Ballou University Professor Division of Applied Mathematics Brown University Providence, RI 02912
DEGREES
Fil. Lic., University of Stockholm, 1948 Fil. Dr., University of Stockholm, 1950
PROFESSIONAL APPOINTMENTS
Visiting Assistant Professor of Statistics, University of Chicago, 1951-52
Visiting Associate Professor of Statistics, University of California, Berkeley, 1952-53
Docent, University of Stockholm, Sweden, 1953-57
Professor of Probability and Statistics, Brown University, 1957-58
Professor and Director, Institute for Insurance Mathematics and Mathematical Statistics, University of Stockholm, 1958-66
Scientific Director, Swedish Institute of Applied Mathematics, 1971-73
Member of the Scientific Board, 1974-1984
L. Herbert Ballou University Professor, Division of Applied Mathematics, Brown University, 1966-present
Member, Institut Mittag-Leffler, Stockholm, Sweden, 1979-80
COMMITTEES
Executive Committee of Neural Sciences Center and Center for Cognitive Sciences.
Inaugurated a new course on insurance mathematics.
1 University course on the influence of technology on mathematics; senior seminar on pattern theory; special topic graduate course on inference in stochastic processes.
Arrangements Committee, International Congress of Mathematics, Helsinki, 1978.
Advisory Committee on Information Science and Technology, National Science Foundation.
Inaugurated a new course on time series analysis.
Inaugurated a new course on applied statistics.
Chairman, Committee on Pattern Research.
Member, Committee on Stochastic Models, Istituto per le Applicazione del Calcolo, Rome.
Member, Visiting Committee, University of Chicago, 1993.
ACADEMIC HONORS
Arhennius Fellow l948 Member, International Statistical Institute 1953 Fellow, Institute of Mathematical Statistics, 1953 Prize of the Nordic Actuarial Societies, 196l Arnberger Prize, Royal Swedish Academy of Science, 1962 Member, Royal Swedish Academy of Science, 1965 Member of the Board, Sweden-America Foundation Member, Swedish Actuarial Society Guggenheim Fellowship, 1979 Honorary Fellow, Royal Statistical Society, London, 1989 D. Sc. (honorary), University of Chicago, 1993 Fellow, American Academy of Arts and Sciences, 1995.
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RESEARCH IN PROGRESS
Creation of a new theory of regular structure (pattern theory) and its application to the actual and man-made world.
Development of the theory of statistical inference on stochastic processes and abstract spaces, by functional analytic methods.
Developing algorithms for medical image processing.
A unified theory of automatic target recognition.
BOOKS
1. Statistical Analysis of Stationary Time Series (with M. Rosenblatt), John Wiley & Sons, 1957, (also in Chinese).
2. Toeplitz Forms and Their Applications (with G. Szego), U. of Calif. Press, 1958, Russian Edition.
3. Probability and Statistics - The Harald Cram´er Volume (Editor), John Wiley & Sons, 1959.
4. Probabilities on Algebraic Structures, John Wiley & Sons, 1963, translated into Russian.
5. Introduction to the Study of Statistics (in Swedish with German translation), Almqvist and Wiksell, Stockholm, 1964.
6. A Short Course in Computational Probability and Statistics (with W. Freiberger), Springer-Verlag, New York 1971.
7. Pattern Synthesis: Lectures in Pattern Theory, Vol. I, Springer-Verlag, New York, 1976.
8. Pattern Analysis: Lectures in Pattern Theory, Vol. II, Springer-Verlag, New York, 1978.
9. Regular Structures: Lectures in Pattern Theory, Vol. III, Springer-Verlag, New York, 1981, also in Russian.
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10. Abstract Inference, John Wiley & Sons, New York, 1981.
11. Mathematical Experiments on the Computer, Academic Press, 1982.
12. HANDS: A Pattern Theoretic Study of Biological Shapes (with Y. Chow and D.M. Keenan) Springer-Verlag, New York, 1990.
13. General Pattern Theory, Oxford University Press, 1993.
14. “Patterns” will be published by Johns Hopkins University Press in 1993.
PAPERS
1. Stochastic processes and integral equations, Arkiv for Mathematik, 1, 8, 67-70, 1949.
2. Stochastic processes and statistical inference, Arkiv for Mathematik, 1, 17, 1950, also appeared as a monograph in Russian, Hungarian and Chinese.
3. On empirical spectral analysis of stochastic processes, Arkiv for Mathematik, 1, 35, 503-531, 1951.
4. On Toeplitz forms and stationary processes, Arkiv for Mathematik, 1, 37, 1951.
5. On spectral analysis of stationary time series, Proc. Nat. Acad. Sci., USA, 38, 519-521, 1952 (with M. Rosenblatt).
6. Comments on statistical spectral analysis, Skand. akt. tidskr., 36, 182-202, 1953 (with M. Rosenblatt).
7. Statistical spectral analysis of time series arising from stationary stochastic processes, Ann. Math. Stat. 24, 537-558, 1953.
8. On the estimation of regression coefficients in the case of an autocorrelated disturbance, Annals Math. Stat., 25, 2, 252-272, 1954.
9. Regression analysis of time series with stationary residual, Proc. Nat. Acad. Sci., USA, 40, 812-816, 1954.
10. An extension of a theorem of G. Szego and its application to the study of stochastic processes, Trans. Amer. Math. Soc. 76, 112-126, 1954.
11. A contribution to the theory of Toeplitz matrices, Trans. Am. Math. Soc., 79, 129- 140, 1955.
4 12. A prediction problem in game theory, Arkiv for Mathematik, 3, 371-379, 1956.
13. Some problems in estimating the spectrum of a time series, Proc. 3rd Berkeley Symposium on Math. Statistics, vol. 7, 77-93, Univ. of Calif. Press, 1956 (with M. Rosenblatt).
14. On the theory of mortality measurement, partr I, Skand. aktuarietidskr. 39, 70-96, 1956.
15. On the theory of mortality measurements, part II, Skand. aktuarietidskr. 39, 125-153, 1957.
16. On heterogeneity in non-life insurance, part I, Skand. akt. tidskr. 40, 71-84, 1957.
17. On heterogeneity in non-life insurance, part II, Skand. akt. tidskr. 41, 153-179, 1958.
18. Some remarks on bonus systems in automobile insurance, Skand. akt. tidskr. 40, 180-197, 1958.
19. Modern trends in time series analysis, Sankhya, 18, 149-158, 1957 (translated into Italian and French).
20. Bandwidth and variance in estimation of the spectrum, J. Roy. Stat. Soc., Ser. B, 20, 172-175, 1958.
21. Approximate distributions of noise power measurement. Q. Appl. Math. 17, 271-283, 1959 (with W. Freiberger).
22. The distribution of quadratic forms in normal varieties: a small sample theory with applications to spectral analysis, J. SIAM7, 374-957 (with H.O. Pollak and D. Slepian).
23. Some non-linear problems in probability theory, The Harald Cramér Volume, John Wiley & Sons, 1959.
24. Stochastic groups, I, Arkiv for Matematik, 4, 163-183, 1960.
25. Stochastic groups, II, Ark. Mat. 4, 189-207, 1960.
26. Stochastic groups, III, Ark. Mat. 4, 333-345, 1961.
27. Stochastic groups and related structures, Proc. 4th Berkeley Symposium on Mathematical Statistics, vol. II, 171-189, U. of Calif. Press, 1961.
28. Matematisk statistik av idag, Statistisk tidskrift, 4, 1964.
5 29. Extremum problems in network planning, FOA report A139, 1964.
30. Operations analysis in banking (in Swedish), unpublished report, 1964.
31. A limit theorem for sums of minima of stochastic variables, Ann. Math. Stat. 36, 3, 1965.
32. Stochastic models in the theory of pursuit, Rev. International Statistical Institute, 33, 2, 1965.
33. On the formulation of statistical meteorology, Rev. Int. Stat. Inst. 33, 59-86, 1965 (with W. Freiberger).
34. Some direct estimates of the mode, Ann. Math. Stat. 36, 1965.
35. An experiment in teaching operations research, J. Oper. Res. Soc. Amer., 13, 1965.
36. Can we look inside an unreliable automaton? Festschrift for J. Neyman, Wiley, 1966.
37. Some properties of statistical reliability functions (with S. Carlsson), Ann. Math. Stat. 37, 4, 1965.
38. Statistical approximation of plane convex sets (with S. Carlsson), Skand. Akt. tidskrift, 1967.
39. Toward a theory of patterns, Proc. Symp. on Probability Methods in Analysis, Springer-Verlag, 1967.
40. Adaptive stochastic control, In: Differential Equations and Dynamical Systems, (Editors, J.K. Hale and J.P. LaSalle), Academic Press, New York, 1967.
41. Syntax-controlled probabilities (unpublished manuscript), 1967.
42. A tactical study of evasive maneuvers, Res. Inst. of National Defense, Stockholm, 1968.
43. A feature logic for clusters (unpublished), 1968.
44. Foundations for pattern analysis, Q. Appl. Math. 27, 1-55, 1969.
45. Looking at convolutions on certain groups with the help of a computer, Proc. Symp.: “Probabilities sur les structuresalgebriques” Clermont-Ferrand, 1969.
46. A unified approach to pattern analysis, Advances in Computers, vol. 10, 175-216, 1970, (edited by W. Freiberger).
6 47. Pattern recognition in control systems (with K.J. Astrom) Proc. 3rd Hawaii Int. Conf. Syst. Sci., 1970.
48. Computer generated image algebras (with W. Freiberger), Proc. Int. Fed. Inf. Processing Societies Congress, North-Holland Pub. Co., 1970.
49. A mutual reinsurance scheme, Astin Bull., 1971 (with H. Bohman).
50. Quantitative methods of evaluating computer systems performance in “Statistical Computer Performance Evaluation” (edited by W. Freiberger), Academic Press, 1972.
51. Reflections on Pavlovian memory (unpublished manuscript), 1972.
52. Computational probability and statistics, SIAM Review, vol. l5, no. 1, 134-192, 1973.
53. Statistical geometry: A tool for pattern analysis, Bulletin of the Amer. Math. Soc., vol. 79, no. 5, Sept. 1973.
54. Large sample discrimination between two Gaussian processes with different spectra, Annals of Statistics, vol. 2, no. 2, March 1974.
55. Dynamical models of geomorphological patterns, Jour. of Mathematical Geology, 1974.
56. Abduction machines that learn syntactic patterns (unpublished manuscript) 1974.
57. Computational probability and statistics, Proc. Symp. Appl. Math., American Mathematical Society, 1974.
58. Restoration of deformed lattice patterns, In: Perspective in Probability and Statistics, Academic Press, 1975.
59. Patterns in program references, IBM J. Res. Vol. 19, No. 3, May 1975.
60. Ideas in computational probability, Proc. 10th. Res. Conf. Com. of Am. Act. Soc.
61. Computer aided identification of eugonic gram-negative bacilli, Computers in Biology and Medicine, 6, 99-109, 1976.
62. Surface patterns in theoretical geography, (with W. Freiberger) Computers & Geosciences, Vol. 3, No. 4, 547-578, 1977.
63. Spectral analysis of networks with random topologies (with Jack Silverstein), SIAM J. Appl. Math., Vol. 32, No. 2, 499-519, March 1977.
7 64. Abduction of semantic patterns, In: Pattern Formation by Dynamic Systems and Pattern Recognition (ed. H. Haken) 186-198, Proceedings of the International Symposium on Synergetics at Schloss Elmau, Bavaria, 1979.
65. Some ideas in computational probability, In: Computational Probability (ed. P.M. Kahn) 1-10, 1980.
66. Developmental matching and the numerical matching hypothesis for neuronal cell death (with M. Katz) J. Theor. Biol. 98, 501-513, 1982.
67. A Mathematical Experiment, 15th Symposium Interface Comp. Sci. and Stat., 1983.
68. Reflections on global tendencies in mathematics, Conference on Parts &Wholes, Lund, Sweden, 1983.
69. Tutorial in Pattern Theory, 1983 (unpublished manuscript), Brown University, Providence, RI.
70. Estimating homomorphisms in mathematical semantics, (with Li-deWu), China-Japan Symp. on Statistics, Beijing, China, 1984.
71. Experimental mathematics (with O. Shisha), Jour. of Approximation Theory, Vol. 43, No. 1, January 1985.
72. A non-quadratic sieve for spectral estimation, Contributions to Probability and Statistics, 1985.
73. A sieve method for the spectral density (with Y.-S. Chow), Ann. Stat. 13, 1985, pp. 998-1100.
74. Pictures as complex systems, Biomathematics, 1986, vol. 16, pp. 62-87.
75. Abstract inference in image processing, Bernoulli Society, Vol. 2, pp.13-25, 1987.
76. Pattern Theory: mathematics for image processing, Adv. in Statistical Signal Processing, vol. 1, pp. 119-156.
77. Mathematics motivated by emergence of different kinds of very powerful computers, Invited Paper, 46th Session of the ISI, 1987.
78. The 1985 Rietz Lecture: Advances in Pattern Theory, Annals of Statistics, Vol. 17, No. 1, pp. 1-30, 1989.
79. Towards automated image understanding (with D.M. Keenan). Journal of Applied Statistics, Vol. 16, No. 2, 1989.
8 80. A computer experiment in pattern theory (with D.M. Keenan), Commun. Statist.- Stochastic Models, 5(4), 531-553, 1989.
80a. Cramér Lecture: Global shape models.
81. Comparing sweep strategies for stochastic relaxation (with Y. Amit), Jour. Multivariate Analysis, Vol. 27, No. 2, May 1991.
81a. Hotelling Lectures: Pattern Theory.
82. Structural image restoration through deformable templates (with Y. Amit and M. Piccioni), Jour. Amer. Statist. Assoc., Vol. 86, No. 414, June 1991.
83. On the shape of plane images (with D. Keenan), SIAM J. Appl. Math., 1993.
84. A stochastic shape model for defect detection in potatoes (with K. Manbeck), Jour. Amer. Statist. Assoc., 1993.
85. Mathematical textbook of deformable neuroanatomies (with M. Miller, G. Christiansen, and Y. Amit), Proc., Nat. Acad., 1993.
86. Membranes, mitochondia and amoeba: shape models, (with M. Miller et at.) Adv. Appl. Stat., 1994.
87. Representations of Knowledge in Complex Systems, (with Michael Miller), J. Royal Stat. Soc. 1994.
88. Mixed limit theorems for pattern analysis (with J. Setharaman), J. Multivariate Analysis, 1994.
89. Multiple target direction of arrival tracking (with A. Srinastava and Michael Miller), IEEE Trans. Signal Processing, 1995.
90. Conditional mean estimation via jump-diffusion processes (with Michael Miller and A. Srinastava), IEEE Trans. Signal Processing, 1995.
91. The Abraham Wald Lectures, Montreal 1995.
92. On the Mathematics of Growth, Quarterly of Applied Mathematics, 2006 (to be published).
Other Publications
Ulf Grenander On the Road to Nowhere. 2006.
Ulf Grenander, Mathematics in Biology. 2006. (PowerPoint Presentation).
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Ulf Grenander: (2005) Patterns of Thought, Version 5.5. March 2005.
Ulf Grenander. (2005) MATLAB software for "Patterns of Thought.
Ulf Grenander. (2005) Executable code (Windows) for "Patterns of Thought"..
Ulf Grenander. (2004) MODALITIES. Supplement to Patterns of Thought.
Ulf Grenander. (2003) TOWARDS A THEORY OF NATURAL SCENES.
Ulf Grenander. (2002) A Useful Hint?, Tech. Rep. D.A.M., Brown University.
Ulf Grenander. (2002) COMPUTER UNDERSTANDING OF NATURAL SCENES.
Ulf Grenander. (2002) Clutter17. Non-Diffeomorphic Background Deformations.
Ulf Grenander. (2002) Heuristic Inference in Sensory Perception with an Application to Computer Vision.
Oddvar Husby and Ulf Grenander. (2001) A Model for Recognition of 3D Non- dense Objects in Range images.
Ulf Grenander, Clutter 5, Tech. Rep., March 1999.
Ulf Grenander, Clutter 6, Tech. Rep., April 1999.
CD-ROMs
Evolving Anatomies, by Ulf Grenander and Larisa Matejic. (presents some elementary ideas about Computational Anatomy).
Automated Target Recognition, by Anuj Srivastava and Ulf Grenander. (deals with object recognition).
Windows on the World, by Ulf Grenander. An invitation to work on a mathematical theory of the mind. Advanced.
A. Srivastava, U. Grenander and X. Liu: NATURAL IMAGE STATISTICS. BESSEL K FORMS .
10 BRIEF BIO
Before coming to Brown my main research interests had been
1) Inference in stochastic processes 2) Time series analysis 3) Insurance mathematics and risk analysis 4) Pursuit game theory 5) Nonparametric statistics
In 1966 I moved to Brown and re-oriented my research. Most of my efforts since have gone into creating a mathematical theory of patterns, starting from algebraic considerations, based on which are probabilistic results (metric pattern theory) and methods of inference (pattern inference). The latter are implemented as algorithms and computer programs intended to analyze and understand patterns of various types: pictures, syntactic patterns, logical structures, social systems, and patterns of doctrines.
Up to the early 1980’s this work was of purely theoretical nature. Starting at this time I and my group in the Division of Applied Mathematics have tried to apply these ideas to practical tasks in pattern analysis, in particular to image restoration. The images can have been acquired using different technologies such as visible light digital cameras, infrared, X-rays, tomographic techniques, and more recently laser radar. Among current research topics that I am studying one can mention global models for highly variable shapes (such that occur in anatomy), 3-D recognition (restoration based on range data), and MRI and CT imaging based on mathematical models using background deformations. The main theme in this research has been to exploit the interaction between mathematics of a new type (pattern theory) and advances in high technology (computer architectures, languages, and new sensors).
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