Stochastic models for generic images
Authors:
David Mumford and Basilis Gidas
Journal:
Quart. Appl. Math. 59 (2001), 85-111
MSC:
Primary 68T45; Secondary 60G60, 62M40
DOI:
https://doi.org/10.1090/qam/1811096
MathSciNet review:
MR1811096
Full-text PDF Free Access
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N. G. Deriugin, The power spectrum and the correlation function of the television signal, Telecommunications 1, 1-12 (1956)
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S. C. Zhu, Y. Wu, and D. Mumford, Minimax Entropy Principle and its Application to Texture Modeling, Neural Computation 9, 1627-1660 (1997)
L. Alvarez, Y. Gousseau, and J. M. Morel, The size of objects in natural images, CMLA preprint, Ecole Normale Sup., Cachan, 1999
D. Cooper, Maximum likelihood estimation of Markov process blob boundaries in noisy images, IEEE Trans PAMI 1, 372-384 (1979)
N. G. Deriugin, The power spectrum and the correlation function of the television signal, Telecommunications 1, 1-12 (1956)
R. L. Dobrushin, Generalized random fields and their renormalization group, in Multicomponent Random Systems, Dekker, NY, pp. 153-198, 1978
K. S. Fu, Syntactic Pattern Recognition, Prentice-Hall, 1982
I. Gelfand and N. Vilenkin, Generalized Functions IV, Academic Press, 1964
S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and Bayesian restoration of images, IEEE Trans. PAMI 6, 721–741 (1984)
D. Geman, S. Geman, C. Graffigne, and P. Dong, Boundary detection by constrained optimization, IEEE Trans. PAMI 12 (1990)
D. Geman and A. Koloydenko, Invariant Statistics and Coding of Natural Microimages, CVPR 99, SCTV workshop
U. Grenander, Lectures in Pattern Theory I, II and III, Springer, 1976-1981
U. Grenander, Y. Chow, and D. Keenan, HANDS, A Pattern-Theoretic Study, Springer, 1991
P. Hallinan, G. Gordon, A. Yuille, P. Giblin, and D. Mumford, Two- and Three-Dimensional Patterns of the Face, A K Peters, Ltd., Natick, MA, 1999
J. Huang and D. Mumford, Statistics of Natural Images and Models, CVPR 99
J. Huang and D. Mumford, Image Statistics for the British Aerospace Segmented Database, MPTC preprint, http://www.dam.brown.edu/mptc
T. Hida, Stationary Stochastic Processes, Princeton Univ. Press, 1970
J. Kingman, Poisson Processes, Oxford Univ. Press, 1993
E. R. Kretzmer, Statistics of television signals, Bell System Tech. J. 31, 751-763 (1952)
W. Linde, Infinitely divisible and stable measures on Banach spaces, Wiley, 1986
S. Mallat, Applied Mathematics meets Signal Processing, in Proc. Internat. Congress Math., Vol. 1, 1998, Documenta Mathematica
Y. Meyer, Wavelets and functions with bounded variations from image processing to pure mathematics, preprint, Ecole Normale-Cachan, 1999
D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions, Comm. Pure and Appl. Math. 42, 577-685 (1989)
D. Mumford, Elastica and Computer Vision, in Algebraic Geometry and its Applications, ed. C. Bajaj, Springer-Verlag, 1993, pp. 507-518
M. Reed, Functional Analysis and Probability, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer Lecture Notes in Physics 25, 1973
D. Ruderman and W. Bialek, Statistics of Natural Images, Phys. Rev. Letters 73, 814-817 (1994)
Kenichi Sato, Levy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999
C. Shannon, Prediction and Entropy of Printed English, Bell System Technical Journal, 50-64, 1951
E. Simoncelli and W. Freeman, The Steerable Pyramid, IEEE Internat. Conference on Image Proc., 1995
J. H. van Hateren and A. van der Shaaf, Independent Component Filters of Natural Images, Proc. Royal Soc. London B 265, 359–366 (1998)
S. C. Zhu, Y. Wu, and D. Mumford, Minimax Entropy Principle and its Application to Texture Modeling, Neural Computation 9, 1627-1660 (1997)
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© Copyright 2001
American Mathematical Society
