Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
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  • [AGM] L. Alvarez, Y. Gousseau, and J. M. Morel, The size of objects in natural images, CMLA preprint, Ecole Normale Sup., Cachan, 1999
  • [Co] D. Cooper, Maximum likelihood estimation of Markov process blob boundaries in noisy images, IEEE Trans PAMI 1, 372-384 (1979)
  • [De] N. G. Deriugin, The power spectrum and the correlation function of the television signal, Telecommunications 1, 1-12 (1956)
  • [Do] R. L. Dobrushin, Generalized random fields and their renormalization group, in Multicomponent Random Systems, Dekker, NY, pp. 153-198, 1978 MR 599535
  • [Fu] K. S. Fu, Syntactic Pattern Recognition, Prentice-Hall, 1982
  • [G-V] I. Gelfand and N. Vilenkin, Generalized Functions IV, Academic Press, 1964 MR 0173945
  • [G-G] S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and Bayesian restoration of images, IEEE Trans. PAMI 6, 721-741 (1984)
  • [GGGD] D. Geman, S. Geman, C. Graffigne, and P. Dong, Boundary detection by constrained optimization, IEEE Trans. PAMI 12 (1990)
  • [G-K] D. Geman and A. Koloydenko, Invariant Statistics and Coding of Natural Microimages, CVPR 99, SCTV workshop
  • [Gr] U. Grenander, Lectures in Pattern Theory I, II and III, Springer, 1976-1981 MR 619018
  • [GCK] U. Grenander, Y. Chow, and D. Keenan, HANDS, A Pattern-Theoretic Study, Springer, 1991 MR 1084371
  • [HGYGM] 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 MR 1695242
  • [H-M1] J. Huang and D. Mumford, Statistics of Natural Images and Models, CVPR 99
  • [H-M2] J. Huang and D. Mumford, Image Statistics for the British Aerospace Segmented Database, MPTC preprint, http://www.dam.brown.edu/mptc
  • [Hi] T. Hida, Stationary Stochastic Processes, Princeton Univ. Press, 1970 MR 0258106
  • [Ki] J. Kingman, Poisson Processes, Oxford Univ. Press, 1993 MR 1207584
  • [Kr] E. R. Kretzmer, Statistics of television signals, Bell System Tech. J. 31, 751-763 (1952)
  • [Li] W. Linde, Infinitely divisible and stable measures on Banach spaces, Wiley, 1986 MR 874529
  • [Ma] S. Mallat, Applied Mathematics meets Signal Processing, in Proc. Internat. Congress Math., Vol. 1, 1998, Documenta Mathematica MR 1648037
  • [Me] Y. Meyer, Wavelets and functions with bounded variations from image processing to pure mathematics, preprint, Ecole Normale-Cachan, 1999 MR 1845666
  • [M-S] D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions, Comm. Pure and Appl. Math. 42, 577-685 (1989) MR 997568
  • [Mu] D. Mumford, Elastica and Computer Vision, in Algebraic Geometry and its Applications, ed. C. Bajaj, Springer-Verlag, 1993, pp. 507-518 MR 1272050
  • [Re] M. Reed, Functional Analysis and Probability, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer Lecture Notes in Physics 25, 1973 MR 0395513
  • [R-B] D. Ruderman and W. Bialek, Statistics of Natural Images, Phys. Rev. Letters 73, 814-817 (1994)
  • [Sa] Kenichi Sato, Levy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999 MR 1739520
  • [Sh] C. Shannon, Prediction and Entropy of Printed English, Bell System Technical Journal, 50-64, 1951
  • [S-F] E. Simoncelli and W. Freeman, The Steerable Pyramid, IEEE Internat. Conference on Image Proc., 1995
  • [vH] J. H. van Hateren and A. van der Shaaf, Independent Component Filters of Natural Images, Proc. Royal Soc. London B 265, 359-366 (1998)
  • [ZWM] 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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DOI: https://doi.org/10.1090/qam/1811096
Article copyright: © Copyright 2001 American Mathematical Society

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