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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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, Automodel generalized random fields and their renorm group, Multicomponent random systems, Adv. Probab. Related Topics, vol. 6, Dekker, New York, 1980, pp. 153–198. MR 599535
  • [Fu] K. S. Fu, Syntactic Pattern Recognition, Prentice-Hall, 1982
  • [G-V] I. M. Gel’fand and N. Ya. Vilenkin, Generalized functions. Vol. 4: Applications of harmonic analysis, Translated by Amiel Feinstein, Academic Press, New York - London, 1964, 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] Ulf Grenander, Regular structures, Applied Mathematical Sciences, vol. 33, Springer-Verlag, New York-Berlin, 1981. Lectures in pattern theory. Vol. III. MR 619018
  • [GCK] U. Grenander, Y. Chow, and D. M. Keenan, Hands, Research Notes in Neural Computing, vol. 2, Springer-Verlag, New York, 1991. A pattern-theoretic study of biological shapes. MR 1084371
  • [HGYGM] Peter W. Hallinan, Gaile G. Gordon, A. L. Yuille, Peter Giblin, and David 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] Takeyuki Hida, Stationary stochastic processes, Mathematical Notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0258106
  • [Ki] J. F. C. Kingman, Poisson processes, Oxford Studies in Probability, vol. 3, The Clarendon Press, Oxford University Press, New York, 1993. Oxford Science Publications. MR 1207584
  • [Kr] E. R. Kretzmer, Statistics of television signals, Bell System Tech. J. 31, 751-763 (1952)
  • [Li] Werner Linde, Probability in Banach spaces—stable and infinitely divisible distributions, 2nd ed., A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1986. MR 874529
  • [Ma] Stéphane Mallat, Applied mathematics meets signal processing, Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), 1998, pp. 319–338. MR 1648037
  • [Me] Yves Meyer, Wavelets and functions with bounded variation from image processing to pure mathematics, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. Special Issue (2000), 77–105. Mathematics towards the third millennium (Rome, 1999). MR 1845666
  • [M-S] David Mumford and Jayant Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42 (1989), no. 5, 577–685. MR 997568, https://doi.org/10.1002/cpa.3160420503
  • [Mu] David Mumford, Elastica and computer vision, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 491–506. MR 1272050
  • [Re] G. Velo and A. Wightman (eds.), Constructive quantum field theory, Springer-Verlag, Berlin-New York, 1973. The 1973 “Ettore Majorana” International School of Mathematical Physics, Erice (Sicily), 26 July–5 August 1973; Lecture Notes in Physics, Vol. 25. MR 0395513
  • [R-B] D. Ruderman and W. Bialek, Statistics of Natural Images, Phys. Rev. Letters 73, 814-817 (1994)
  • [Sa] Ken-iti Sato, Lévy processes and infinitely divisible distributions, Cambridge Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999. Translated from the 1990 Japanese original; Revised by the author. 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)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 68T45, 60G60, 62M40

Retrieve articles in all journals with MSC: 68T45, 60G60, 62M40

Additional Information

DOI: https://doi.org/10.1090/qam/1811096
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society