Markov random fields and images

At the intersection of statistical physics and probability theory, M a rkov random elds and Gibbs distributions have emerged in the early eighties as powerful tools for modeling images and coping with high-dimensional inverse problems from low-level vision. Since then, they have been used in many studies from the image processing and computer vision community. A b rief and simple introduction to the basics of the domain is proposed.

[1]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[2]  Basilis Gidas,et al.  Parameter Estimation for Gibbs Distributions from Partially Observed Data , 1992 .

[3]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[4]  Stan Z. Li,et al.  Markov Random Field Modeling in Computer Vision , 1995, Computer Science Workbench.

[5]  Gerhard Winkler,et al.  Image analysis, random fields and dynamic Monte Carlo methods: a mathematical introduction , 1995, Applications of mathematics.

[6]  P. Pérez,et al.  Multiscale minimization of global energy functions in some visual recovery problems , 1994 .

[7]  W. Clem Karl,et al.  Efficient multiscale regularization with applications to the computation of optical flow , 1994, IEEE Trans. Image Process..

[8]  Donald Geman,et al.  Constrained Restoration and the Recovery of Discontinuities , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Charles A. Bouman,et al.  Multiple Resolution Segmentation of Textured Images , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Fabrice Heitz,et al.  Hierarchical statistical models for the fusion of multiresolution image data , 1995, Optics + Photonics.

[11]  Anil K. Jain,et al.  Markov random fields : theory and application , 1993 .

[12]  F. Comets.  On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice , 1992 .

[13]  Michael J. Black,et al.  On the unification of line processes , 1996 .

[14]  Charles A. Bouman,et al.  A multiscale random field model for Bayesian image segmentation , 1994, IEEE Trans. Image Process..

[15]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

[16]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[17]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[18]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[19]  C. Geyer,et al.  Constrained Monte Carlo Maximum Likelihood for Dependent Data , 1992 .

[20]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[21]  L. Younes.  Parametric Inference for imperfectly observed Gibbsian fields , 1989 .

[22]  A. Sokal.  Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms , 1997 .

[23]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[24]  L. Younes.  Estimation and annealing for Gibbsian fields , 1988 .

[25]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[26]  X. Guyon.  Champs aléatoires sur un réseau , 1993 .

[27]  David Mumford,et al.  Bayesian Rationale for the Variational Formulation , 1994, Geometry-Driven Diffusion in Computer Vision.

[28]  B. Gidas,et al.  A Variational Method for Estimating the Parameters of MRF from Complete or Incomplete Data , 1993 .

[29]  Bernard Chalmond,et al.  An iterative Gibbsian technique for reconstruction of m-ary images , 1989, Pattern Recognit..

[30]  Josiane Zerubia,et al.  Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood , 1999, IEEE Trans. Image Process..

[31]  Goodman,et al.  Multigrid Monte Carlo method. Conceptual foundations. , 1989, Physical review. D, Particles and fields.

[32]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[33]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[34]  Haluk Derin,et al.  Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.