Abstract
With emphasis on the graph structure of energy-based models devoted to image analysis, we investigate efficient procedures for sampling and inferring. We show that triangulated graphs, whom trees are simple instances of, always support causal models for which noniterative procedures can be devised to minimize the energy, to extract probabilistic descriptions, to sample from corresponding prior and posterior distributions, or to infer from local marginals. The relevance and efficiency of these procedures are illustrated for image restoration problems.
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References
J. BESAG. Spatial interaction and the statistical analysis of lattice systems. J. Royal Statist. Soc., 36 B:192–236, 1974.
C. BOUMAN and M. SHAPIRO. A multiscale image model for bayesian image segmentation. IEEE Trans. Image Proc, 3(2):162–177, March 1994.
H. DERIN and P. A. KELLY. Discrete-index Markov-type random processes. Proc. IEEE, 77(10):1485–1509, 1989.
P.A. DEVIJVER. Real-time modeling of image sequences based on hidden Markov Mesh random field models. Technical Report M-307, Philips Research Lab., June 1989.
P. FIEGUTH. Application of multiscale estimation to large scale multidimensional imaging and remote sensing problems. PhD thesis, MIT Dept. of EECS, June 1995.
J. GOUTSIAS. Mutually compatible Gibbs random fields. IEEE Trans. Information Theory, 35(6):1233–1249, 1989.
J. GOUTSIAS. Unilateral approximation of Gibbs random field images. Graph. Mod. Image Proc., 53:240–257, 1991.
J. GOUTSIAS. Markov random fileds: interacting particles systems for statistical image modeling and analysis. Technical Report JHU/ECE 96-01, The Johns Hopkins Univ., 1996.
A. WILLSKY K. CHOU and A. BENVENISTE. Multiscale recursive estimation, data fusion, and regularization. IEEE Trans. Automatic Control, 39(3):464–477, 1994.
J.-M. LAFERTé, F. HEITZ, P. PéREZ, and E. FABRE. Hierarchical statistical models for the fusion of multiresolution image data. In Proc. Int. Conf. Computer Vision, Cambridge, USA, June 1995.
M. LUETTGEN, W. KARL, and A. WILLSKY. Efficient multiscale regularization with applications to the computation of optical flow. IEEE Trans. Image Processing, 3(1):41–64, 1994.
M. LUETTGEN and A. WILLSKY. Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination. IEEE Trans. Image Processing, 4(2):194–207, 1995.
J. MOURA and N. BALRAM. Recursive structure of noncausal Gauss-Markov random fields. IEEE Trans. Information Theory, 38(2):335–354, 1992.
D. PICKARD. Unilateral Markov fields. Advances in Applied Probability, 12:655–671, 1980.
J. WHITTAKER. Graphical models in applied multivariate statistics. Wiley, 1990.
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© 1997 Springer-Verlag Berlin Heidelberg
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Pérez, P., Laferté, JM. (1997). Noniterative manipulation of discrete energy-based models for image analysis. In: Pelillo, M., Hancock, E.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1997. Lecture Notes in Computer Science, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62909-2_78
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DOI: https://doi.org/10.1007/3-540-62909-2_78
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