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Pairwise Markov trees. (Arbres de Markov couple.) (French) Zbl 1006.60032

The hidden Markov chain models have been recently generalized by W. Pieckzunaski and A. N. Tebbache to “pairwise” Markov chains models. The author generalizes the hidden Markov trees to “pairwise” Markov trees, which present the same processing advantages and better modelling power.

MSC:

60G20 Generalized stochastic processes
Full Text: DOI

References:

[1] Baum, L. E.; Petrie, T.; Soules, G.; Weiss, N., A maximization technique occuring in the statistical analysis of probabilistic functions of Markov chains, Ann. Math. Statist., 41, 164-171 (1970) · Zbl 0188.49603
[2] Daoudi, K.; Frakt, A.; Willsky, A., Multiscale autoregressive models and wavelets, IEEE Trans. Inform. Theory, 45, 3, 828-845 (1999) · Zbl 0946.94005
[3] Derin, H.; Elliot, H., Modelling and segmentation of noisy and textured images using Gibbs random fields, IEEE Trans. PAMI, 9, 1, 39-55 (1987)
[4] Laferté, J.-M.; Pérez, P.; Heitz, F., Discrete Markov image modeling and inference on the quadtree, IEEE Trans. Image Processing, 9, 3, 390-404 (2000) · Zbl 0962.94005
[5] Luettgen, M.; Karl, W.; Willsky, A., Efficient multiscale regularization with applications to the computation of optical flow, IEEE Trans. SP, 41, 12, 3377-3396 (1993) · Zbl 0844.60087
[6] Pieczynski, W.; Tebbache, A.-N., Pairwise Markov random fields and segmentation of textured images, Machine Graphics & Vision, 9, 3, 705-718 (2000)
[7] Pieczynski, W., Pairwise Markov chains and Bayesian unsupervised fusion, (Proceedings of 3rd ICIF, Vol. 1, FUSION 2000, July 10-13 (2000), Paris: Paris France), MoD4-24-MoD4-31
[8] W. Pieczynski, Pairwise Markov Chains, IEEE Trans. PAMI, submitted; W. Pieczynski, Pairwise Markov Chains, IEEE Trans. PAMI, submitted · Zbl 1006.60032
[9] Whittaker, J., Graphical Models in Applied Multivariate Statistics. Graphical Models in Applied Multivariate Statistics, Wiley Ser. Probab. Math. Statist. (1996)
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