F.C. Jeng. Subsampling of Markov random fields. J. Visual Com. And Image Repres., 3(3):225--229, Sept 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....lack of fill for such elimination orders has a simple interpretation: If we subsample the random field or graphical model by eliminating a set of variables, this restricted model remains Markov with respect to a restriction of the original graph. That is, no additional edges need to be added (see [164, 200] and, in particular, 269] for discussions of this issue for general graphical models) Similarly and as we saw in Section 4.3, the computation of likelihoods for loop free models can also be performed e#ciently. While this can also be interpreted in terms of the existence of elimination orders ....

....While it is certainly possible to view such coarse to fine algorithms as purely computationally motivated constructs, 209] makes clear that there are statistical interpretations of at least some of the computations and representations embedded in such algorithms. As a result, a number of authors [164, 200, 144, 269] have looked in more detail at the following question: Suppose we begin with an MRF model at the finest resolution; what is the corresponding statistical structure of a coarsened version of the field (e.g. corresponding to a coarse wavelet approximation or to a subsampled version of the field) ....

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F.C. Jeng. Subsampling of Markov random fields. J. Visual Com. And Image Repres., 3(3):225--229, Sept 1992.

....from particular models and scale transformations [16] because of the loss of locality of the model at the coarse scales. In [26] Lakshmanan has shown that simple resolution transformations such as subsampling or block averaging also result in a loss of locality for Gaussian MRF models. Jeng [21] has studied the loss of locality in a periodic subsampling of MRF models with infinite support. Other approaches introduced recently aim at defining MRF models on hierarchical structures such as trees [3] 6] 28] or other pyramidal graph structures [6] 22] 28] See [17] for a comprehensive ....

....are derived. These general results may be applied to the different multiresolution approaches previously mentioned. Several special cases related to various multiresolution MRF based image analysis approaches are studied. This study generalizes and unifies in some sense the works of Jeng [21] and Lakshmanan [26] both devoted to the subsampling of MRF s. Lakshmanan [26] studies the subsampling of Gauss Markov random fields. The mathematical framework described here applies to general classes of nonlinear MRF s and handles several other approaches to multiresolution MRF modeling. In ....

[Article contains additional citation context not shown here]

F.C. Jeng, "Subsampling of Markov random fields," J. of Visual Com. and Image Representation, vol. 3, no. 3, pp. 225-229, 1992.

....from particuliar models and scale transformations [21] because of the loss of locality of the model at the coarse scales. In [32] Lakshmanan has shown that simple resolution transformations such as subsampling or block averaging also result in a loss of locality for gaussian MRF models. Jeng [27] has studied the loss of locality in a periodic subsampling of MRF models with infinite support. Other approaches ( 1 ) introduced recently aim at defining MRF models on hierarchical structure such as trees, 3, 7, 34] or other pyramidal graph structures [7, 29, 34] 1 Alternate approaches, ....

....markovian model on a multilevel graph structure (tree or pyramid [3, 7] ffl stochastic transform of a random field using the renormalization group approach [21] ffl expression of the restriction in the particular case of a gaussian MRF. This study generalizes and unifies the works of Jeng [27] and Lakshmanan [32] both devoted to the subsampling of MRFs. Lakshmanan [32] studies the subsampling of linear MRFs (namely Gaus Markov random fields) The mathematical framework described here applies to general classes of non linear MRFs and handles several other approaches to multiresolution ....

[Article contains additional citation context not shown here]

F.C. JENG. -- Subsampling of Markov random fields. -- J. of Visual Com. and Image Representation, Vol. 3, No. 3 : pages 225--229, September 1992.

....[21] because of the loss of locality of the model at the coarse scales. In [32] RR n2170 4 Patrick P erez, Fabrice Heitz Lakshmanan has shown that simple resolution transformations such as subsampling or block averaging also result in a loss of locality for Gaussian MRF models. Jeng [27] has studied the loss of locality in a periodic subsampling of MRF models with infinite support. Other approaches ( 1 ) introduced recently aim at defining MRF models on hierarchical structure such as trees [3, 7, 34] or other pyramidal graph structures [7, 29, 34] For a practical use of these ....

....model on a multilevel graph structure (tree or pyramid [3, 7] ffl stochastic transform of a Markov random field using the renormalization group approach [21] ffl expression of the restriction in the particular case of a Gaussian MRF. This study generalizes and unifies the works of Jeng [27] and Lakshmanan [32] both devoted to the subsampling of MRFs. Lakshmanan [32] studies the subsampling of linear MRFs (namely Gauss Markov random fields) The mathematical framework described here applies to general classes of nonlinear MRFs and handles several other approaches to multiresolution ....

[Article contains additional citation context not shown here]

F.C. JENG. -- Subsampling of Markov random fields. -- J. of Visual Com. and Image Representation, Vol. 3, No. 3 : pages 225--229, September 1992.

....from particular models and scale transformations [16] because of the loss of locality of the model at the coarse scales. In [26] Lakshmanan has shown that simple resolution transformations such as subsampling or block averaging also result in a loss of locality for Gaussian MRF models. Jeng [21] has studied the loss of locality in a periodic subsampling of MRF models with infinite support. Other approaches introduced recently aim at defining MRF models on hierarchical structures such as trees [3] 6] 28] or other pyramidal graph structures P EREZ AND HEITZ: RESTRICTION OF A MARKOV ....

.... minimal are derived. These general results may be applied to the different multiresolution approaches previously mentioned. Several special cases related to various multiresolution MRF based image analysis approaches are studied. This study generalizes and unifies in some sense the works of Jeng [21] and Lakshmanan [26] both devoted to the subsampling of MRF s. Lakshmanan [26] studies the subsampling of Gauss Markov random fields. The mathematical framework described here applies to general classes of nonlinear MRF s and handles several other approaches to multiresolution MRF modeling. In ....

[Article contains additional citation context not shown here]

F.C. Jeng, "Subsampling of Markov random fields," J. of Visual Com. and Image Representation, vol. 3, no. 3, pp. 225-229, 1992.

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