A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification

Abstract

cation [6,7, 14, 15]. It is well known that multigrid methods can improve significantly the convergence rate and the In this paper, we are interested in massively parallel multiscale relaxation algorithms applied to image classification. quality of the final results of iterative relaxation techniques. It is well known that multigrid methods can improve signifi-There are many approaches in multigrid image segmencantly the convergence rate and the quality of the final results tation. A well known approach is the renormalization of iterative relaxation techniques. First, we present a classical group algorithm which is based on renormalization group multiscale model which consists of a label pyramid and a whole ideas from statistical physics. This technique has been observation field. The potential functions of coarser grids are adapted by Gidas [13] to image processing. The main adderived by simple computations. The optimization problem is vantage of the method is that it provides a mechanism for first solved at the higher scale by a parallel relaxation algorithm; relating the processing at different scales with one another. potentials, and hence one can use classical relaxation algorithms to minimize the energy at coarser grids. Unfortunately, such approximations are available only for certain then the next lower scale is initialized by a projection of the INTRODUCTIONsimple models, mainly in image restoration [13]. Another Markov random fields (MRF) have become more and interesting model has been proposed by Bouman and Shamore popular during the past few years in image processing piro [7]. This model consists of a label pyramid where each [1,5,8,9, 12, 27]. A good reason for this is that MRF level is causally dependent on the coarser layer above it. require less a priori information on the world model. On The model results in a new optimization criterium called the other hand, the local behavior of MRF allows for the sequential MAP estimate. This model yields to a noniteradevelopment of highly parallel algorithms in combinatorial tive segmentation algorithm and direct methods of parameoptimization problems.ter estimation. In this paper, we are interested in massively parallelThe basis of our approach is a consistent multiscale MRF multiscale relaxation algorithms applied to image classifi-model originally proposed by Heitz et al. in [14, 15] for motion analysis. Related models can also be found in [6] for texture segmentation and in [17] for image reconstruction. * This work has been partially funded by CNES (French Space This model consists of a label pyramid and a whole obser-

Multiscale Gaussian Graphical Models and Algorithms for Large-Scale Inference

“…We construct a pyramidal graphical model shown in Figure 1 (top) by placing the original field at the bottom of the hierarchy and introducing hidden variables at coarser scales. Unlike multigrid methods and the models considered in [2], the measurements are not replicated at coarser scales. We denote the coarsest scale in our pyramidal graph as Scale 1 and the finest scale as Scale M.…”

“…Other approaches, motivated by multigrid methods, use multiple-scale algorithms for computational efficiency but do not have consistent stochastic structures between different scales. These limitations have been recognized by a number of researchers, who consider models that incorporate both intra-and interscale interactions [1], [2]. However, due to the resulting model complexity, they either allow only a limited extension of multiscale trees or use computationally expensive methods such as simulated annealing to get solutions.…”

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

“…To address the problems associated with nonhierarchical models, multiscale MRF models were formulated and have been extensively discussed in the image processing literature (Bouman and Shapiro, 1994;Kato et al 1996Kato et al , 1999Laferté et al, 2000;Liang and Tjahjadi, 2006;Mignotte et al, 2000;Wilson and Li, 2003). In those hierarchical MRF models, there is a series of random fields at a range of scales or resolutions, and the random field at each scale depends only on the next coarser random field above it.…”

“…In our multiscale MRF model, the value of a site at a given scale depends not only on its parent in the layer above but also on its neighbors at the same scale. In this respect, our model is closely related to the models presented in (Kato et al 1996(Kato et al , 1999Mignotte et al, 2000;Wilson and Li, 2003). However, unlike the models described by these authors, we solve the statistical inference problem by means of a sequence of related multi-resolution problems rather than as a single problem representing the entire quadtree.…”

A Hierarchical Spatio-Temporal Markov Model for Improved Flood Mapping Using Multi-Temporal X-Band SAR Data

“…These models can be applied in a non-iterative way on simple regular structures of quadtrees [26][27][28][29][30][31] or on more complex, however still regular, trees which try to overcome the blockiness of the classification result that is related to the nonstationarity of MRFs on quadtrees [26,32].…”