Hierarchical Markov Random Field Research Articles

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

In this paper, we are interested in massively parallel multiscale relaxation algorithms applied to image classification. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. First, we present a classical multiscale model which consists of a label pyramid and a whole observation field. The potential functions of coarser grids are derived by simple computations. The optimization problem is first solved at the higher scale by a parallel relaxation algorithm; then the next lower scale is initialized by a projection of the result. Second, we propose a hierarchical Markov random field model based on this classical model. We introduce new interactions between neighbor levels in the pyramid. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price. This model results in a relaxation algorithm with a new annealing scheme: the multitemperature annealing (MTA) scheme, which consists of associating higher temperatures to higher levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalization of the annealing theorem of S. Geman and D. Geman (IEEE Trans. Pattern Anal. Mach. Intell.6, 1984, 721–741).

Data‐driven segmentation of textured images using hierarchical markov random fields

AbstractThis paper proposes an algorithm for a data‐driven segmentation of an image consisting of multiple textures. The method uses hierarchical Markov random fields (MRF) consisting of two layers: the first layer MRF representing invisible regional images; and the second layer MRF representing a different texture in each region. This method is based on the EM algorithm for estimating the maximum likelihood of incomplete data, to treat invisible regional processes. The algorithm repeats an estimation of the MRF parameters and a segmentation (estimation of region processes). The former is carried out by maximizing a pseu‐dolikelihood function; the latter is carried out by applying [the deterministic iterative relaxation algorithm] (developed by the authors) to the textured images. The proposed algorithm has been confirmed successfully by computer simulations using artificially composed textures.

Image classification using spectral and spatial information based on MRF models

A new criterion for classifying multispectral remote sensing images or textured images by using spectral and spatial information is proposed. The images are modeled with a hierarchical Markov Random Field (MRF) model that consists of the observed intensity process and the hidden class label process. The class labels are estimated according to the maximum a posteriori (MAP) criterion, but some reasonable approximations are used to reduce the computational load. A stepwise classification algorithm is derived and is confirmed by simulation and experimental results.

Texture segmentation based on a hierarchical Markov random field model

This paper presents a new texture segmentation technique for both supervised and unsupervised segmentation. The textured images under study are modeled by a proposed hierarchical Markov random field (MRF) model. This model is formed by combining the binomial model for textures and the multi-level logistic model for region distributions. The supervised segmentation is achieved by a new algorithm which can reach the global maxima of the posteriori distribution even if the textures are modeled by an MRF model. For unsupervised segmentation, a new parameter estimation scheme is proposed to estimate the model parameters directly from a given image. The new technique is verified by a variety of textured images, such as synthesized textures, natural textures and aerial images, in both supervised and unsupervised segmentation cases.