A tree-structured Markov random field model for bayesian image segmentation

Abstract

We present a new image segmentation algorithm based on a tree-structured binary MRF model. The image is recursively segmented in smaller and smaller regions until a stopping condition, local to each region, is met. Each elementary binary segmentation is obtained as the solution of a MAP estimation problem, with the region prior modeled as an MRF. Since only binary fields are used, and thanks to the tree structure, the algorithm is quite fast, and allows one to address the cluster validation problem in a seamless way. In addition, all field parameters are estimated locally, allowing for some spatial adaptivity. To improve segmentation accuracy, a split-and-merge procedure is also developed and a spatially adaptive MRF model is used. Numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on "flat" MRF models, and its performance, in terms of segmentation accuracy and map smoothness, is comparable or even superior.

A Hierarchical Finite-State Model for Texture Segmentation

“…Among all the possible choices we have selected for this purpose the tree-structured MRF (TS-MRF) model-based algorithm presented in [7,23] and briefly recalled here. This algorithm has several characteristics which are attractive in this context.…”

“…Due to the inherent high complexity of this model, which can be optimized by stochastic relaxation algorithms or other similar procedures, a faster algorithm for unsupervised image segmentation, which is based on "tree-structured" MRF modeling, has been developed in [7].…”

“…The growth of the tree, that is the choice of the node to be split from time to time is controlled by a test local to each node, namely the split gain, which accounts for the likelihood of the hypothesis of split of the corresponding node with respect to the hypothesis of non split of the same node, on the basis of the observed local test segmentation (see [7] for further details). Also, when all such tests on the current terminal leaves indicate to not split, the tree growth is stopped and the number of classes is automatically given by the number of leaves.…”

“…Eventually, the TS-MRF algorithm used here differs form the version presented in [7] in the way how the tree growth is controlled. In particular the split gain defined above does not contain an additional term, namely the prior probability p(x t ) (see [7]), which accounts for the shape regularity of the children regions but is unnecessary in this context. Also the growth is stopped when the required number of classes is reached and not when all gains are under a threshold.…”

“…Image segmentation [4,7,13,23] is a low-level processing which is of critical importance for many applications in several domains, like medical imaging, remote sensing, source coding, and so on. Although it has been widely studied in the last decades in many cases it remains still open, as for textured images, where the spatial interactions may cover long ranges asking for high order complex modeling.…”