This paper investigated the problem of image modeling and segmentation using random field models. The paper presented the MLL(multi-level logistic) model, the auto-binomial model, and the GMRF(Gaussian Markov random field) model which are commonly used in image processing, and the characteristics of these models were examined. CM(Coding method), pseudo-likelihood maximization, and minimizing the sum of square errors were shown to estimate the parameters of the above models for various synthesized and natural texture images. For image segmentation, a doubly stochastic or hierarchical model was presented and applied to the segmentation of noisy images and textured images. This paper investigated the problem of phase transition phenomena appearing in the random field model-based image processing. The phase transition problem makes it difficult to realize images which consist of moderate-to-large scale regions. It also gives a negative effect on image segmentation and degrades segmentation performance. To solve the problems we proposed a Gibbs random field model whose energy function consists of interaction energy and magnetic energy between the neighbor pixels. It is shown that the proposed model can realize images having moderate-size clusters (or regions) and that the size of clusters can be controlled by the weighting factor between the two energy terms. The proposed model and the 2nd order neighborhood MLL model were applied to the segmenting binary and 4-level geometric images corrupted by additive Gaussian noise of three different levels. Both the models gave good results in the case of SNR=1. However, for the case of the very low SNR of 2/3 or 1/2, the proposed model turned out to be better.
