The approach presented in this paper was intended for extending conventional Markov random field (MRF) models to a more practical problem: the unsupervised and adaptive segmentation of gray-level images. The "unsupervised" segmentation means that all the model parameters, including the number of image classes, are unknown and have to be estimated from the observed image. In addition, the "adaptive" segmentation means that both the region distribution and the image feature within a region are all location-dependent and their corresponding parameters must be estimated from location to location. We estimated local parameters independently from multiple small windows under the assumption that an observed image consists of objects with smooth surfaces, no texture. Due to this assumption, the intensity of each region is a slowly varying function plus noise, and the conventional homogeneous hidden MRF (HMRF) models are appropriate for these windows. In each window, we employed the EM algorithm for maximum-likelihood (ML) parameter estimation, and then, the estimated parameters were used for "maximizer of the posterior marginals" (MPM) segmentation. To keep continuous segments between windows, a scheme for combining window fragments was proposed. The scheme comprises two parts: the programming of windows and the Bayesian merging of window fragments. Finally, a remerging procedure is used as post processing to remove the over-segmented small regions that possibly exist after the Bayesian merging. Since the final segments are obtained from merging, the number of image classes is automatically determined. The use of multiple parallel windows makes our algorithm to be suitable for parallel implementation. The experimental results of real-world images showed that the surfaces (objects) consistent with our reasonable model assumptions were all correctly segmented as connected regions.

The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.