Hidden Markov random field model for segmentation of brain MR images
Zhang Y., Brady M., Smith S.
The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain MR images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation - no spatial information is taken into account. This causes the FM model to work only on well-defined images with low noise level. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a Markov random field whose state sequence cannot be observed directly but which can be observed through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighbouring sites. To fit the HMRF model, an expectation-maximization (EM) algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into an HMRF-EM framework, an accurate and robust segmentation can be achieved, which is demonstrated by comparison experiments with the FM model-based segmentation.