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Hidden Markov Random Field Model and Segmentation of Brain MR Images

FMRIB Technical Report TR00YZ1
(A related paper has been submitted to IEEE Trans. Medical Imaging)

Yongyue Zhang, Stephen Smith, and Michael Brady

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK


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; unfortunately, this is often not the the case due to artifacts such as partial volume effect and bias field distortion. Under such conditions, FM model-based methods produce unreliable results. 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. Although MRF modelling has been employed in MR image segmentation by other researchers, most reported methods are limited to using MRF as a general prior in an FM model-based approach. Moreover, they either lack a proper parameter estimation step to fit the FM model [14,16] or the parameter estimation procedure they use, such as ML or EM [33,27,20], suffers greatly from the limitation of the FM model mentioned above. 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 a HMRF-EM framework, an accurate and robust segmentation can be achieved. Moreover, the HMRF-EM framework can easily be combined with other techniques. As an example, we show how the bias field correction algorithm of Guillemaud and Brady [13] can be incorporated into this framework. A three-dimensional fully automated approach for brain MR image segmentation is achieved and significant improvement is obtained compared to the Guillemaud-Brady algorithm.

Keywords: MRI, Segmentation, Hidden Markov Random Field, HMRF, Expectation-Maximization, Bias Field Correction.

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Yongyue Zhang