A heavy tailed expectation maximization hidden markov random field model with applications to segmentation of MRI

Abstract

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposedmodel is a generalization of the widely used EM-HMRF algorithmwith Gaussian distributions.We test the α-stable EM-HMRFmodel in synthetic data and brainMRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI.