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 proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI 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.
Highlights
The segmentation of brain magnetic resonance images (MRI) consist in the parcellation of the brain areas into their main tissue components: white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF)
We studied the improvement of the hidden Markov random field model with α-stable distributions over the HMRF assuming Gaussian which is usually considered in the literature
We test the hidden Markov random field model to perform the segmentation of a synthetic 3D image with impulsive α-stable noise
Summary
The segmentation of brain MRI consist in the parcellation of the brain areas into their main tissue components: white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). A wide range of segmentation approaches assumes that the distribution of the histogram of intensity for each brain tissue can be modeled using a Gaussian distribution or a mixture of Gaussians (Laidlaw et al, 1998; Ruan et al, 2000). Additional works using a Gaussian mixture model for describing the brain tissue histograms are Ashburner and Friston (2005), Greenspan et al (2006), Ashburner and Friston (2007), and Merisaari et al (2009). Da Silva (2009) presents a Markov chain sampling technique for exploring normal mixture models when the numbers of components are unknown. A Gaussian mixture model with more than three components is used to explain the three brain tissues: GM, WM, and CSF
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