A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI

• Published in: Frontiers in neuroinformatics Vol. 11; p. 66
• Main Authors: Castillo-Barnes, Diego, Peis, Ignacio, Martínez-Murcia, Francisco J., Segovia, Fermín, Illán, Ignacio A., Górriz, Juan M., Ramírez, Javier, Salas-Gonzalez, Diego
• Format: Journal Article
• Language: English
• Published: Switzerland Frontiers Research Foundation 21.11.2017; Frontiers Media S.A
• Subjects: Brain research; brain tissue segmentation; gray matter; hidden Markov random fields; Image processing; magnetic resonance image; Magnetic resonance imaging; Markov analysis; Mathematical models; Neuroscience; Normal distribution; Random variables; Segmentation; Substantia alba; Substantia grisea; white matter; α-stable distribution; Spain; brain tissue segmentation; magnetic resonance image; white matter; α-stable distribution; gray matter; hidden Markov random fields
• ISSN: 1662-5196; 1662-5196
• DOI: 10.3389/fninf.2017.00066

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.