A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI - Castillo-Barnes, Diego; Peis, Ignacio; Martínez-Murcia, Francisco J.; Segovia, Fermín; Illán, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Salas-Gonzalez, Diego (Frontiers in Neuroinformatics, 2017)
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 modelled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Grey 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) modelling the components using the alpha-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the alpha-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 neighbouring voxels in tomographic brain MRI.