Parameterization of the distribution of white and grey matter in MRI using the αα-stable distribution

This work presents a study of the distribution of the grey matter (GM) and white matter (WM) in brain magnetic resonance imaging (MRI). The distribution of GM and WM is characterized using a mixture of αα-stable distributions. A Bayesian αα-stable mixture model for histogram data is presented and unknown parameters are sampled using the Metropolis–Hastings algorithm. The proposed methodology is tested in 18 real images from the MRI brain segmentation repository. The GM and WM distributions are accurately estimated. The αα-stable distribution mixture model presented in this paper can be used as previous step in more complex MRI segmentation procedures using spatial information. Furthermore, due to the fact that the αα-stable distribution is a generalization of the Gaussian distribution, the proposed methodology can be applied instead of the Gaussian mixture model, which is widely used in segmentation of brain MRI in the literature.