Bayesian pixel classification using spatially variant finite mixtures and the generalized EM algorithm

TLDR

Gaussian densities are commonly used for simplicity, though the algorithm can be adapted to other component models. The study proposes a spatially variant finite mixture model for pixel labeling and image segmentation. For spatially varying Gaussian mixtures with unknown means and variances, an EM algorithm is derived for maximum‑likelihood estimation of pixel labels and mixture parameters, and a generalized EM algorithm incorporating a prior density and gradient projection is developed, yielding a grouped coordinate ascent scheme. The algorithm’s accuracy was quantified by Monte Carlo simulation and qualitatively validated on CT and MRI images.

Abstract

A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).