Differential evolution based variational Bayes inference for brain PET-CT image segmentation

The variational expectation maximization (VEM) algorithm has recently been increasingly used to replace the expectation maximization (EM) algorithm in Gaussian mixture model (GMM) based statistical image segmentation. However, the VEM algorithm, similar to its traditional counterpart, suffers from the sensitiveness to initializations, and hence is prone to be trapped into local minima. In this paper, we introduce the differential evolution (DE), which is a population-based global optimization approach, to the variational Bayes inference of posterior distributions, and thus propose the DE-VEM algorithm for the segmentation of gray matter, white matter, and cerebrospinal fluid in brain PET-CT images. By combining the advantages of both variational inference and evolutionary computing, this algorithm has the ability to avoid over-fitting and local convergence. To use the prior anatomical knowledge available for brain images, we also incorporate the spatial constraints derived from the probabilistic brain atlas into the segmentation process. We compare our algorithm to the VEM algorithm and the segmentation routine used in the statistical parametric mapping package in 27 clinical PET-CT studies. Our results show that the proposed algorithm can segment brain PET-CT images more accurately.