Model parameter estimation and tissue mixture segmentation by a MAP-EM algorithm

Quantitative volumetric measurement and feature analysis for various clinical applications require image segmentation. Most important clinical features are derived from the borders of a region of interest, which reflects the shape characteristics and volumetric variation of the target. The partial volume (PV) effect renders a significant error for current hard segmentation which assigns a single tissue label to each image voxel. We have proposed an expectation-maximization (EM) framework for soft image segmentation which aims to quantify the tissue mixture percentages in each voxel. By imposing a priori Markov random field (MRF) penalty on the spatial distribution of each tissue mixture, the algorithm searches a maximum a posteriori (MAP) solution for the tissue model parameters of the given image and the tissue mixture percentages in each voxel. This work studied the sensitivity of the iterative MAP-EM algorithm to the initial estimate and the properties of its convergence for the estimation of the model parameters and tissue mixtures in the presence of noise. By computer simulations, it was found that the estimation of the model parameters is not sensitive to the parameters´ initial estimate (even with greater than 100% error) if the initial estimate of the tissue mixtures is within 10% error from the phantom values. The MRF penalty on the tissue mixture spatial distribution is necessary to ensure the convergence of the iterative tissue mixture estimation in the case of noise level proportional to mean (i.e., similar to Poisson noise). The noise level and initial estimate error are fully within practical conditions, demonstrating that the MAP-EM algorithm is potentially valid in practice. It provides a theoretical or deterministic solution to the PV effect, and its successful implementation could improve quantitative volumetric and feature analyses.