Comparison of the trust-region and the expectation-maximization algorithm for the application of automatic liver segmentation

Automatic liver segmentation is a crucial step for aiding in liver surgery and in diagnosing liver pathologies. Its goal is to find the following anatomical structures: the liver vessels and segments, and the present lesions and tumors. Herein, we describe a liver segmentation algorithm based on the gray-level histogram of volumetric and dynamic contrast enhanced computer tomography images. We give a comparison of two optimization methods used to fit a Gaussian mixture model to the histogram: the trust-region and the expectation-maximization algorithm. We show that the trust-region algorithm behaves more robustly and gives promising segmentation results. The expectation-maximization algorithm requires very good model estimation and elimination of the histogram data outside the 3 range of the outermost Gaussians. Moreover, in some cases the expectation-maximization algorithm converges to a smoother, but less accurate solution.