A new statistical and Dirichlet integral framework applied to liver segmentation from volumetric CT images

Accurate liver segmentation from computed tomography (CT) images is problematic due to non-uniform density, weak boundaries and because there may be multiple liver tumors that have heterogeneous intensities in region(s) of interest (ROIs). So we propose a generalized energy framework that harnesses the statistical intensity approximation with image data on graphs. Our statistical energy term takes advantage of the mixture-of-mixtures Gaussian model to approximate the probability density distribution of the liver and background to better differentiate between the two. The probability density estimation can be combined with the spatial cohesion of the graph-based Dirichlet integral by using graph calculus. Matrix decomposition and differentiation are used to minimize our proposed energy functional. We tested our approach on 20 public high-contrast CT images with single and multiple liver tumors. Our method had an average dice similarity coefficient (DSC) of 93.75±1.29%, an average false positive (FP) rate of 9.43±3.52% and an average false negative (FN) rate of 3.48±1.48%. Our method outperformed the benchmark graph-based Random Walker algorithm (average DSC=81.97±4.09%, average FP rate 34.10±10.53%, and average FN rate 7.10±4.35%).