Segmenting Images Analytically in Shape Space

Abstract

This paper presents a novel analytic technique to perform shape-driven segmentation. In our approach, shapes are represented using binary maps, and linear PCA is utilized to provide shape priors for segmentation. Intensity based probability distributions are then employed to convert a given test volume into a binary map representation, and a novel energy functional is proposed whose minimum can be analytically computed to obtain the desired segmentation in the shape space. We compare the proposed method with the log-likelihood based energy to elucidate some key differences. Our algorithm is applied to the segmentation of brain caudate nucleus and hippocampus from MRI data, which is of interest in the study of schizophrenia and Alzheimer's disease. Our validation (we compute the Hausdorff distance and the DICE coefficient between the automatic segmentation and ground-truth) shows that the proposed algorithm is very fast, requires no initialization and outperforms the log-likelihood based energy.