Statistical Shape Analysis of Brain Structures

Abstract

The purpose of this work is to study structural differences of the left hippocampus between patients with Parkinson's disease (PD) and healthy control group (CG) based on shape models like skeletal representation (s-rep) and spherical harmonics point distribution model (SPHARM-PDM). We apply a permutation test on the s-reps of CG and PD to detect significant differences between the means of their geometric object properties (GOPs). We also introduce a parametric test for s-rep, constructed on multivariate Hotelling's T2 test. We discuss different methods of alignment, their impact on the result, and propose the elimination algorithm to have an adequate alignment. To make the test independent from the alignment, we propose a method according to distance matrices. We explain possible approaches to define mean and variation of directional data, including principal nested spheres (PNS), and principal geodesic analysis (PGA). Besides, we propose a non-linear PGA (NLPGA) on rotating tangent space of the unit sphere. Finally, we discuss the results of the hypothesis tests and show there are statistically significant differences between PD and CG.