Invariant SPHARM Shape Descriptors for Complex Geometry in MR Region of Interest Analysis

In earlier work, we have shown the importance of including 3D shape characteristics when analyzing regions of interest (ROIs) in magnetic resonance imaging (MRI) data. Spherical harmonics (SPHARM) based ROI shape descriptors were proposed and shown to provide important complementary information to traditionally used simple volumetric ROI measures. In this paper we extend our SPHARM shape parameterization technique by using functions defined on concentric spherical shells. We then propose the use of a novel radial transform to obtain unique features even under independent rotations of the constituting shells. These enhanced features enable the analysis of 3D ROIs with complex topologies including those with possible disconnections (e.g. ventricles). We validate the proposed 3D shape descriptors on synthetic data and demonstrate their sensitivity to subtle shape changes in the presence of inter-subject variability. We also apply our approach to real MRI data and detect significant shape changes in the left and right thalamus in Parkinson´s disease (PD) patients when compared against normal volunteers, complementing the observed volumetric changes.