Open and closed anatomical surface description via hemispherical area-preserving map

Abstract

Spherical harmonics, one of the most widely used basis functions for shape description, rely heavily on a spherical parameterization of the given surface. Additionally, spherical harmonics based 3D modeling works well only for closed surfaces, while many anatomical structures are hemisphere-like open objects. Therefore, it is more natural to have a hemisphere-based approach for their shape description. In this work, we propose a novel framework for the shape description of open and closed hemisphere-like surfaces. We first develop two hemispherical area-preserving parameterization methods for simply-connected open and closed surfaces respectively, and then utilize the hemispherical harmonics basis functions to yield an accurate representation of hemisphere-like anatomical surfaces. We assess the performance of the proposed framework for the shape description of human head. In particular, 60 hemispherical anatomical surfaces (20 closed brain surfaces, 20 closed skull surfaces, and 20 open scalp surfaces) constructed from human head MRI scans are utilized for this purpose. For the three types of surfaces, our framework achieves a significant improvement in the surface reconstruction accuracy by 75%, 80% and 50% respectively when compared to the spherical harmonics based approach. This suggests that our new shape description framework can facilitate the biomedical analysis of hemisphere-like anatomical objects.