Hippocampus shape analysis via skeletal models and kernel smoothing

Abstract

Skeletal representations ($s$-reps) have been successfully adopted to parsimoniously parametrize the shape of three-dimensional objects, and have been particularly employed in analyzing hippocampus shape variation. Within this context, we provide a fully-nonparametric dimension-reduction tool based on kernel smoothing for determining the main source of variability of hippocampus shapes parametrized by $s$-reps. The methodology introduces the so-called density ridges for data on the polysphere and involves addressing high-dimensional computational challenges. For the analyzed dataset, our model-free indexing of shape variability reveals that the spokes defining the sharpness of the elongated extremes of hippocampi concentrate the most variation among subjects.