Kernel Regression on Manifolds and Its Application to Modeling Disconnected Anatomic Structures

TL;DR

This paper introduces a unified statistical method using Laplace-Beltrami eigenfunctions for modeling noisy disconnected 3D anatomical structures, demonstrated on the growth analysis of the human hyoid bone.

Contribution

It proposes a novel kernel regression approach on manifolds for analyzing disconnected anatomical structures in medical imaging.

Findings

Detected significant age effects on parts of the hyoid bone

Successfully smoothed noisy 3D data with LB eigenfunctions

Applied method to characterize growth patterns

Abstract

We present a unified statistical approach to modeling disconnected 3D anatomical structures extracted from medical images. Due to image acquisition and preprocessing noises, it is expected the imaging data is noisy. The surface coordinates of the structures are regressed using the weighted linear combination of Laplace-Beltrami (LB) eigenfunctions to smooth out noisy data and perform statistical analysis. The method is applied in characterizing the 3D growth pattern of human hyoid bone between ages 0 and 20. We detected a significant age effect on localized parts of the hyoid bone.