Curve Matching with Applications in Medical Imaging
Provides computational tools for Riemannian shape analysis, benefiting medical imaging researchers studying biological shape variability.
The paper develops numerical methods for second-order Sobolev metrics on curve spaces, enabling geodesic computation and Karcher mean estimation, and applies them to analyze shape variation in HeLa cell nuclei and cardiac deformation cycles.
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of finding geodesics. These two methods are combined in a Riemannian gradient-based optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.