Analysis of AneuRisk65 data: Elastic shape registration of curves

Abstract

Shapes of carotid arteries are analyzed here as elastic curves under the framework introduced in [2]. Using a mathematical representation of parameterized curves, termed square-root velocity function (SRVF), in conjunction with an elastic Riemannian metric, the framework provides (1) parameterization-invariant shape metrics for comparing curves, (2) simultaneous registration of coordinate functions across curves, and (3) computation of statistical summaries and models of shapes of given curves. The method is applicable to curves in $\mathbb{R} ^{n}$ for $n\geq1$. Thus, we study the shapes and alignments of carotid arteries using their 3D coordinates and other geometric properties along the curves, such as radii and curvatures. The results show a significant improvement in curve alignments, leading to a compact phase-amplitude PCA representation and modeling of artery data.