Varifold-based matching of curves via Sobolev-type Riemannian metrics

TL;DR

This paper introduces a novel approach combining second order Sobolev metrics with varifold-based inexact matching to compute geodesics between unparametrized curves, demonstrated on mosquito wings and compared to LDDMM.

Contribution

It presents a new method integrating Sobolev metrics with varifold-based matching for shape analysis of curves, enhancing geodesic computation accuracy.

Findings

Effective in matching unparametrized curves

Demonstrates improved geodesic computation

Applicable to biological shape analysis

Abstract

Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, apply it to study the shape of mosquito wings and compare our method to curve matching in the LDDMM framework.