Varifold-based matching of curves via Sobolev-type Riemannian metrics
Provides a new computational strategy for shape analysis of curves, relevant to researchers in geometric shape matching and computational anatomy.
The paper combines second-order Sobolev metrics with varifold-based inexact matching to compute geodesics between unparametrized curves, demonstrating the method on mosquito wing shapes and comparing it to LDDMM curve matching.
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.