Shape Analysis of Surfaces Using General Elastic Metrics
Abstract
In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence it induces a metric on the "shape space" of surfaces. This new class of metrics generalizes a previously studied family of elastic metrics and includes in particular the Square Root Normal Function (SRNF) metric, which has been proven successful in various applications. We demonstrate our framework by showing several examples of geodesics and compare our results with earlier results obtained from the SRNF framework.
Cite
@article{arxiv.1910.02045,
title = {Shape Analysis of Surfaces Using General Elastic Metrics},
author = {Zhe Su and Martin Bauer and Stephen C. Preston and Hamid Laga and Eric Klassen},
journal= {arXiv preprint arXiv:1910.02045},
year = {2019}
}
Comments
18 pages, 10 figures (Corrected referenced equation numbers in v2)