Shape Analysis of Surfaces Using General Elastic Metrics

TL;DR

This paper introduces a new family of elastic metrics for surface shape analysis in 3D, providing a numerical framework for geodesic computation that generalizes existing methods like SRNF.

Contribution

It develops a generalized elastic metric framework for surfaces, enabling shape analysis invariant under rigid motions and reparametrizations, extending previous SRNF-based approaches.

Findings

Framework successfully computes geodesics between surfaces.

Generalized metrics include the SRNF metric as a special case.

Results demonstrate improved flexibility in shape analysis.

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.