The Square Root Normal Field Distance and Unbalanced Optimal Transport
Differential Geometry
2022-02-22 v3
Abstract
This paper explores a novel connection between two areas: shape analysis of surfaces and unbalanced optimal transport. Specifically, we characterize the square root normal field (SRNF) shape distance as the pullback of the Wasserstein-Fisher-Rao (WFR) unbalanced optimal transport distance. In addition, we propose a new algorithm for computing the WFR distance and present numerical results that highlight the effectiveness of this algorithm. As a consequence of our results we obtain a precise method for computing the SRNF shape distance directly on piecewise linear surfaces and gain new insights about the degeneracy of this distance.
Keywords
Cite
@article{arxiv.2105.06510,
title = {The Square Root Normal Field Distance and Unbalanced Optimal Transport},
author = {Martin Bauer and Emmanuel Hartman and Eric Klassen},
journal= {arXiv preprint arXiv:2105.06510},
year = {2022}
}
Comments
36 pages, 6 figures, 1 table