Paper Info
Title
A Numerical Framework For Elastic Surface Matching, Comparison, And Interpolation
Abstract
Surface comparison and matching is a challenging problem in computer vision. While elastic Riemannian metrics provide meaningful shape distances and point correspondences via the geodesic boundary value problem, solving this problem numerically tends to be difficult. Square root normal fields considerably simplify the computation of certain distances between parametrized surfaces. Yet they leave open the issue of finding optimal reparametrizations, which induce corresponding distances between unparametrized surfaces. This issue has concentrated much effort in recent years and led to the development of several numerical frameworks. In this paper, we take an alternative approach which bypasses the direct estimation of reparametrizations: we relax the geodesic boundary constraint using an auxiliary parametrization-blind varifold fidelity metric. This reformulation has several notable benefits. By avoiding altogether the need for reparametrizations, it provides the flexibility to deal with simplicial meshes of arbitrary topologies and sampling patterns. Moreover, the problem lends itself to a coarse-to-fine multi-resolution implementation, which makes the algorithm scalable to large meshes. Furthermore, this approach extends readily to higher-order feature maps such as square root curvature fields and is also able to include surface textures in the matching problem. We demonstrate these advantages on several examples, synthetic and real.
Year
DOI
Venue
2021
10.1007/s11263-021-01476-6
INTERNATIONAL JOURNAL OF COMPUTER VISION
Keywords
DocType
Volume
Elastic shape analysis, Surfaces, Square root normal fields, Varifolds
Journal
129
Issue
ISSN
Citations 
8
0920-5691
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Martin Bauer15210.45
Nicolas Charon2689.78
Philipp Harms341.80
Hsi-Wei Hsieh400.34