A Numerical Framework for Elastic Surface Matching, Comparison, and Interpolation

Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances point correspondences via the geodesic boundary value problem, solving this numerically tends to be difficult. Square root normal fields (SRNF) considerably simplify computation of certain between parametrized surfaces. Yet they leave open issue finding optimal reparametrizations, which induce unparametrized This has concentrated much effort recent years led development several numerical frameworks. In paper, we take an alternative approach bypasses direct estimation reparametrizations: relax constraint using auxiliary parametrization-blind varifold fidelity metric. reformulation notable benefits. By avoiding altogether need for it provides flexibility deal with simplicial meshes arbitrary topologies sampling patterns. Moreover, lends itself coarse-to-fine multi-resolution implementation, makes algorithm scalable large meshes. Furthermore, extends readily higher-order feature maps such as square curvature also able include surface textures problem. We demonstrate these advantages on examples, synthetic real.