Point-wise Map Recovery and Refinement from Functional Correspondence

TL;DR

This paper presents a new probabilistic method for accurately recovering point-to-point correspondences from functional maps, even when shapes are not nearly-isometric, improving over existing approaches.

Contribution

It introduces a general, assumption-free approach for point-wise map recovery from functional maps, expanding applicability beyond nearly-isometric shapes.

Findings

Achieves significant accuracy improvements in challenging cases

Does not require shapes to be nearly-isometric

Provides an efficient recovery process

Abstract

Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape matching and image segmentation, to exploration of large shape collections. Despite the numerous advantages of such representation, however, the problem of converting a given functional map back to a point-to-point map has received a surprisingly limited interest. In this paper we analyze the general problem of point-wise map recovery from arbitrary functional maps. In doing so, we rule out many of the assumptions required by the currently established approach -- most notably, the limiting requirement of the input shapes being nearly-isometric. We devise an efficient recovery process based on a simple probabilistic model. Experiments confirm that this approach achieves remarkable accuracy improvements in very challenging cases.