Wormhole Loss for Partial Shape Matching

TL;DR

This paper introduces a novel loss function based on geodesic and extrinsic distances to improve partial shape matching, achieving state-of-the-art results by effectively handling surface point correspondence challenges.

Contribution

It proposes a new criterion for consistent distance measurement that enhances partial shape matching by considering intrinsic and extrinsic surface distances.

Findings

Achieves state-of-the-art accuracy in partial shape matching tasks.

The new loss function outperforms previous measures in experiments.

Provides a less restrictive criterion for surface point correspondence.

Abstract

When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of whether distances measured between pairs of surface points should influence the matching process. The approach we propose treats surfaces as manifolds equipped with geodesic distances, and addresses the partial shape matching challenge by introducing a novel criterion to meticulously search for consistent distances between pairs of points. The new criterion explores the relation between intrinsic geodesic distances between the points, geodesic distances between the points and surface boundaries, and extrinsic distances between boundary points measured in the embedding space. It is shown to be less restrictive compared to previous measures and achieves state-of-the-art results when used as a loss function in training networks for partial shape matching.