Wormhole Loss for Partial Shape Matching
This addresses the challenge of matching parts of surfaces to their whole in computer vision and graphics, with incremental improvements over prior methods.
The paper tackles the problem of partial shape matching by introducing a novel criterion that leverages intrinsic geodesic distances, distances to boundaries, and extrinsic boundary distances to search for consistent point pairs, achieving state-of-the-art results when used as a loss function in training networks.
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.