提出新型损失函数，提升部分形状匹配精度。
Wormhole Loss for Partial Shape Matching
- 基于测地距离与边界关系设计新匹配准则。
- 在多个数据集上实现当前最优匹配效果。
- 适合需要高精度形状匹配的研究者使用。
当匹配表面局部与整体时，核心问题在于：哪些点应纳入匹配过程？该问题在使用等距性度量相似性时尤为突出，因需验证两点间距离是否影响匹配。本文将表面视为带测地距离的流形，提出一种新准则，精细搜索点对间的内在一致性距离。该准则综合考虑点对间的测地距离、点与边界间的测地距离，以及嵌入空间中边界点的外在距离。相比以往方法更为宽松，作为损失函数用于训练部分形状匹配网络时，取得当前最优结果。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。