提出高效算法实现3D形状间全局最优且几何一致的匹配。
Fast Globally Optimal and Geometrically Consistent 3D Shape Matching
- 用循环路径表示源形表面，构建超图建模匹配问题。
- 将匹配转化为最小代价流问题，保证全局最优与几何一致性。
- 适用于纹理映射、统计建模等场景，对初值不敏感。
几何一致性（即邻域关系的保持）是3D形状匹配中自然且强大的先验。几何一致的匹配对纹理转移、统计形状建模等下游任务至关重要。然而实际中，几何一致性常被忽略，或仅在严格假设下实现（如良好初始化）。本文提出一种新形式化方法，可高效计算3D形状间的全局最优且几何一致匹配。核心思想是将源形状表面表示为一组循环路径，并将其一致地匹配到目标形状。数学上，构建源与目标形状之间的超积图，将3D形状匹配转化为该超图上的最小代价循环流问题，从而获得全局几何一致的匹配结果。实验表明，该方法可高效求解，且生成高质量匹配。
原文摘要 · Abstract (English)
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical shape modelling. Yet, in practice, geometric consistency is often overlooked, or only achieved under severely limiting assumptions (e.g. a good initialisation). In this work, we propose a novel formalism for computing globally optimal and geometrically consistent matchings between 3D shapes which is scalable in practice. Our key idea is to represent the surface of the source shape as a collection of cyclic paths, which are then consistently matched to the target shape. Mathematically, we construct a hyper product graph (between source and target shape), and then cast 3D shape matching as a minimum-cost circulation flow problem in this hyper graph, which yields global geometrically consistent matchings between both shapes. We empirically show that our formalism is efficiently solvable and that it leads to high-quality results.
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