面向拓扑噪声三维形状匹配的快速马尔可夫随机场优化
Fast Markov Random Field Optimisation for Topologically Noisy 3D Shape Matching
把非刚性形状匹配写成三角形级多标签 MRF，并用定制化的 alpha expansion 在保留近似保证的前提下大幅加速，为处理带拓扑噪声（亏格变化）的网格匹配提供了一个可直接复用的优化框架。
原文依据 we cast non-rigid 3D shape matching as a multi-labelling problem in which each triangle of the source shape is assigned a label
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论在非刚性形状匹配的许多实际应用中，形状会受到拓扑噪声的影响（即亏格发生变化）。本文提出一种基于马尔可夫随机场（MRF）的新形式化方法，能够处理这类带有拓扑噪声的情形。我们的优化问题的解可以通过 alpha 扩展算法高效近似，且该算法具有理论上的近似保证。具体而言，我们将非刚性三维形状匹配建模为一个多标签问题，其中源形状的每个三角形被赋予一个标签，该标签表示其与目标形状上某个特定表面元素的匹配关系。我们提出一种新的成对项，使匹配更倾向于源形状上相邻三角形在目标形状上仍保持接近的解。此外，通过利用标签空间的特定结构，我们证明可以对 alpha 扩展算法进行定制化改造，从而在保持其近似保证的同时实现显著的加速。我们在多个形状匹配数据集上评估了本方法，包括形状带有拓扑伪影的设置。
英文原文摘要 1147 字符
In many real-world applications of non-rigid shape matching, the shapes are subject to topological noise (i.e. varying genus). In this paper, we propose a novel formulation based on Markov Random Fields (MRF) that can handle these cases with topological noise. The solutions to our optimisation problem can be approximated efficiently using the alpha expansion algorithm, which comes with theoretical approximation guarantees. In particular, we cast non-rigid 3D shape matching as a multi-labelling problem in which each triangle of the source shape is assigned a label that represents the matching to a specific surface element on the target shape. We propose a novel pairwise term that imposes that our matching prefers solutions in which neighbouring triangles on the source shape remain close on the target shape. Further, by exploiting the specific structure of our label space, we show that the alpha expansion algorithm can be customised to achieve significant speed-ups, while maintaining its approximation guarantees. We evaluate our method on various shape matching datasets including settings in which shapes have topological artefacts.