Most recent unsupervised non-rigid 3D shape matching methods are based on the functional map framework due to its efficiency and superior performance. Nevertheless, respective methods struggle to obtain spatially smooth pointwise correspondences due to the lack of proper regularisation. In this work, inspired by the success of message passing on graphs, we propose a synchronous diffusion process which we use as regularisation to achieve smoothness in non-rigid 3D shape matching problems. The intuition of synchronous diffusion is that diffusing the same input function on two different shapes results in consistent outputs. Using different challenging datasets, we demonstrate that our novel regularisation can substantially improve the state-of-the-art in shape matching, especially in the presence of topological noise.

翻译：当前大多数无监督非刚性三维形状匹配方法基于函数映射框架，因其高效性与优越性能。然而，由于缺乏适当的正则化，现有方法难以获得空间平滑的点对应关系。本研究受图神经网络中消息传递机制成功的启发，提出一种同步扩散过程，并将其作为正则化方法以实现非刚性三维形状匹配中的平滑性约束。同步扩散的核心思想是：在两个不同形状上对同一输入函数进行扩散将产生一致的输出结果。通过在多个具有挑战性的数据集上进行实验，我们证明所提出的新型正则化方法能够显著提升形状匹配领域的现有技术水平，尤其在存在拓扑噪声的情况下表现突出。