We propose a novel unsupervised learning approach for non-rigid 3D shape matching. Our approach improves upon recent state-of-the art deep functional map methods and can be applied to a broad range of different challenging scenarios. Previous deep functional map methods mainly focus on feature extraction and aim exclusively at obtaining more expressive features for functional map computation. However, the importance of the functional map computation itself is often neglected and the relationship between the functional map and point-wise map is underexplored. In this paper, we systematically investigate the coupling relationship between the functional map from the functional map solver and the point-wise map based on feature similarity. To this end, we propose a self-adaptive functional map solver to adjust the functional map regularisation for different shape matching scenarios, together with a vertex-wise contrastive loss to obtain more discriminative features. Using different challenging datasets (including non-isometry, topological noise and partiality), we demonstrate that our method substantially outperforms previous state-of-the-art methods.

翻译：我们提出了一种新颖的无监督学习方法，用于非刚性三维形状匹配。该方法改进了近期基于深度函数映射的最前沿技术，并可应用于多种不同挑战性场景。以往的深度函数映射方法主要关注特征提取，致力于获取更具表达力的特征以用于函数映射计算。然而，函数映射计算本身的重要性常被忽略，且函数映射与逐点映射之间的关系尚未得到充分探索。本文系统研究了函数映射求解器得出的函数映射与基于特征相似性的逐点映射之间的耦合关系。为此，我们提出了一种自适应函数映射求解器，可根据不同形状匹配场景调整函数映射正则化，并结合顶点级对比损失来获取更具判别力的特征。通过使用包含非等距、拓扑噪声和局部性等多种挑战性数据集，我们证明该方法显著优于先前的最优方法。