The matching of 3D shapes has been extensively studied for shapes represented as surface meshes, as well as for shapes represented as point clouds. While point clouds are a common representation of raw real-world 3D data (e.g. from laser scanners), meshes encode rich and expressive topological information, but their creation typically requires some form of (often manual) curation. In turn, methods that purely rely on point clouds are unable to meet the matching quality of mesh-based methods that utilise the additional topological structure. In this work we close this gap by introducing a self-supervised multimodal learning strategy that combines mesh-based functional map regularisation with a contrastive loss that couples mesh and point cloud data. Our shape matching approach allows to obtain intramodal correspondences for triangle meshes, complete point clouds, and partially observed point clouds, as well as correspondences across these data modalities. We demonstrate that our method achieves state-of-the-art results on several challenging benchmark datasets even in comparison to recent supervised methods, and that our method reaches previously unseen cross-dataset generalisation ability.

翻译：三维形状匹配问题已在以表面网格和点云表示的形状上得到广泛研究。尽管点云是原始真实三维数据（如激光扫描仪数据）的常见表示形式，网格编码了丰富且富有表现力的拓扑信息，但其创建通常需要某种形式（往往需人工）的干预。相应地，纯依赖点云的方法无法达到利用额外拓扑结构的基于网格的方法的匹配质量。本研究通过引入一种自监督多模态学习策略来弥合这一差距，该策略将基于网格的函数映射正则化与耦合网格和点云数据的对比损失相结合。我们的形状匹配方法能够获得三角形网格、完整点云和部分观测点云内的模态内对应关系，以及跨这些数据模态的对应关系。我们证明，即使在近期有监督方法的对比下，该方法在多个具有挑战性的基准数据集上仍能达到最优结果，并且实现了前所未有的跨数据集泛化能力。