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.

我们提出了一种用于非刚性 3D 形状匹配的新型无监督学习方法。通过改进最新的深度功能映射方法，我们的方法适用于广泛的不同挑战性场景。我们系统地研究了功能映射解算器生成的功能映射和基于特征相似性的逐点映射之间的耦合关系，并提出了一种自适应功能映射解算器和顶点级对比损失以获得更具区别性的特征。在包括非同构形变、拓扑噪声和部分性等不同挑战性数据集上，我们证明了我们的方法明显优于现有的最先进方法。