Topology Constrained Shape Correspondence.

To better address the deformation and structural variation challenges inherently present in 3D shapes, researchers have shifted their focus from designing handcrafted point descriptors to learning point descriptors and their correspondences in a data-driven manner. Recent studies have developed deep neural networks for robust point descriptor and shape correspondence learning in consideration of local structural information. In this article, we developed a novel shape correspondence learning network, called TC-NET, which further enhances performance by encouraging the topological consistency between the embedding feature space and the input shape space. Specifically, in this article, we first calculate the topology-associated edge weights to represent the topological structure of each point. Then, in order to preserve this topological structure in high-dimensional feature space, a structural regularization term is defined to minimize the topology-consistent feature reconstruction loss (Topo-Loss) during the correspondence learning process. Our proposed method achieved state-of-the-art performance on three shape correspondence benchmark datasets. In addition, the proposed topology preservation concept can be easily generalized to other learning-based shape analysis tasks to regularize the topological structure of high-dimensional feature spaces.