Li Xiang, Wen Congcong, Wang Lingjing, Fang Yi
IEEE Trans Vis Comput Graph. 2021 Oct;27(10):3926-3937. doi: 10.1109/TVCG.2020.2994013. Epub 2021 Sep 1.
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.
为了更好地应对3D形状中固有的变形和结构变化挑战，研究人员已将重点从设计手工制作的点描述符转向以数据驱动的方式学习点描述符及其对应关系。最近的研究考虑到局部结构信息，开发了用于鲁棒点描述符和形状对应学习的深度神经网络。在本文中，我们开发了一种新颖的形状对应学习网络，称为TC-NET，它通过鼓励嵌入特征空间和输入形状空间之间的拓扑一致性来进一步提高性能。具体而言，在本文中，我们首先计算与拓扑相关的边权重以表示每个点的拓扑结构。然后，为了在高维特征空间中保留这种拓扑结构，定义了一个结构正则化项，以在对应学习过程中最小化拓扑一致的特征重建损失（Topo-Loss）。我们提出的方法在三个形状对应基准数据集上取得了领先的性能。此外，所提出的拓扑保留概念可以很容易地推广到其他基于学习的形状分析任务，以规范高维特征空间的拓扑结构。
