Relation Constrained Capsule Graph Neural Networks for Non-Rigid Shape Correspondence

Non-rigid 3D shape correspondence aims to establish dense correspondences between two non-rigidly deformed 3D shapes. However, the variability and symmetry of non-rigid shapes usually lead to mismatches due to shape deformation, topological changes, or data with severe noise. To finding an accurate correspondence between 3D dynamic shapes for the local deformation complexity, this article proposes a Relation Constrained Capsule Graph Network (RC-CGNet), which combines global and local features by encouraging the relation constraints between the embedding feature space and the input shape space based on the functional maps framework. Specifically, we design a Diffusion Graph Attention Network (DGANet) to segment the surface into parts with correct edge boundary between two regions. The Minimum Spanning Tree (MST) of geodesic curves among the singularities obtained from the segmented parts is added as relation constraints, which can compute isometric correspondences in both direct and symmetric directions. Besides that, the relation-and-attention constrained neural networks are designed to learn the shape correspondence via attention-aware CapsNet and functional maps under relation constraints. To improve the convergence speed and matching accuracy, we propose an optimized residual network structure based on the Nesterov Accelerated Gradient (NAG) to extract local features, and use graph convolution structure to extract global features. Moreover, a lightweight Gated Attention Module (GAM) is designed to fuse global and local features to obtain a richer feature representation. Since the capsule network has better spatial reasoning ability than the traditional convolutional neural network, our novel network architecture is a dual-route capsule network based on Routing Attention Fusion Block (RAFB), filtering low-discriminative capsules from a holistic view by exploiting geometric hierarchical relationships of semantic parts. Experiments on open datasets show that our method has excellent accuracy and wide adaptability.