Subdivision-Based Mesh Convolution Networks

Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, the irregular structure of meshes makes it hard to exploit the power of CNNs directly. A subdivision surface provides a hierarchical multi-resolution structure, and each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two properties, this paper introduces a novel and flexible CNN framework, named SubdivNet, for 3D triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from adjacent faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g. variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we propose a spatial uniform pooling layer which merges four faces into one and an upsampling method which splits one face into four. As a result, many popular 2D CNN architectures can be readily adapted to processing 3D meshes. Meshes with arbitrary connectivity can be remeshed to hold Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Experiments on mesh classification, segmentation, correspondence, and retrieval from the real-world demonstrate the effectiveness and efficiency of SubdivNet.