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.

本文介绍了SubdivNet，一个创新且多功能的卷积神经网络框架，用于具有Loop细分序列连接性的三维三角网格，其利用网格卷积算子从附近面收集局部特征，支持标准的2D卷积网络概念并应用于3D三角网格结构中，通过深度池化和上采样等方式可轻松调整2D CNN结构以处理3D mesh。

基于子网格的网格卷积网络