Convolutional neural networks (CNNs) have made great breakthroughs in 2D
computer vision. However, their irregular structure makes it hard to harness
the potential of CNNs directly on meshes. A subdivision surface provides a
hierarchical multi-resolution structure, in which each face in a closed
2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these
two observations, this paper presents SubdivNet, an innovative and versatile
CNN framework 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 nearby 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 make use of
pooling layers which uniformly merge four faces into one and an upsampling
method which splits one face into four. Thereby, many popular 2D CNN
architectures can be easily adapted to process 3D meshes. Meshes with arbitrary
connectivity can be remeshed to have Loop subdivision sequence connectivity via
self-parameterization, making SubdivNet a general approach. Extensive
evaluation and various applications demonstrate SubdivNet's effectiveness and
efficiency.

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。