论文标题
量规模棱两可的网状CNN：几何图上的各向异性卷积
Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs
论文作者
论文摘要
定义网格卷积的一种常见方法是将其解释为图形，并应用图形卷积网络（GCN）。这样的GCN使用各向同性核，因此对顶点的相对方向不敏感，因此对整个网格的几何形状。我们提出了量规范的网状CNN，该网状CNN概括了GCN以施用各向异性量规元内核。由于所得的功能携带方向信息，因此我们引入了一个几何消息传递方案，该方案通过平行运输特征在网格边缘上定义。我们的实验验证了所提出的模型对常规GCN和其他方法的表达显着提高。
A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs). Such GCNs utilize isotropic kernels and are therefore insensitive to the relative orientation of vertices and thus to the geometry of the mesh as a whole. We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Since the resulting features carry orientation information, we introduce a geometric message passing scheme defined by parallel transporting features over mesh edges. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.
