Primal-Dual Mesh Convolutional Neural Networks

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution --and sometimes pooling-- operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input, and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion.