Primal-Dual Mesh Convolutional Neural Networks

TL;DR

This paper introduces a novel primal-dual mesh convolutional neural network that effectively captures local topology and geometric properties of 3D meshes, improving shape classification and segmentation tasks.

Contribution

It extends primal-dual graph neural network frameworks to triangle meshes, incorporating attention-based feature aggregation and a geometrically interpretable pooling operation.

Findings

Achieves comparable or superior performance to state-of-the-art methods.

Provides theoretical insights using mesh-simplification tools.

Effectively handles variations in mesh connectivity.

Abstract

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. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.