Primal-Dual Mesh Convolutional Neural Networks
This work addresses limitations in geometric deep learning for 3D mesh processing, offering a method that combines graph-based and mesh-specific approaches to improve feature aggregation and downsampling.
The paper tackles the problem of performing inference on 3D triangle meshes by proposing a primal-dual mesh convolutional neural network that dynamically aggregates features using attention and includes a geometrically interpretable pooling operation, achieving comparable or superior performance in shape classification and segmentation tasks.
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.