Mesh representation by random walks has been shown to benefit deep learning. Randomness is indeed a powerful concept. However, it comes with a price—some walks might wander around non-characteristic regions of the mesh, which might be harmful to shape analysis, especially when only a few walks are utilized. We propose a novel walk-attention mechanism that leverages the fact that multiple walks are used for a single mesh representation. The key idea is that the walks may provide each other with information regarding the meaningful (attentive) features of the mesh. We utilize this mutual information to extract a single descriptor of the mesh. This differs from common attention mechanisms that use attention to improve the representation of each individual descriptor. Our approach achieves SOTA results for two basic 3D shape analysis tasks: classification and retrieval. Even a handful of walks along a mesh suffice for learning. Furthermore, our approach provides insight into mesh importance detection.

Most attempts to represent 3D shapes for deep learning have focused on volumetric grids, multi-view images and point clouds. In this paper we look at the most popular representation of 3D shapes in computer graphics---a triangular mesh---and ask how it can be utilized within deep learning. The few attempts to answer this question propose to adapt convolutions & pooling to suit Convolutional Neural Networks (CNNs). This paper proposes a very different approach, termed MeshWalker to learn the shape directly from a given mesh. The key idea is to represent the mesh by random walks along the surface, which "explore" the mesh's geometry and topology. Each walk is organized as a list of vertices, which in some manner imposes regularity on the mesh. The walk is fed into a Recurrent Neural Network (RNN) that "remembers" the history of the walk. We show that our approach achieves state-of-the-art results for two fundamental shape analysis tasks: shape classification and semantic segmentation. Furthermore, even a very small number of examples suffices for learning. This is highly important, since large datasets of meshes are difficult to acquire.