Local geometry-perceptive mesh convolution with multi-ring receptive field

Learning 3D mesh representation is necessary for many computer vision and graphic tasks. Recently, some works have studied convolution methods for directly processing input meshes. However, these methods are usually weak in extracting local geometry information because of the disadvantages such as isotropic filter, neglect of mesh topology, and a small convolution field. In this paper, we introduce a local geometry-perceptive mesh convolution, which pays attention to mesh irregular structures for efficiently capturing geometry features in a multi-ring receptive field. Specifically, we define each template node's dynamic neighbor-attention weights used in multiple attention aggregation operations for obtaining local mesh change information of different vertices in the multi-ring field. After each aggregation, a shared anisotropic filter maps the catenation of each new vertex and its neighbors for extracting geometry features of the current ring. Then, complete local geometry features of each vertex in its large local field are obtained by summing the mapped results of each aggregation. Moreover, the position features of each vertex are added to its local geometry features to get the final representation vector of the vertex. We demonstrate the proposed mesh convolution method's strong ability in modeling 3D mesh shapes.