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Convolutional networks have been extremely successful for regular data structures such as 2D images and 3D voxel grids. The transposition to meshes is, however, not straight-forward due to their irregular structure. We explore how the dual, face-based representation of triangular meshes can be leveraged as a data structure for graph convolutional networks. In the dual mesh, each node (face) has a fixed number of neighbors, which makes the networks less susceptible to overfitting on the mesh topology, and also al-lows the use of input features that are naturally defined over faces, such as surface normals and face areas. We evaluate the dual approach on the shape correspondence task on theFaust human shape dataset and variants of it with differ-ent mesh topologies. Our experiments show that results of graph convolutional networks improve when defined over the dual rather than primal mesh. Moreover, our models that explicitly leverage the neighborhood regularity of dual meshes allow improving results further while being more robust to changes in the mesh topology.

Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. CNNs do not easily extend, however, to data that are not represented by regular grids, such as 3D shape meshes or other graph-structured data, to which traditional local convolution operators do not directly apply. To address this problem, we propose a novel graph-convolution operator to establish correspondences between filter weights and graph neighborhoods with arbitrary connectivity. The key novelty of our approach is that these correspondences are dynamically computed from features learned by the network, rather than relying on predefined static coordinates over the graph as in previous work. We obtain excellent experimental results that significantly improve over previous state-of-the-art shape correspondence results. This shows that our approach can learn effective shape representations from raw input coordinates, without relying on shape descriptors.