  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.
