  Polygonal meshes provide an efficient representation for 3D shapes. They
explicitly capture both shape surface and topology, and leverage non-uniformity
to represent large flat regions as well as sharp, intricate features. This
non-uniformity and irregularity, however, inhibits mesh analysis efforts using
neural networks that combine convolution and pooling operations. In this paper,
we utilize the unique properties of the mesh for a direct analysis of 3D shapes
using MeshCNN, a convolutional neural network designed specifically for
triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized
convolution and pooling layers that operate on the mesh edges, by leveraging
their intrinsic geodesic connections. Convolutions are applied on edges and the
four edges of their incident triangles, and pooling is applied via an edge
collapse operation that retains surface topology, thereby, generating new mesh
connectivity for the subsequent convolutions. MeshCNN learns which edges to
collapse, thus forming a task-driven process where the network exposes and
expands the important features while discarding the redundant ones. We
demonstrate the effectiveness of our task-driven pooling on various learning
tasks applied to 3D meshes.
