Toward Mesh-Invariant 3D Generative Deep Learning with Geometric
  Measures
Thomas Besnier Sylvain Arguillère Emery Pierson Mohamed Daoudi
3D generative modeling is accelerating as the technology allowing the capture
of geometric data is developing. However, the acquired data is often
inconsistent, resulting in unregistered meshes or point clouds. Many generative
learning algorithms require correspondence between each point when comparing
the predicted shape and the target shape. We propose an architecture able to
cope with different parameterizations, even during the training phase. In
particular, our loss function is built upon a kernel-based metric over a
representation of meshes using geometric measures such as currents and
varifolds. The latter allows to implement an efficient dissimilarity measure
with many desirable properties such as robustness to resampling of the mesh or
point cloud. We demonstrate the efficiency and resilience of our model with a
generative learning task of human faces.