  Mesh autoencoders are commonly used for dimensionality reduction, sampling
and mesh modeling. We propose a general-purpose DEep MEsh Autoencoder (DEMEA)
which adds a novel embedded deformation layer to a graph-convolutional mesh
autoencoder. The embedded deformation layer (EDL) is a differentiable
deformable geometric proxy which explicitly models point displacements of
non-rigid deformations in a lower dimensional space and serves as a local
rigidity regularizer. DEMEA decouples the parameterization of the deformation
from the final mesh resolution since the deformation is defined over a lower
dimensional embedded deformation graph. We perform a large-scale study on four
different datasets of deformable objects. Reasoning about the local rigidity of
meshes using EDL allows us to achieve higher-quality results for highly
deformable objects, compared to directly regressing vertex positions. We
demonstrate multiple applications of DEMEA, including non-rigid 3D
reconstruction from depth and shading cues, non-rigid surface tracking, as well
as the transfer of deformations over different meshes.
