Representation learning of 3D meshes using an Autoencoder in the spectral domain

Learning on surfaces is a difficult task: the data being non-Euclidean makes the transfer of known techniques such as convolutions and pooling non trivial. Common methods deploy processes to apply deep learning operations to triangular meshes either in the spatial domain by defining weights between nodes, or in the spectral domain using first order Chebyshev polynomials followed by a return in the spatial domain. In this study, we present a Spectral Autoencoder (SAE) enabling the application of deep learning techniques to 3D meshes by directly giving spectral coefficients obtained with a spectral transform as inputs. With a dataset composed of surfaces having the same connectivity, it is possible with the Graph Laplacian to express the geometry of all samples in the frequency domain. Then, by using an Autoencoder architecture, we are able to extract important features from spectral coefficients without going back to the spatial domain. Finally, a latent space is built from which reconstruction and interpolation is possible. This method allows the treatment of meshes with more vertices by keeping the same architecture, and allows to learn on big datasets with short computation times. Through experiments, we demonstrate that this architecture is able to give better results than state of the art methods in a faster way.