  We propose a method to learn 3D deformable object categories from raw
single-view images, without external supervision. The method is based on an
autoencoder that factors each input image into depth, albedo, viewpoint and
illumination. In order to disentangle these components without supervision, we
use the fact that many object categories have, at least in principle, a
symmetric structure. We show that reasoning about illumination allows us to
exploit the underlying object symmetry even if the appearance is not symmetric
due to shading. Furthermore, we model objects that are probably, but not
certainly, symmetric by predicting a symmetry probability map, learned
end-to-end with the other components of the model. Our experiments show that
this method can recover very accurately the 3D shape of human faces, cat faces
and cars from single-view images, without any supervision or a prior shape
model. On benchmarks, we demonstrate superior accuracy compared to another
method that uses supervision at the level of 2D image correspondences.
