  One of the key challenges of visual perception is to extract abstract models
of 3D objects and object categories from visual measurements, which are
affected by complex nuisance factors such as viewpoint, occlusion, motion, and
deformations. Starting from the recent idea of viewpoint factorization, we
propose a new approach that, given a large number of images of an object and no
other supervision, can extract a dense object-centric coordinate frame. This
coordinate frame is invariant to deformations of the images and comes with a
dense equivariant labelling neural network that can map image pixels to their
corresponding object coordinates. We demonstrate the applicability of this
method to simple articulated objects and deformable objects such as human
faces, learning embeddings from random synthetic transformations or optical
flow correspondences, all without any manual supervision.
