  We introduce an unsupervised feature learning approach that embeds 3D shape
information into a single-view image representation. The main idea is a
self-supervised training objective that, given only a single 2D image, requires
all unseen views of the object to be predictable from learned features. We
implement this idea as an encoder-decoder convolutional neural network. The
network maps an input image of an unknown category and unknown viewpoint to a
latent space, from which a deconvolutional decoder can best "lift" the image to
its complete viewgrid showing the object from all viewing angles. Our
class-agnostic training procedure encourages the representation to capture
fundamental shape primitives and semantic regularities in a data-driven
manner---without manual semantic labels. Our results on two widely-used shape
datasets show 1) our approach successfully learns to perform "mental rotation"
even for objects unseen during training, and 2) the learned latent space is a
powerful representation for object recognition, outperforming several existing
unsupervised feature learning methods.
