  Non-Rigid Structure from Motion (NRSfM) refers to the problem of
reconstructing cameras and the 3D point cloud of a non-rigid object from an
ensemble of images with 2D correspondences. Current NRSfM algorithms are
limited from two perspectives: (i) the number of images, and (ii) the type of
shape variability they can handle. These difficulties stem from the inherent
conflict between the condition of the system and the degrees of freedom needing
to be modeled -- which has hampered its practical utility for many applications
within vision. In this paper we propose a novel hierarchical sparse coding
model for NRSFM which can overcome (i) and (ii) to such an extent, that NRSFM
can be applied to problems in vision previously thought too ill posed. Our
approach is realized in practice as the training of an unsupervised deep neural
network (DNN) auto-encoder with a unique architecture that is able to
disentangle pose from 3D structure. Using modern deep learning computational
platforms allows us to solve NRSfM problems at an unprecedented scale and shape
complexity. Our approach has no 3D supervision, relying solely on 2D point
correspondences. Further, our approach is also able to handle missing/occluded
2D points without the need for matrix completion. Extensive experiments
demonstrate the impressive performance of our approach where we exhibit
superior precision and robustness against all available state-of-the-art works
in some instances by an order of magnitude. We further propose a new quality
measure (based on the network weights) which circumvents the need for 3D
ground-truth to ascertain the confidence we have in the reconstructability. We
believe our work to be a significant advance over state-of-the-art in NRSFM.
