  Supervised 3D reconstruction has witnessed a significant progress through the
use of deep neural networks. However, this increase in performance requires
large scale annotations of 2D/3D data. In this paper, we explore inexpensive 2D
supervision as an alternative for expensive 3D CAD annotation. Specifically, we
use foreground masks as weak supervision through a raytrace pooling layer that
enables perspective projection and backpropagation. Additionally, since the 3D
reconstruction from masks is an ill posed problem, we propose to constrain the
3D reconstruction to the manifold of unlabeled realistic 3D shapes that match
mask observations. We demonstrate that learning a log-barrier solution to this
constrained optimization problem resembles the GAN objective, enabling the use
of existing tools for training GANs. We evaluate and analyze the manifold
constrained reconstruction on various datasets for single and multi-view
reconstruction of both synthetic and real images.
