  We introduce visual deprojection: the task of recovering an image or video
that has been collapsed along a dimension. Projections arise in various
contexts, such as long-exposure photography, where a dynamic scene is collapsed
in time to produce a motion-blurred image, and corner cameras, where reflected
light from a scene is collapsed along a spatial dimension because of an edge
occluder to yield a 1D video. Deprojection is ill-posed-- often there are many
plausible solutions for a given input. We first propose a probabilistic model
capturing the ambiguity of the task. We then present a variational inference
strategy using convolutional neural networks as functional approximators.
Sampling from the inference network at test time yields plausible candidates
from the distribution of original signals that are consistent with a given
input projection. We evaluate the method on several datasets for both spatial
and temporal deprojection tasks. We first demonstrate the method can recover
human gait videos and face images from spatial projections, and then show that
it can recover videos of moving digits from dramatically motion-blurred images
obtained via temporal projection.
