  Recent works have demonstrated non-line of sight (NLOS) reconstruction by
using the time-resolved signal frommultiply scattered light. These works
combine ultrafast imaging systems with computation, which back-projects the
recorded space-time signal to build a probabilistic map of the hidden geometry.
Unfortunately, this computation is slow, becoming a bottleneck as the imaging
technology improves. In this work, we propose a new back-projection technique
for NLOS reconstruction, which is up to a thousand times faster than previous
work, with almost no quality loss. We base on the observation that the hidden
geometry probability map can be built as the intersection of the three-bounce
space-time manifolds defined by the light illuminating the hidden geometry and
the visible point receiving the scattered light from such hidden geometry. This
allows us to pose the reconstruction of the hidden geometry as the voxelization
of these space-time manifolds, which has lower theoretic complexity and is
easily implementable in the GPU. We demonstrate the efficiency and quality of
our technique compared against previous methods in both captured and synthetic
data
