  Non-line-of-sight reconstruction (NLoS) is a novel indirect imaging modality
that aims to recover objects or scene parts outside the field of view from
measurements of light that is indirectly scattered off a directly visible,
diffuse wall. Despite recent advances in acquisition and reconstruction
techniques, the well-posedness of the problem at large, and the recoverability
of objects and their shapes in particular, remains an open question. The
commonly employed Fermat path criterion is rather conservative with this
regard, as it classifies some surfaces as unrecoverable, although they
contribute to the signal.
  In this paper, we use a simpler necessary criterion for an opaque surface
patch to be recoverable. Such piece of surface must be directly visible from
some point on the wall, and it must occlude the space behind itself. Inspired
by recent advances in neural implicit representations, we devise a new
representation and reconstruction technique for NLoS scenes that unifies the
treatment of recoverability with the reconstruction itself. Our approach, which
we validate on various synthetic and experimental datasets, exhibits
interesting properties. Unlike memory-inefficient volumetric representations,
ours allows to infer adaptively tessellated surfaces from time-of-flight
measurements of moderate resolution. It can further recover features beyond the
Fermat path criterion, and it is robust to significant amounts of
self-occlusion. We believe that this is the first time that these properties
have been achieved in one system that, as an additional benefit, is trainable
and hence suited for data-driven approaches.
