  Implicit neural field generating signed distance field representations (SDFs)
of 3D shapes have shown remarkable progress in 3D shape reconstruction and
generation. We introduce a new paradigm for neural field representations of 3D
scenes; rather than characterizing surfaces as SDFs, we propose a
Poisson-inspired characterization for surfaces as indicator functions optimized
by neural fields. Crucially, for reconstruction of real scan data, the
indicator function representation enables simple and effective constraints
based on common range sensing inputs, which indicate empty space based on line
of sight. Such empty space information is intrinsic to the scanning process,
and incorporating this knowledge enables more accurate surface reconstruction.
We show that our approach demonstrates state-of-the-art reconstruction
performance on both synthetic and real scanned 3D scene data, with 9.5%
improvement in Chamfer distance over state of the art.
