  Neural volume rendering became increasingly popular recently due to its
success in synthesizing novel views of a scene from a sparse set of input
images. So far, the geometry learned by neural volume rendering techniques was
modeled using a generic density function. Furthermore, the geometry itself was
extracted using an arbitrary level set of the density function leading to a
noisy, often low fidelity reconstruction. The goal of this paper is to improve
geometry representation and reconstruction in neural volume rendering. We
achieve that by modeling the volume density as a function of the geometry. This
is in contrast to previous work modeling the geometry as a function of the
volume density. In more detail, we define the volume density function as
Laplace's cumulative distribution function (CDF) applied to a signed distance
function (SDF) representation. This simple density representation has three
benefits: (i) it provides a useful inductive bias to the geometry learned in
the neural volume rendering process; (ii) it facilitates a bound on the opacity
approximation error, leading to an accurate sampling of the viewing ray.
Accurate sampling is important to provide a precise coupling of geometry and
radiance; and (iii) it allows efficient unsupervised disentanglement of shape
and appearance in volume rendering. Applying this new density representation to
challenging scene multiview datasets produced high quality geometry
reconstructions, outperforming relevant baselines. Furthermore, switching shape
and appearance between scenes is possible due to the disentanglement of the
two.
