  Neural 3D implicit representations learn priors that are useful for diverse
applications, such as single- or multiple-view 3D reconstruction. A major
downside of existing approaches while rendering an image is that they require
evaluating the network multiple times per camera ray so that the high
computational time forms a bottleneck for downstream applications. We address
this problem by introducing a novel neural scene representation that we call
the directional distance function (DDF). To this end, we learn a signed
distance function (SDF) along with our DDF model to represent a class of
shapes. Specifically, our DDF is defined on the unit sphere and predicts the
distance to the surface along any given direction. Therefore, our DDF allows
rendering images with just a single network evaluation per camera ray. Based on
our DDF, we present a novel fast algorithm (FIRe) to reconstruct 3D shapes
given a posed depth map. We evaluate our proposed method on 3D reconstruction
from single-view depth images, where we empirically show that our algorithm
reconstructs 3D shapes more accurately and it is more than 15 times faster (per
iteration) than competing methods.
