  In this work we target a learnable output representation that allows
continuous, high resolution outputs of arbitrary shape. Recent works represent
3D surfaces implicitly with a Neural Network, thereby breaking previous
barriers in resolution, and ability to represent diverse topologies. However,
neural implicit representations are limited to closed surfaces, which divide
the space into inside and outside. Many real world objects such as walls of a
scene scanned by a sensor, clothing, or a car with inner structures are not
closed. This constitutes a significant barrier, in terms of data pre-processing
(objects need to be artificially closed creating artifacts), and the ability to
output open surfaces. In this work, we propose Neural Distance Fields (NDF), a
neural network based model which predicts the unsigned distance field for
arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high
resolutions as prior implicit models, but do not require closed surface data,
and significantly broaden the class of representable shapes in the output. NDF
allow to extract the surface as very dense point clouds and as meshes. We also
show that NDF allow for surface normal calculation and can be rendered using a
slight modification of sphere tracing. We find NDF can be used for multi-target
regression (multiple outputs for one input) with techniques that have been
exclusively used for rendering in graphics. Experiments on ShapeNet show that
NDF, while simple, is the state-of-the art, and allows to reconstruct shapes
with inner structures, such as the chairs inside a bus. Notably, we show that
NDF are not restricted to 3D shapes, and can approximate more general open
surfaces such as curves, manifolds, and functions. Code is available for
research at https://virtualhumans.mpi-inf.mpg.de/ndf/.
