  Neural networks that map 3D coordinates to signed distance function (SDF) or
occupancy values have enabled high-fidelity implicit representations of object
shape. This paper develops a new shape model that allows synthesizing novel
distance views by optimizing a continuous signed directional distance function
(SDDF). Similar to deep SDF models, our SDDF formulation can represent whole
categories of shapes and complete or interpolate across shapes from partial
input data. Unlike an SDF, which measures distance to the nearest surface in
any direction, an SDDF measures distance in a given direction. This allows
training an SDDF model without 3D shape supervision, using only distance
measurements, readily available from depth camera or Lidar sensors. Our model
also removes post-processing steps like surface extraction or rendering by
directly predicting distance at arbitrary locations and viewing directions.
Unlike deep view-synthesis techniques, such as Neural Radiance Fields, which
train high-capacity black-box models, our model encodes by construction the
property that SDDF values decrease linearly along the viewing direction. This
structure constraint not only results in dimensionality reduction but also
provides analytical confidence about the accuracy of SDDF predictions,
regardless of the distance to the object surface.
