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

A Deep Signed Directional Distance Function for Object Shape Representation