A Deep Signed Directional Distance Function for Object Shape Representation

TL;DR

This paper introduces a novel continuous signed directional distance function (SDDF) model for object shape representation, enabling shape synthesis and interpolation from partial data without 3D supervision, and directly predicting distances in specific directions.

Contribution

It proposes a new SDDF model that measures distance in specific directions, allowing shape synthesis without 3D supervision and eliminating post-processing steps like surface extraction.

Findings

Enables shape synthesis from partial data using only distance measurements.

Removes need for surface extraction or rendering by direct distance prediction.

Provides analytical confidence in SDDF predictions regardless of object distance.

Abstract

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.