A Deep Signed Directional Distance Function for Object Shape Representation
This provides a more efficient and analytically grounded method for shape modeling in computer vision, though it is incremental as it builds on existing deep SDF and view-synthesis techniques.
The paper tackles the problem of 3D object shape representation by developing a signed directional distance function (SDDF) model that synthesizes novel distance views without 3D shape supervision, using only depth measurements from sensors like Lidar, and it removes post-processing steps by directly predicting distances at arbitrary locations and directions.
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.