Gradient Distance Function
This work addresses a problem in 3D reconstruction for computer vision and graphics researchers, offering an incremental improvement over UDFs.
The authors tackled the brittleness and learning difficulty of Unsigned Distance Functions (UDFs) for representing non-watertight surfaces by proposing Gradient Distance Functions (GDFs), which are differentiable at the surface and demonstrated effectiveness on ShapeNet Car, Multi-Garment, and 3D-Scene datasets.
Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is non-differentiable. In this work, we show that Gradient Distance Functions (GDFs) can remedy this by being differentiable at the surface while still being able to represent open surfaces. This is done by associating to each 3D point a 3D vector whose norm is taken to be the unsigned distance to the surface and whose orientation is taken to be the direction towards the closest surface point. We demonstrate the effectiveness of GDFs on ShapeNet Car, Multi-Garment, and 3D-Scene datasets with both single-shape reconstruction networks or categorical auto-decoders.