Voronoi-Assisted Diffusion for Computing Unsigned Distance Fields from Unoriented Points
This work addresses the need for stable and efficient UDF computation in 3D shape representation, particularly for open, non-manifold, and non-orientable surfaces, offering a practical solution for applications in computer graphics and geometry processing.
The paper tackled the problem of computing Unsigned Distance Fields (UDFs) from unoriented point clouds, which is challenging due to numerical instability and high computational cost in existing methods, and presented Voronoi-Assisted Diffusion (VAD), a lightweight, network-free method that robustly handles various geometries while being computationally efficient and stable.
Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Diffusion (VAD), for computing UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.