Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes
Authors: Yujie Lu, Long Wan, Nayu Ding, Yulong Wang, Shuhan Shen, Shen Cai, Lin Gao

Neural implicit representation of geometric shapes has witnessed considerable advancements in recent years. However common distance field based implicit representations specifically signed distance field (SDF) for watertight shapes or unsigned distance field (UDF) for arbitrary shapes routinely suffer from degradation of reconstruction accuracy when converting to explicit surface points and meshes. In this paper we introduce a novel neural implicit representation based on unsigned orthogonal distance fields (UODFs). In UODFs the minimal unsigned distance from any spatial point to the shape surface is defined solely in one orthogonal direction contrasting with the multi-directional determination made by SDF and UDF. Consequently every point in the 3D UODFs can directly access its closest surface points along three orthogonal directions. This distinctive feature leverages the accurate reconstruction of surface points without interpolation errors. We verify the effectiveness of UODFs through a range of reconstruction examples extending from simple watertight or non-watertight shapes to complex shapes that include hollows internal or assembling structures.