Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes

Abstract

Neural implicit representation of geometric shapes has witnessed considerable advancements in recent years. However, common distance field based implicit represen-tations, specifically signed distance field (SDF) for water-tight 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 de-fined 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 di-rections. This distinctive feature leverages the accurate re-construction of surface points without interpolation errors. We verify the effectiveness of UODFs through a range of re-construction examples, extending from simple watertight or non-watertight shapes to complex shapes that include hol-lows, internal or assembling structures.