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

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.

1. Introduction

Neural implicit representation (NIR) of three-dimensional (3D) shapes has emerged as a noteworthy area of research in computer vision and graphics. Currently, the most prevalent NIR for 3D shapes is based on signed distance field (SDF), utilized in various applications such as shape reconstruction [6, 12,24,26,29-32], or new view synthesis [22], [36], [37], [39], [41]. For any 3D shape, the SDF value of each spatial point reveals two properties: (1) whether the point is inside the shape (indicated by the SDF sign); (2) the minimal distance among all directions from this point to the shape surface (depicted by its absolute value). Despite the advantages offered by SDF based NIR in multiple contexts, there still exist several scenarios where SDF is not applicable.