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

TL;DR

This work introduces unsigned orthogonal distance fields (UODFs) as a neural implicit representation that defines minimal distances to a surface along three orthogonal directions. By regressing three independent UODFs and applying an interpolation-free surface-point estimation with a fusion step, the method achieves high fidelity for watertight, non-watertight, and complex shapes, including internal structures. Key contributions include a formal definition of UODFs, characteristics such as 1D derivative magnitude equal to 1 and ray-discontinuities, a dedicated network and loss design, and a fusion-based GEP/mesh extraction pipeline with strong empirical results across diverse datasets. The approach improves surface reconstruction accuracy over state-of-the-art SDF/UDF methods and offers a robust, unified framework for open and complex geometries with potential for real-time rendering and further neural-network integration.

Abstract

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.

Figures (16)

• Figure 1: Overview of unsigned orthogonal distance fields (UODFs) based NIR. Unlike SDF or UDF based NIR, which suffers from interpolation errors in surface point reconstruction, UODFs directly estimate surface points and mitigate fitting errors by averaging predictions for each GEP. The upper zoom-in grids illustrate the inaccuracies in traditional methods, where the middle grid edge point (colored purple) is approximately estimated with the distance values (denoted by two dotted circles) of two grid corners. This estimated GEP is far from its true position (colored red) which is jointly predicted by values of our UODFs (two red arrows), as shown in the lower zoom-in grids.
• Figure 2: Sketch of UODFs. For understanding the three orthogonal components, 1D derivative, and possible discontinuity between adjacent rays of UODFs, refer to the three characteristics concluded in Sec. \ref{['sec:method_character']}.
• Figure 3: One slice from the $U\!O\!D\!F_{U\!D}$ of the 3D model 'Dragon'. Discontinuity between adjacent ‘UD’ rays occurs when there is a change in intersection with the surface. The grayscale areas denote undefined $U\!O\!D\!F_{U\!D}$ in ground truth calculation and our prediction.
• Figure 4: Network architecture and processing pipeline. Each UODF is individually regressed using a UODF and mask network. The grid edge points in one orthogonal direction can be estimated from its UODF, followed by points fusion to form final reconstruction results.
• Figure 5: Surface points estimation along a ray.