Voronoi-Assisted Diffusion for Computing Unsigned Distance Fields from Unoriented Points

2025-10-14

AI Summary

This work addresses the challenge of reconstructing unsigned distance fields (UDFs) from unoriented point clouds without neural networks. We propose VAD, a lightweight, non-learning method that constructs a geometric energy function based on the Voronoi diagram to enable robust bidirectional normal estimation and alignment. Subsequently, UDF recovery is achieved via gradient field diffusion and integration, supporting arbitrary topologies—including open/closed surfaces, non-manifold geometries, and non-orientable shapes (e.g., Möbius strips). Compared to state-of-the-art approaches, VAD achieves superior numerical stability, enhanced controllability, and higher computational efficiency, while significantly improving UDF reconstruction quality on complex geometries. By eliminating reliance on training data or neural architectures, VAD establishes an interpretable, training-free paradigm for geometric processing and implicit modeling.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Computing unsigned distance fields from unoriented point clouds
• Addressing numerical instability in neural UDF methods
• Handling complex geometries like non-manifold structures

Innovation

• Assigns bidirectional normals using Voronoi-based geometric criteria
• Diffuses aligned normals to form approximate UDF gradient field
• Integrates gradient field to recover final unsigned distance field