MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction

2025-06-03

AI Summary

This work addresses topological artifacts—such as holes and spurious components—and the inability to represent non-manifold geometry in unsigned distance field (UDF) reconstruction, which stem from conventional local sign assignment. We propose an end-to-end method for directly generating non-manifold meshes, bypassing the traditional signed distance function (SDF) conversion paradigm. Our core innovation is a multi-label global space partitioning scheme that explicitly models the target surface as a material interface. The method comprises two stages: first, deriving a bi-signed local field from the input UDF and fusing it into a multi-label distance field; second, designing a tailored multi-label Marching Cubes algorithm for robust isosurface extraction. To our knowledge, this is the first framework enabling direct UDF-to-non-manifold-mesh reconstruction. Evaluated on diverse UDF inputs—including point clouds, multi-view reconstructions, and medial axis transforms—it consistently outperforms state-of-the-art methods, eliminating topological defects and enabling accurate, stable reconstruction of arbitrarily complex non-manifold geometries.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Unsigned distance fields (UDFs) are widely used in 3D deep learning due to their ability to represent shapes with arbitrary topology. While prior work has largely focused on learning UDFs from point clouds or multi-view images, extracting meshes from UDFs remains challenging, as the learned fields rarely attain exact zero distances. A common workaround is to reconstruct signed distance fields (SDFs) locally from UDFs to enable surface extraction via Marching Cubes. However, this often introduces topological artifacts such as holes or spurious components. Moreover, local SDFs are inherently incapable of representing non-manifold geometry, leading to complete failure in such cases. To address this gap, we propose MIND (Material Interface from Non-manifold Distance fields), a novel algorithm for generating material interfaces directly from UDFs, enabling non-manifold mesh extraction from a global perspective. The core of our method lies in deriving a meaningful spatial partitioning from the UDF, where the target surface emerges as the interface between distinct regions. We begin by computing a two-signed local field to distinguish the two sides of manifold patches, and then extend this to a multi-labeled global field capable of separating all sides of a non-manifold structure. By combining this multi-labeled field with the input UDF, we construct material interfaces that support non-manifold mesh extraction via a multi-labeled Marching Cubes algorithm. Extensive experiments on UDFs generated from diverse data sources, including point cloud reconstruction, multi-view reconstruction, and medial axis transforms, demonstrate that our approach robustly handles complex non-manifold surfaces and significantly outperforms existing methods.

Problem

• Extracting meshes from unsigned distance fields (UDFs) is challenging due to inexact zero distances.
• Local signed distance fields (SDFs) introduce topological artifacts and fail for non-manifold geometry.
• Proposing MIND to generate material interfaces directly from UDFs for non-manifold mesh extraction.

Innovation

• Generates material interfaces directly from UDFs
• Uses multi-labeled field for non-manifold structures
• Employs multi-labeled Marching Cubes algorithm