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

TL;DR

MIND addresses the challenge of extracting non-manifold surfaces from unsigned distance fields by generating material interfaces directly from UDFs. It introduces a three-stage pipeline: a local two-signed field to differentiate sides of local patches, a global multi-labeled field to separate all sides of a non-manifold surface, and a multi-label Marching Cubes-based extraction with subsequent refinement to produce accurate non-manifold meshes. The method is validated across UDFs learned from point clouds, multi-view images, and medial-axis transforms, demonstrating robust topology preservation and superiority over baselines like DCUDF and DMUDF. This work broadens the applicability of UDFs in 3D reconstruction by enabling universal, topology-aware mesh extraction without requiring predefined region labels.

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. The source code is available at https://github.com/jjjkkyz/MIND.

Figures (17)

• Figure 1: An open non-manifold surface (a) with 7 sides, including the top, bottom, left, right, front, back, and inner regions. Given the input unsigned distance field (A cross section is illustrated in (b)), we generate the corresponding material interface (c). For supporting open surfaces, we generate an envelope $\Omega_1$ (the dashed lines in (c)) enclosing the surface. To generate MI partitions, it needs to fill the gaps, e.g., the gap within the red box in (c), between $\Omega_1$ and the surface boundaries. We extend the surface boundaries slightly to intersect with $\Omega_1$. The redundant faces are removed while extracting the surface by M3C Wu2003M3C. The reconstructed mesh in shown in four views (d) where each side is highlighted in a different color for clarity.
• Figure 2: Pipeline: Starting with a learned UDF, we first sample a point cloud to compute a local two-signed field to differentiate the two sides of local manifold patches (a). We do not calculate regions far from the target face and label them as background (the green region in (a)). This is followed by generating a global multi-labeled field based on the two-signed field, which distinguishes all sides of the non-manifold surface (b). Finally, the non-manifold surface is extracted from the multi-labeled distance field using a multi-label MC algorithm (c).
• Figure 3: Illustration of global multi-labeled field generation from the local two-signed field on a T-shaped model. The close-up view of the cross-section on the non-manifold structure is provided. The local two-signed field $w^l_S$ is first computed (a). Applying connected component labeling to the local two-signed field introduces artifacts due to small "tubes" (b). Erosion effectively removes these connected "tubes" (c). We solve the Equation \ref{['eqn:assign_labels']} to fill the blank region (d). Comparing to dilate operation, it produce a more consistent boundary to the origin labeling (dash line). But our current result is over-segmented. We introduce an envelope $\Omega_2$ that is closer to the target surface than $\Omega_1$. As shown in (e), the partition boundaries inside $\Omega_2$ is shown in green and outside in red. We merge two regions whose most adjacent boundaries are in red to get the final labeling result (e).
• Figure 4: The Multi-Labeled Field computed from the point cloud, while having the correct topology, generates a noisy mesh because its zero level set is misaligned with the target surface (a). We use the input UDF to refine the result (b).
• Figure 5: Laplacian constraint of non-manifold edges. For a point (orange) on a non-manifold edge, traditional Laplacian constraint fails to prevent adjacent faces from folding. By computing the Laplacian loss within each labeled region separately, our method effectively avoids self-intersections of the surface.