MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction
Authors: Xuhui Chen
Fei Hou
Wencheng Wang
Hong Qin
Ying He
Venue: NeurIPS 2025 poster ()
Keywords: Unsigned distance fields
neural implicit field
zero-level sets
non-manifold surface reconstruction
material interfaces
Primary area: other

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 ($\mathrm{\underline{M}aterial}$ $\mathrm{\underline{I}nterface}$ $\mathrm{from}$ $\mathrm{\underline{N}on}$-$\mathrm{manifold}$ $\mathrm{\underline{D}istance}$ $\mathrm{fields}$), 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.

MIND; Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction
Xuhui Chen Fei Houl
Wencheng Wang"?; Hong Qin', Ying He*
Key Laboratory of System Software (CAS) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences University of Chinese Academy of Sciences
Department of Computer Science, Stony Brook University
*College of Computing and Data Science, Nanyang Technological University [chenxh, houfei, whn] ac. qinêcs stonybrook edu yheentu. edu. sg
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 fo- cused on learning UDFs from point clouds or multi-view images, extracting meshes from UDFs remains challenging, as the learned fields rarely attain exact zero dis- tances. A common workaround 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 ge- ometry, 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 non-manifold mesh extraction from a global perspective. The core of our method lies deriving a meaningful spatial partitioning from the UDF, where the target surface emerges as the interface between distinct regions. We begin by computing two-signed local field to distinguish the two sides of manifold patches, and then extend this multi-labeled global field capable of separating all sides of non-manifold structure. By combining this multi-labeled field with the input UDF, construct material interfaces that support non-manifold mesh extraction via a multi-labeled Marching Cubes algorithm. Extensive experiments on UDFs generated from di- verse data sources, including point cloud reconstruction, multi-view reconstruction, and medial axis transforms, demonstrate that our approach robustly handles com- plex non manifold surfaces and significantly outperforms existing methods. The source code is available https//githb..om/jjkk////MM com/jjjkkZ//MIND.
Introduction
Signed Distance Fields (SDFs) are a widely adopted implicit representation for watertight surfaces due to their simplicity and effectiveness. The sign in SDFs clearly distinguishes the inside and outside of surface, enabling straightforward surface extraction via well-established methods such as Marching Cubes (MC) [ While recent adaptations of SDF (245) incorporate constraints to support open surface reconstruction, they remain inadequate for capturing non-manifold structures.
Unsigned Distance Fields (UDFs), in contrast, eliminate the need for sign information and provide more flexible framework capable of representing wide range of surface topologies, including
"Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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open and closed surfaces, non-manifold geometries, and shapes with complex internal structures [6 19]. However, this flexibility comes at a significant cost: the absence of sign information makes significantly harder to identify zero-level sets, especially in the presence of non-manifold structures.
Several methods have been proposed for surface extraction from UDFs. A common strategy in- volves reconstructing local SDFs from UDFs using gradient-based estimation [6 20 or neural prediction [21] approximate sign information and identify zero-level intersections. While
these methods benefit from the efficiency of Marching Cubes, they are highly sensitive to UDF
inaccuracies, often resulting in holes and redundant components. Other approaches 22 23 gener-
alize dual contouring (24) to improve reconstruction quality, but they often introduce unintended non-manifold artifacts due inconsistent topologiaal handling. Mesh deformation methods, such as DCUDF 225 [26]. improve robustness by iteratively shrinking an initial double-layered manifold surface to fit the target geometry. However, since the initial surface always manifold and the deformation process preserves this structure, these methods are inherently incapable of capturing non-manifold geometries. Mesh extraction algorithms based on Dual Contouring (24] have the ability to extract non-manifold structures, but they also generate large number of non-manifold faces in manifold regions. To our knowledge, there is currently no method that can effectively extract the correct non-manifold structures from UDFs.
(b)
(a)
(c)
(d)
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)), generate the corresponding material interface (c). For supporting open surfaces, we generate an envelope Qi (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 Q2 and the surface boundaries. We extend the surface boundaries slightly to intersect with 22. The redundant faces are removed while extracting the surface by M3C (27]. The reconstructed mesh in shown in four views (d) where each side highlighted in a different color for clarity.
Figure 1:
On the other hand, non-manifold structures ubiquitous in many applications, such anatomical modeling 28 29], composite materials 330 31,. multi-phase fluids (3) and bubble simula-
tions 36 37 These structures characterized by complex topologies and often arise as interfaces
between multiple materials, commonly referred to as material interfaces (MIs) (38) An MI defines a partitioning of the spatial domain into multiple labeled regions (Fi,.., F.)) shown in Figure Ic).
Traditional MI representations are limited to closed surfaces, i.c., surfaces without boundaries. As illustrated in Figure define an enclosing envelope 22 around the surface. The surface boundaries are extended slightly to intersect with 22 to form MI partitions inside f2 The outside Ω is treated as background and assigned the label Fg. This generalization allows to deal with not only closed but also certain open non- manifold surfaces and to apply multi-label Marching Cubes methods, such M3C (27). reconstruct non- non-manifold meshes from such labeled partitions. Redundant surfaces, such as faces adjacent to the background, are removed.
However, MI is not universal representation, as it requires predefined partition domain information. In practical applications, MIs are typically defined by known functions (e.g., from fluid simulations) or derived based on numerical priors (c.g., from CT images). In contrast, UDFs serve more universal

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representation and have been widely adopted in many classic 3D reconstruction tasks, such as point
cloud reconstruction [2] multi-view image reconstruction [3 and 3D generation [7719]
To address these limitations, we introduce a novel algorithm to generate MIs from the input UDFs without requiring predefined partition domain information, which enables accurate non-manifold surface extraction from MIs.
Our method consists of three key steps. First, we generate two-labeled field to distinguish between the two sides local surface patch using positive and negative signs. Second, we extend the local two-signed field into global multi-labeled field, assigning unique labels each side of non non-manifold surface. The multi-labeled field is then combined with the input UDF to generate the target MI. Third, we refine the extracted mesh from the MI ensure both visual accuracy and topological coherence. We evaluate our method on a variety of datasets and UDF learning methods. Experimental results demonstrate that approach generates clean meshes that accurately capture non-manifold structures, where existing methods often fail.
The main contributions of the paper are follows:
1. We develop an algorithm for generating MIs from learned UDFs, enabling robust non- manifold surface reconstruction without requiring prior knowledge of MIs. By extending the definition of the MI, Our approach effectively handles both closed models and open models.
2. We introduce novel algorithm that extends the local two-sided field- calddee of distin- guishing the two sides of local manifold patches-ing global multi-labeled field, enabling the differentiation of multiple sides of non- non-manifold surfaces.
3. We conduct extensive evaluations across diverse datasets and UDF learning methods. Exper- imental results demonstrate the capability of our method in extracting clean and accurate manifold and non-manin con-manifold meshes, outprrforiing existing techniques.
2 Related Works
2.1 Manifold Reconstruction
Recently, deep learning approaches have gained traction in surface reconstruction. These methods learn SDFs [39 or occupancy fields [50] 51] using neural networks directly from point clouds or multi-view images. These methods typically extract surfaces from signed distance fields [[52), which inherently guarantee watertight manifold models. Extensions of SDFs to support open surfaces typically involve introducing additional constraints or masks (215). While these methods offer greater adaptability and flexibility in modeling, they remain fundamentally restricted to manifold surfaces.
2.2 Non-manifold Reconstructions
Unsigned distance fields have emerged as promising alternative for representing surfaces with diverse topologies, including open surfaces, non-manifold geometries, and shapes with complex By discarding the sign term of SDFs, UDFs offer greater flexibility, enabling the representation of complex models, including non-manifole surfaces. However, most UDF-based methods primarily focus open manifold surfaces, with limited exploration of non-manifold surface reconstruction. The primary obstacle lies in the lack of robust mesh extraction algorithm tailored for non-manifold structures from UDFs.
internal structures 16 13 53
Recent advancements have focused on extracting the zero-level sets from UDFs using modified Marching Cubes. Some methods 66. [1 20 21] reconstruct local sign information to determine edge intersections. DCUDF (25] refines the mesh of non-zero level sets to approximate the zero-level set through shrinking, producing double-layered results. However, these methods fail to effectively handle non- manifold geometries.
For non mon-fooifold structures, sampling point clouds from UDFs and applying non seaanifodd-speciin methods (54) have been explored but suffer from low accuracy and robustness. Dual Contouring- based methods, such as NDC [22) and DMUDF 233. have the potential to generate non-manifold geometries but either lack generalizability or introduce unintended non-manifold artifacts. Manifold DC [55) avoids such artifacts but cannot model non-manifold structures.
3

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Existing non-mn aon-mmiifold mesh extraction algorithms are predominantly applied in the context of material interfaces (MIs). MI represents a collection of regions where the target surface corresponds the intersection of different regions. MI is widely utilized in partitioned domains, such as anatomical
structures 28 29, composite materials [30 31 bubbles [36 37, and multi-phase fluids (5)
where space is naturally segmented into distinct regions. Using the MI as input, multi-label algorithms, such as M3C [27]. handle non non-manifold surfaces by leveraging explicit material interface definitions. While effective, they require predefined region labels or arrangements, limiting their applicabilityy.
In this paper, we aim to address the limitations of these approaches by introducing novel method for generating MIs directly from UDFs. Unlike previous methods, our approach does not require prior knowledge of material interfaces or region labels, enabling the robust extraction of non-manifold surfaces directly from UDFs.
Local two-signed field
Global multi-labeled field
Non-manifold result
Input UDF
(a) Figure 2: Pipeline: Starting with a learned UDF, we first sample a point cloud to compute 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 global multi-labeled field based 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 multi-label MC algorithm (c).
(b)
(c)
3 Method
In this work, we generate MIs from input UDFs to enable the extraction of non non-manifold meshes from UDFs. As illustrated in Figure 2 our method consists of three key steps: In Section [.1] we construct a local two-signed field to distinguish the two sides of manifold patches within the input UDF. Section 3.2 the local two-signed field extended to global multi-labeled field to capture the sides of non-manifold surfaces, forming the target MI. Finally, in Section 3.3 we describe how to extract non mon-molifold surface meshes from the MI.
3.1 Local Two-Signed Fields
To generate the MI of the input UDF, need to segment the 3D space into different partitions. As shown in Figure our first step is to generate a two-signed local side field that distinguishes the two sides of local manifold patches. Similar to the generalized winding number [56. 57], on surface S, given consistently oriented normals n, of points x E 5, we introduce the following indicator function w's (q) to compute side field for query point q:
(g)(a)) -
(x
Dlx dx. q
(xENs(g)
||x
(1)
where is small positive to avoid division by zero. Different from the generalized winding number, the region of integration modified from the entire surface S local neighborhood (s(q)) on S around the point q. This adjustment allows w/y distinguish between the two sides of local manifold using positive and negative signs.
Implementation Details We extract a point cloud from the given UDF. Points are sampled randomly in space Ω where the UDF values are equal to threshold ri and these points are projected toward local minima, similar the approach in [10. The point cloud is then downsampled using uniform grid voxels to obtain uniform initial point cloud P. Next, apply (58) to compute oriented

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normals for the points. Although [38 may result in flipped normals, the orientations are piecewise consistent, ensuring that most are oriented consistently. The discrete form of w's(q) is,
(x; q) n. |
(')
(2)
We discretize the space into voxels and compute the side field only for the voxels o; inside Q2, as points far from the surface not of interest. Any voxel outside Q2 is considered background and assigned the label Fo- w'g (q) is locally defined and is able to distinguish the two sides where the normals are properly defined. In particular, in regions near non-manifold edges regions with flipped normals, w'g is not well-defined. These issues will be refined in the following Section 3.2
VTT (b)
(a)
(d)
(e)
Figure 3: Illustration of global multi-labeled field generation from the local two-signed field on T-shaped model. The close-up view of the cross-section on the non-manifold structure is provided. The local two-signed field w's is first computed (a). Applying connected component labeling the local two-signed field introduces artifacts due to small "tubes" (b). Erosion effectively removes these connected "tubes" (c). We solve the Equation 3 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 Q2 that is closer to the target surface than Ω2 As shown in (c), the partition boundaries inside 12g 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 (c).
3.2 Global Multi-Labeled Fields
In this section, we generate the global multi-laheled distance field, which is able to distinguish all sides of non-manifold surface, from the local two-signed side field. We cluster voxels based the two signs of w/g by applying the 3D connected component labeling algorithm This algorithm assigns label to each voxel that connected and has the same sign (positive negative). As result, voxels within 92 are split into a set of partitions [. However, non-manifold or normal flipping regions, where three or more partitions coincide, are scarcely possible be properly divided only by the two signs of wg. As shown in Figure a partition may span across non-manifold edges via a narrow "tube". Since this tube is thin, a simple morphological erosion can remove it, causing the remaining voxels of the partition to become disconnected.
We denote the eroded voxels by Rg and the remaining voxels by R. For the voxels in all the connected components of Ry we assign different new labels F& to different connected components of R. Each voxel in R& should be labeled by one of the labels of Fx. The goal is minimize variations in neighboring labels of Re. Therefore, we minimize the following energy for labeling:
min Σ D(S(0:)) Σ V(f(a))
O.E
(omD))EN
s.t. f(o:) = fa(o)), or EURR
D(f(o)) = (0,
-10, if f(xi) E F& or F6 =
(3)
(o: R
otherwise
v(f(o)))(o))) = fo, if ((,) = f(o,)
otherwise
Here, f(o,) represents the to be solved label assigned voxel o,, fo:) denotes the label assigned to voxels in R which are fixed, and N refers to the set of neighboring voxels. The function V-)) minimizes label changes, while D(-) ensures that most of the interfaces between partitions remain
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invariant. Occasionally. Rg may be so small that R2 and Fj; are empty sets. In such cases, we omit the constraint. Equation (3) can be solved using a-expansion [59].
After refinement, the partitions ensure that the two sides of non-manifold belong to different partitions. However, over-segmented partitions may exist, shown in Figure which are unavoidable in the two-signed field near non-manifold edges. These over-partitions should be merged. Otherwise they would lead redundant surfaces in the reconstructed mesh. Two partitions that are not separated by the surface S should be merged. Directly assessing this condition can be tricky, so instead, we construct another envelope, $2g, by extracting an iso-surface at value 12 (r2 < rr) from the UDF. This gives us the relation S C S2 C S2, If two partitions are separated by S, their boundary voxels should lie within f2g. Conversely. two partitions are not separated by S, most of their boundary voxels should be outside f2, but still within S2 Ω2 As illustrated in Figure 3) through these simple tests, we can effectively merge redundant partitions, ensuring that different sides of non-man manifold surface belong to different partitions, and no further merging of partitions is needed. These partition labels along with the input UDF constitute the target MI.
3.3 Non-Manifold Surface Extraction
With the target MI, we can extract the non-manifold mesh M using a multi-label Marching Cubes algorithm. Specifically, we adopt the M3C method [27] with minor modifications. Instead of interpolating the midpoint of each cube edge, we use the value of w's determine the intersection points, enhancing accuracy. We do not generate the face associated with the background label Fo because there is no target surface at the interface between the background and other regions, which also enables open model reconstruction. To further refine the mesh, redundant triangular faces extending from surface boundaries outside f2g are removed.
(b)
Figure 4: The 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).
Field computed from the point cloud, while having the correct topology.
However, the accuracy of wts remains limited by discretization. To address this limitation, we refine the extracted mesh M by optimizing its alignment with the input UDF shown in Figure Inspired by DCUDF (25), we fine-tune M by minimizing its UDF values for improved accuracy while incorporating Laplacian regularization term to maintain the mesh's 's shape and prevent face folding. Unlike DCUDF, our mesh M contains non-manifold edges, where traditional Laplacian computation is not well-defined. For point Pm to compute the Laplacian fails to prevent face folding, illustrated in Figure To overcome this, we group adjacent triangular faces based on the labels they border. Every triangular face belongs to two groups. Each group of triangular faces forms a manifold mesh. For a point ps E M, the Laplacians are computed separately in each group of adjacent faces. For example, for a point on the manifold edge of T-shape, there are groups of adjacent faces and 3 Laplacian terms. We optimize the following loss function to refine the mesh,
non-manifold edge, using all adjacent points
min
Σ ((((p)) + Σ T(p.)) [p.p Py (PE)
Σ =(ps))(')
(4)
PIEM
P.E.a
where f(-) denotes the UDF values and (p::) the new location of point p. after optimization. S denotes the set of signs and M is the sub-mesh whose faces border on the sign > denotes the 1 I-ring neighboring points of p, in M The first term, [( (p:)). drives the points pa toward the local minima of the UDF. The second Laplacian term prevents the triangular face from folding.

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(b)
(c)
(d)
Figure 5: Laplacian constraint of non-manifold edges. For a point (orange) on a non-manifold edge, traditional Laplacian constraint fails prevent adjacent faces from folding. By computing the Laplacian loss within each labeled region separately, our method effectively avoids seff-intersections of the surface.
4 Experimental Results
4.1 Experimental Setup and Hyperparameters
We normalize 3D models fit within [-0.5, 0.5) and use bounding box of [-0.6, 0.6] to contain the UDFs. For calculating the local two-signed field, we sample million points on the rı level set and optimize their positions to align with the local minima of the UDF. The resolution is set 256 resulting in a voxel size of 0.0046. The voxel size for point cloud downsampling is set to 0.005, which is slightly higher than 0.0046. While the downsampled point cloud has a density of 0.005, we set 22 = 0.01 to generate a continuous f2y. To ensure Q is larger than Ω2 is set to 0.05. We erode local two-signed field times before generating the global multi-labeled field. Two partitions in the global multi-labeled field are merged if the number of boundary voxels within Q2 O2 is three times greater than the number of voxels within 22 A more detailed experiment of hyperparameters can be found in Section of appendix.
We use M3C [27 to extract meshes, implemented in Dream3D We then optimize the output of M3C with Equation 4 for 200 iterations, using a Laplacian weight of 1000, to generate the final result. Although several hyperparameters are introduced our paper, most of them correspond the resolution and exhibit generalizability across different types of learned distance fields. All results are tested on single NVIDIA V100 GPU.
4.2 Comparisons
Baselines To the best of our knowledge, prior work investigates generating MIs from UDFs. Since the extracted meshes depend on MI qualities, we compare our method against two unsupervised UDFs mesh extraction algorithmss, including DCUDF (25 and DMUDF (23]. While DCUDF uses double-layered manifold meshes to approximate non-manine non-manifold structures, DMUDF is capable of generating non-manifold edges. To assess the topological correctness of the extracted meshes, compute geodesic distances, which are highly sensitive to topological features. Specifically, we the heat method (60) with non-manifold Laplacian (61] applied to the extracted meshes. For comparison, geodesic distances are also computed on dense points, serving as a reference.
UDFs Learned from Point Clouds learn UDFs from unoriented point clouds using CA- PUDF O LevelSetUDF (7) and DEUDF g. respectively. The results are shown in Figure 6 with non-manifold edges highlighted in red. We compare our method with DMUDF and DCUDE.
DMUDF 23], a Dual Contouring variant, is capable of generating non non-manifold edges. However, the process of generating non-manifolds in DC is often uncontrolled, resulting in significant number of non-manifold edges appearing in regions that should remain manifold. Furthermore, DMUDF utilizes an octree structure to accelerate the algorithm. To determine whether the target surface exists within specific leaf node. DMUDF relies on key criterion based on the UDF value at the node's center point. This approach is highly sensitive to UDF accuracy. making prone to failure in the presence of noise or inaccuracies in the UDF Such issues can cause the octree subdivision process to terminate prematurely. highlighted in DUDF 9 most UDF learning methods prioritize accurate distance predictions near the target surface but neglect accuracy in regions farther away. This limitation can
httpe://www.opna2/ org

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CAPUDF
LevelsetUDE
Sample point cloud
DMUDF
DCUDF
Ours
Sample point cloud
DMUDF
DCUDF
Ours
DEUDF
LevelsetUDF
Sample cloud DMUDF
DCUDF
Ours
Sample cloud
DMUDF
DCUDF
Ours
N.A.
N.A.
Figure 6: Non-manifold surface extraction from UDFs learned by CAPUDF 66, LevelSetUDF ( and DEUDF g. We present the sampled point cloud on the UDFs as the GT (Ground Truth). We compare our surface extraction method with DCUDF and DMUDF, highlighting non-manifold edges red in the results. While DMUDF frequently produces non-manifold edges in regions that should be manifold, DCUDF consistently generates double-layered manifold meshes, leading failure in preserving the correct topology of the target surfaces.
GT
DMUDF
DCUDF
Ours
Figure 7: Surface extraction from UDFs learned by CAPUDF 66 the ShapeNet- dataset 622
result in significant missing regions in DMUDF's output when node's center point is far from the vicinity of the target surface. DCUDF (25) approximates the target non-manifold surfaces using double-layer mesh. Although the results visually align with the target surface, the lack of exact coincidence between the two layers often introduces undesired artifacts, such as redundant shadows, during rendering.
To assess the quality of the extracted meshes, we sample 100K points on the mesh and employ the Chamfer distance L2 geometrical metric. Table the results the ShapeNet-Ci Car [62 dataset and DeepFashion3D (63] dataset. The visualization results of ShapeNet-Car dataset are shown in Figure 7 where our visual results the best.
Table 1: Evaluation on the ShapeNer-Car 62 dataset learned from CAP-UDF 6 and DeepFashion
dataset 633 learned from DCUDF
DMUDF
DCUDE
Ours
Dataset
Mean
Median
Std
Mean
Median
Std
Mean
Median
Std
ShapeNet-Car
3.086
2,564
2.112
3,290
2.770
2.252
2.917
2.447
2.107
DespFashion3D
1.792
1.383
0.512
1.825
1.495
0.535
1.770
1.339
0.507

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UDFs Learned from Multi-view Images Extracting surfaces from UDFs learned via multi-view images presents significant challenges, especially in scenes involving transparent objects or thin structures, where non-manifold surfaces are prevalent.
We evaluate method and compare it with baselines on UDFs generated by NU-NeRF 4 multi-view images of transparent objects. NU-NeRF learns two separate SDFs, corresponding to the outer and inner objects, and extracts their respective meshes using Marching Cubes. To prevent the inner SDF from producing meshes in the outer region, NU-NeRF uses the outer SDF as a mask during extraction. However, this masking approach often leads to redundant components forming along the mask boundaries. Although NU-NeRF employs post-processing step to remove these redundant components, it creates discontinuities between the inner and outer meshes.
Reference image
Sample point cloud
NU-NeRF
DCUDF
Ours
Non-manifold edges
Reference image
Sample point cloud
NeLDF
DCUDF
Ours
Non manifold edges
Figure 8: Non-manifold surface extraction from UDFs learned by NU-NeRF 43
(top) and
NeUDF [15] (bottom). Geodesic distances computed on the extracted meshes are visualized to validate their non-manifold topology. The geodesic distances computed on sampled point clouds are used as reference for comparison. All baseline methods fail to accurately preserve the non-manifold structures in the extracted meshes.
To address this, we combine the two SDF single UDF for mesh extraction. The outer SDF value is directly applied in the outer region, while for the inner region, we use the minimum absolute value of the two SDFs. As shown in Figure g adopting the geodesic distance measure, we confirm that our results preserve the correct topology. For comparison, we also use DCUDF to extract the target surface. While DCUDF produces visually pleasing results, its double-layered structure prevents geodesic distances from diffusing between layers, highlighting its limitation in preserving topological consistency.
We also adopt NeUDF [15] for learning UDFs from multi-view images of transparent objects. The results are presented in Figure g NeUDF employs MeshUDF (2)). gradient-based Marching Cubes, for mesh extraction from learned UDFs. However, this approach fails in non-manifold regions due to the lack of suitable lookup table for non-manifolds in standard Marching Cubes. Furthermore, unlike opaque objects whose boundary surfaces align with zero-level sets. transparent objects typically exhibit iso-values that are not close zero, leading to complete reconstruction failure for transparent objects. DCUDF addresses this limitation by extracting non-zero level sets, allowing capture transparent objects. However, its double-layered mesh structure significantly compromises topological accuracy. In contrast, our method successfully reconstructs transparent objects and accurately models their non- con-maiioold surfaces. This highlights the robustness and versatility of our approach compared to existing methods.
Non- Non-manifold structures frequently appear in medial axes. Q- MDF (64] computes medial axes for watertight models through the joint learning of signed distance fields and medial fields (MF) [65] It has been shown that the difference between the SDF and MF yields an unsigned distance field (64 In the original Q-MDF pipeline, medial axes are extracted using DCUDF 25.. which, as mentioned above, generates double-layered manifold mesh. Consequently,
UDFs Induced from Q-MDF 64
'e use the SDFs provided directly by the NU-NeRF authors.

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Sample point
Sample point cloud
Ours Geodesic distance
Geodesic distance
Non-manifood edge
Non-manifold edge
Figure 9: Non-manifold surface extraction from UDFs learned by Q-MDF The target surfaces are medial axes, characterized by numerous non non-manifold structures. For clarity, we render both the watertight surfaces and their corresponding medial axes. Geodesic distances are computed on the extracted non-manifold medial axes and compared with those on the sampled point clouds for validation.
this approach fails to preserve the non-manifold characteristics of medial axes. By utilizing MIND, we extract high-quality, single-layered non-maninn manifold medial axes, as demonstrated in Figure 9
Limitations We use a-expansion [59] label voxel grids, which is conssminnninng. The primary bottleneck arises from evaluating all potential label distributions across the entire voxel grid for each candidate label. A feasible acceleration strategy involves partitioning the voxel grid into blocks, where block-wise a-expansion computation effectively reduces costs. Another alternative is to use dilation instead of alpha expansion, which has time cost independent of the number of labels but yields an approximate solution. On the other hand, our approach requires erosion operation, which may inadvertently remove small or thin MI regions and lead to missing facets, as shown in Figure I0
GT
Ours
Figure 10: For small MI region (upper part) (a), the inner voxels of its local two-signed field (b) will removed during the erosion process, resulting no seed region in the entire internal space (c). Consequently, the structure cannot be recovered after a-expansion (d).
Conclusions
In this paper, we introduce MIND, novel algorithm to extract MIs from UDFs for non-manifold mesh extraction. By combining the strengths of material interfaces and unsigned distance fields, MIND supports non-manifold reconstruction from UDFs. MIND does not require pre-defined partition information, making it suitable for broader range of scenarios. Our experimental results across various types of UDFs demonstrate the effectiveness of MIND in generating MIs for accurate non- manifold mesh reconstruction. In its current form, our implementation generates MI from pre-leamned UDFs, making the presented method primarily a zero-level set extraction algorithm. It is highly desired to develop techniques that learn an MI directly from raw input data, such as point clouds or multi-view images. Such advancements could significantly broaden the range of applications for MI and enhance its utility in tackling complex reconstruction tasks.
10

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Acknowledgments and Disclosure of Funding
This project was partially supported by the National Key R&D Program of China (2023YFB:3002001) the Research Projects of ISCAS (ISCAS-JCMS-2023)) ISCAS-2D-202401, ISCAS-JCZD--202402 ISCAS-JCMS-2024033) and the Ministry of Education, Singapore, under its Academic Research Fund Grant (RT19/22).
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A Hyper-parameter study
In our pipeline, shows, a smaller voxel size does not affect the result but introduces a larger computational overhead. Conversely, if the voxel size is too large (e.g., 0.01), the point cloud becomes too sparse and holes appear in the reconstructed model. Our ri and 122 values are also set according to the resolution to maintain them within proper ranges. As shown in Figure [2] moderate changes in these parameters are acceptable, but excessive adjustments can cause problems. Though large ri does not introduce issues beyond computational overhead, an overly small rı (e.g.. 0.03) could cause the erosion step to delete all regions, leading to reconstruction failure. An excessively large r2 (e.g., 0.02) can lead insufficient region merging, whereas an overly small 72 (e.g.. 0.0025) can result in unnecessary merging.
r.rsolutionnddeeendeee voxel size to downsample the point cloud. As Figure IT
0.002
0.005
0.0075
0.01
Figure 11: The reconstruction results with different downsampling voxel size.
= 0.1
= 0.075
=
0.05
= 0.04
0.03
N.A.
= 0.02
= 0.015
T2 = 0.01
= 0.0075
F2 = 0.0025
Figure 12: Mesh reconstruction with different Fi and N.A. means reconstruction failed.
B More Results
We present additional results in the appendix, including point cloud reconstruction, multi-view reconstruction, and medial axis transforms. As illustrated in Figure. 13 our method can model real-world non-manifold structures defined by multi-view images, such intersections between transparent objects and overlapping thin plate structures. These configurations represent challenging cases for signed distance fields represent in practical scenarios. For point cloud reconstruction and medial axis transformations, we present additional results in Figure. 14fand Figure. [5] demonstrating the versatility of our approach. We also collected some more complex data further illustrate the robustness of our method, as shown in Figure [6
C Failed Case
As illustrated in Figure 17 the two sides of the non-orientable surface are indistinguishable, resulting the absence of well-defined MI. Consequently, our method fails to generate MIs for the surface, leading to artifacts in the extracted mesh.
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LLLL Reference image
Sample point cloud
NU-NeRF
DCUDF
Ours
Non-manifold edges
Reference image
Sample point cloud
NcUDF
DCUDF
Ours
Figure 13: More results of Non-manifold surface extraction from SDFs/UDFs learned by NU-NeRF (top) and NeUDF (bottom). We use the SDFs provided directly by the NU-NeRF authors and convert them to UDFs.
CAPUDF
DEUDF
Sample cloud DMUDF
DCUDF
Ours
Sample cloud
DMUDE
DCUDE
Ours
N.A.
N.A.
Figure 14: More results of non-manifold surface extraction from CAPUDF and DEUDE.
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Sample point cloud
Ours
Ours Non-manifold edge
Sample point cloud
Ours Geodesic distance
Ours
Geodesic distance
Non-mamifold edge
Figure 15: More results of non-manifold surface extraction from UDFs learned by Q-MDF [64]
Figure 16: Results on more data, where the UDFs are learned by DEUDF 8 We demonstrate the reconstruction results of indoor data, medical images, objects, and high fidelity surface data, which illustrates the applicability of our method.
(a)
(b)
(c)
(d)
Figure 17: Non-orientable surfaces do not have proper MI definitions. (a) and (b) illustrate non- orientable non-manifold surface where walker can traverse from one side of a point to the opposite side without crossing boundary. In such case, the multi-labeled field is undefined and thus fails to generate (c), from which the non-manifold surfaces cannot be extracted properly (d).
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Reviews:
[{"review_id": "GSkAggLTiA", "reviewer": "Reviewer_yUiZ", "summary": "This paper introduces MIND, a new method for extracting non-manifold meshes directly from Unsigned Distance Fields (UDFs). Unlike traditional approaches that reconstruct Signed Distance Fields (SDFs) locally—often resulting in topological artifacts or inability to handle non-manifold geometries—MIND derives a global multi-labeled field to identify material interfaces. This enables accurate surface extraction via a multi-labeled Marching Cubes algorithm, effectively managing complex non-manifold surfaces across diverse data sources, including point clouds and multi-view reconstructions. The approach outperforms existing methods in robustness and accuracy.", "questions": "Why in Eq. 1 and 2 are the indicator functions normalized by a cubic term? It would be really good to have a limitations section in the paper. The MI insight seems cool, but is it always applicable. Further insights into where it works and where it fails would be invaluable.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The promise of UDFs have been well understood for some time, and the authors do a good job of walking the reader through the drawbacks of current approaches for extracting surfaces – in particular the sensitivity of Marching Cubes. The authors claim that at the time of publication, there is no method that can effectively extract non-manifold surfaces directly from a UDF. The central idea of the paper is to employ material interfaces (MIs), which is essentially a partitioning of the spatial domain into multiple labelled regions. What makes this work novel, is that they extend the concept of MIs to support both closed and open manifolds. They do this by introducing an additional label category for background material excluding all faces adjacent to it. The proposed approach offers impressive performance against DMUDF [22] and DCUDF [24]. The surface extraction results on the ShapeNet-Car dataset in Fig. 6 are impressive. The advantage of their approach over techniques like NU-NERF [41] is compelling.", "was_revised": false, "final_justification": "", "rebuttal": "## Why in Eq.1 and 2 are the indicator functions normalized by a cubic term?\n\nThe sign of a query point in our local side field is determined based on the normal vectors of nearby surface points. In manifold regions, these normals are typically consistent, leading to a stable sign determination. However, near non-manifold structures, multiple surface patches with differing normals may intersect. This can make the sign assignment ambiguous or unstable. \n\nTo address this, we adopt a formulation inspired by the generalized winding number, where the contribution of each neighboring point is inversely weighted by the cube of its distance to the query point. This cubic normalization gives more influence to points that are closer, effectively biasing the sign toward the dominant local geometry. In particular, it encourages alignment with the normal vector of the nearest surface patch, helping to suppress fluctuations caused by distant conflicting normals.\n\nThis weighting strategy improves robustness and locality in sign estimation, especially near regions with complex topology or non-manifold junctions.\n\n## It would be really good to have a limitations section in the paper. The MI insight seems cool, but is it always applicable. Further insights into where it works and where it fails would be invaluable.\n\nThanks for your suggestions. Our method can reliably generate non-manifold features where needed, in contrast to dual contouring variants that may introduce spurious non-manifold elements even in manifold regions. However, some limitations remain.\n\nFirst, our approach requires an erosion operation, which may inadvertently remove small geometric structures and lead to missing facets. We generally advise against using excessively low resolutions during erosion. If a lower resolution is necessary elsewhere (e.g., for sampling the unsigned distance field), we recommend applying erosion after upsampling the data.\n\nSecond, due to the optimization step involved in our pipeline, the method is more computationally expensive than non-optimization-based approaches. Nevertheless, this additional cost is justified by the significant improvement in reconstruction quality—particularly in faithfully preserving non-manifold structures, which existing methods are unable to achieve.\n\nPlease also see the discussion on limitations in the supplementary material."}, {"review_id": "eT0iRDtcam", "reviewer": "Reviewer_TBUd", "summary": "The authors propose MIND for generating material interfaces directly from unsigned distance fields by deriving a spatial partitioning. A three stage strategy is used - i) construction of a local two-signed distance field, (ii) extending the local two-signed field to a global multi-labeled field, and (iii) extraction of non-manifold surface meshes from the material interface. Qualitative results seem to show strong performance.", "questions": "1. How are your input UDF's obtained?\n2. Given that you are using voxel-based downsampling of point clouds, can you provide an ablation study of voxel resolution vs accuracy of capturing fine details?\n3. the non-manifold surface extraction method mentions using the value of $w_S^l$ to determine the intersection points. Can the authors explain how is this different from Neural Dual Contouring's approach (which uses the corner signs on a grid)?\n4. Laplacian smoothing tends to smooth/blur sharp features. Have the authors considered using a quadratic error function optimization to preserve the sharp features?\n5. Can the authors provide information on the computational time for MIND and compare it against baselines?\n6. Have the authors considered comparing against MeshCAP, MeshUDF?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "strengths:\n- Addresses a fundamental gap no other work has proposed before\n- Local two-signed field to global multi-labeled field strategy is novel\n- Adoption of laplacian smoothing is justified\n- Qualitative results indicate strong performance\n\nweaknesses:\n- Voxel resolution dependence causes missing out on finer geometric features\n- The performance of the method seems to be bottlenecked by the accuracy of the underlying UDF prediction method\n- Laplacian smoothing strategy makes it harder to judge the impact of the global labeling aspect of MIND\n- Lack of quantitative metrics like resolution sensitivity, parameter sensitivity (r1, r2)", "was_revised": true, "final_justification": "After reading responses to my questions and other reviewer's questions, I have decided to increase my rating.", "rebuttal": "## Voxel resolution dependence causes missing out on finer geometric features\n\nWe agree that resolution imposes fundamental limits on geometric accuracy. However, this limitation is not unique to our method, as it is shared by all voxel-based surface extraction techniques, including MC, DC and their many variants. \n\nThese methods generate discrete mesh representations, whose level of detail is inherently constrained by the grid resolution. While increasing resolution can recover finer details, the discrete and resolution-dependent nature  is a general characteristic of the entire class of methods.\n\n\n\n\n\n## The performance of the method seems to be bottle-necked by the accuracy of the underlying UDF prediction method.\n\nThis is in fact a common challenge for all mesh extraction algorithms. In general, no surface extraction method can recover geometric details that are not already encoded in the input distance field. However, different methods vary in how well they handle noise or imperfections in the UDF.\n\nOur method demonstrates improved robustness to UDF noise due to the erosion operation, which stabilizes region labeling and removes spurious fragments. Furthermore, the DCUDF-based optimization further refines the extracted geometry, improving accuracy up to the intrinsic limit imposed by the input UDF quality.\n\nMoreover, our method can further improve accuracy without increasing resolution by directly subdividing the mesh extracted from M3C and then performing the optimization process. For example, we trained a UDF on the Armadillo model using DEUDF, achieving a Chamfer Distance (CD) of 0.003484 at a resolution of 256. By applying one subdivision step (splitting each triangle into four), the CD decreases to 0.003335.\n\n\n## Laplacian smoothing strategy makes it harder to judge the impact of the global labeling aspect of MIND\n\nThanks for raising this question. It is important to note that the global multi-labeled field in MIND is responsible for determining the topological structure of the reconstructed surface, specifically, how different regions are partitioned and connected. \n\nIn contrast, Laplacian smoothing and subsequent DCUDF optimization refine only the geometry of the surface without altering its topology. \n\nThe impact of MIND’s global labeling can therefore be assessed through the topology-related results presented in the paper, such as geodesic distance comparisons and highlighted non-manifold edges. These reflect the correctness of the extracted connectivity structure, regardless of geometric smoothing.\n\n\n## Lack of quantitative metrics like resolution sensitivity, parameter sensitivity (r1, r2)\n\nThank you for the suggestion. \nThe parameters $r_1$ and $r_2$ depend on the grid size and can be flexibly adjusted as long as the conditions provided in the experimental section are met. We will provide quantitative results at different resolutions. \n\n\n## How are your input UDF's obtained?\n\nOur work focuses on extracting zero level sets from learned UDFs. Several prior works have developed methods to learn UDFs from point clouds or multi-view images. In our experiments, we use UDFs generated by a variety of state-of-the-art learning-based approaches, including CAPUDF, LevelSetUDF, DEUDF, NU-NeRF, and NeUDF. We use them as input to our method to evaluate the effectiveness of MIND in extracting non-manifold surfaces. \n\n\n\n\n## Given that you are using voxel-based downsampling of point clouds, can you provide an ablation study of voxel resolution vs accuracy of capturing fine details?\n\nThank you for your suggestion. We use PCA to calculate normals of point clouds. Generally, point cloud orientation algorithms require a dense point cloud to obtain sufficiently reliable normal vectors. Since calculating normals from point clouds and obtaining the local side field is not time-consuming, we do not recommend reducing the resolution of the point cloud downsampling. An excessively low point cloud density will decrease the reliability of normals, thereby generating unnecessary topological structures. We will supplement the relevant experimental results in the revision.\n\n\n## Can the authors explain how is this different from Neural Dual Contouring's approach (which uses the corner signs on a grid)?\n\nNDC uses a neural network to directly predict the corner signs of grid cells, which are then used to extract surfaces. However, this approach is sensitive to prediction errors due to inherent instability and lack of spatial consistency. For example, NDC may assign inconsistent signs to adjacent cubes where no surface is present, leading to redundant faces in the reconstructed mesh. \n\nIn contrast, our method computes the initial local side field using optimization based on geometric cues, rather than learned predictions. This provides enhanced stability and consistency, especially in regions with complex or ambiguous geometry. As a result, our method significantly reduces the types of artifacts commonly observed in NDC.\n\n## Laplacian smoothing tends to smooth/blur sharp features. Have the authors considered using a quadratic error function optimization to preserve the sharp features?\n\nThank you for your insightful suggestion. We agree that using the quadratic error function to compute vertex positions is effective for preserving sharp features. However, in this work, we focus on the non-manifold topology identification and non-manifold mesh extraction. Hence, we would like to leave this as a future work to improve the mesh accuracy.\n\n\n\n\n## Have the authors considered comparing against MeshCAP, MeshUDF?\n\nBoth MeshUDF and MeshCAP extend Marching Cubes to support surface extraction from UDFs. However, Marching Cubes is inherently limited to generating manifold structures, and these methods cannot preserve non-manifold structures by design. Since our method specifically targets non-manifold surface reconstruction, we believe it would be inappropriate to perform a direct comparison against approaches that are fundamentally restricted to manifold outputs.\n\nThat said, MeshUDF and MeshCAP remain useful baselines for evaluating performance on manifold regions, and we include them where relevant in our experiments. In particular, the original NeUDF employs MeshUDF for mesh extraction, and we reported the NeUDF results in both the main paper and the supplementary material. We will make this connection more explicit in the revised version."}, {"review_id": "NAC1g2zHq1", "reviewer": "Reviewer_duN2", "summary": "This paper presents a method for extracting meshes from arbitrary unsigned distance fields, including non-manifold structures. It comprises three stages – firstly a local assignment of 'sides' to near-zero regions of the UDF; then fusion into a single global label field (a material interface) by propagating information outwards from edges; then meshing of the label field. Experiments are conducted on UDFs derived from several applications – from point-clouds, images, and medial fields; these show the proposed method works better than two baselines.", "questions": "The bolded claim at L44 seems inconsistent with e.g. DMUDF and NDC – while these do not always work perfectly, they do address the relevant task/setting and can in principle achieve non-manifold surface reconstructions.\n\nIs it possible to perform the qualitative evaluation of similarity of geodesic distance fields instead quantitatively on the shapenet / deepfashion experiments?\n\nSee above regarding ablation experiments to justify design decisions – it would be valuable to know the quantitative effect that different aspects of the proposed method have on the final results, in order to help readers judge their importance.", "limitations": "Yes, limitations discussed, though in supplementary. No broader impacts", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper addresses an interesting problem of UDF reconstruction from points, that has received much less attention than the equivalent for SDFs.\n\nThe proposed method is novel. While there are ideas drawn from various other works, overall the approach is quite different in flavor to existing methods solving the task. The different stages of the pipeline are generally well-motivated.\n\nThe evaluation is quite comprehensive. Experiments are conducted on UDFs from different real-world pipelines – using two methods for UDF inference from point-clouds, and one for UDF inference from images. Results are significantly better than two other approaches.\n\nQualitative results exhibit non-manifold edges in reasonable locations while conforming closely to the desired geometry; the result on the shapenet car in fig. 6 is particularly impressive with very fine details of single-sheet geometry correctly recovered.\n\nQuantitative results exceed the performance of the baselines DMUDF and DCUDF, when measuring chamfer distance of reconstructed meshes from a point-cloud, to the original mesh the point-cloud was derived from. \n\nThere are no results on variants / ablations of the approach, which would reveal the benefit to the reader of certain design decisions. For example, at L182, small enhancements to M3C are described, which \"enhance accuracy\" and \"further refine\", yet there is no experimental validation of the extent to which these help; similarly for the refinement in the paragraph at L185.\n\nThe evaluation visualises geodesic distance fields as a way to show the topology of the mesh is similar to a corresponding point-cloud, i.e. that the mesh has not for example 'fattened' surfaces to be watertight. However, this evaluation is only qualitatively, and only shown on two examples. It would be valuable to do this also for the shapenet / deepfashion experiments in Table 2, since chamfer distance is a much poorer measure of topological correctness than similarity of the geodesic distance field. One easy way to achieve this would be to measure mean similarity of geodesic fields at pairs of nearest-points in original and reconstructed meshes.\n\nThe subject area is only borderline appropriate for NeurIPS – it is pure computer graphics / geometry processing, with no machine learning involved in the proposed approach (it can be applied to neural UDFs, but that is not in any way intrinsic to the method).", "was_revised": true, "final_justification": "Given the rebuttal responses and discussion, I still favor acceptance. However I am not increasing my rating further, mainly due to the lack of ablations on different aspects of the method (which the authors did not provide even in quantitative form during the rebuttal period), and also the lack of numerical results for topological similarity (which is somewhat important given the focus of the paper on reconstructing specific topologies faithfully).", "rebuttal": "## There are no results on variants / ablations of the approach, which would reveal the benefit to the reader of certain design decisions. For example, at L182, small enhancements to M3C are described, which \"enhance accuracy\" and \"further refine\", yet there is no experimental validation of the extent to which these help; similarly for the refinement in the paragraph at L185.\n\n\nThank you for pointing this out. We agree that ablation studies are valuable for understanding the contribution of each component. \n\nIn the revision, we will include additional mesh extraction results that compare our method to the original M3C and our pipeline without DCUDF optimization. \n\nHowever, due to this year's NeurIPS rebuttal guidelines that prohibit uploading additional figures, we are unable to include these visual results in the current response. We will ensure that these ablations are clearly presented and discussed in the revised submission.\n\n\n\n## The bolded claim at L44 seems inconsistent with e.g. DMUDF and NDC – while these do not always work perfectly, they do address the relevant task/setting and can in principle achieve non-manifold surface reconstructions.\n\nThank you for the observation. We agree that both DMUDF and NDC are capable of generating non-manifold surfaces in principle. \nWe will revise the statement to clarify our intended meaning: while these methods may produce non-manifold structures, they often do so without explicitly controlling for manifold corrrectness. As a result, they may introduce unintended non-manifold artifacts even in regions that should be manifold. \n\nIn contrast, our method is specifically designed to capture non-manifold features where they are required, while preserving the integrity of manifold regions. \n\nWe will revise the statement and clarify this distinction in the revision. \n\n\n## Is it possible to perform the qualitative evaluation of similarity of geodesic distance fields instead quantitatively on the shapenet / deepfashion experiments?\n\nThank you for the suggestion. ShapeNet could indeed be a suitable candidate for evaluating the effectiveness of MIND. However, in practice, many ShapeNet models are constructed by stacking individually modeled manifold parts, which are not truly non-manifold in a topological sense, and would require extensive data preprocessing and remeshing to convert them into a clean dataset with genuine non-manifold topology. \n\nOnce such preprocessing is completed, it would be possible to perform quantitative evaluations, such as comparing geodesic distance fields computed on the extracted surfaces against ground-truth mesh surfaces. \n\nHowever, because of the significant preprocessing effort required, we consider this to be a direction for future work.\n\n\n\n## The subject area is only borderline appropriate for NeurIPS – it is pure computer graphics / geometry processing, with no machine learning involved in the proposed approach (it can be applied to neural UDFs, but that is not in any way intrinsic to the method).\n\nOur method is designed to address a critical bottleneck in UDF-based 3D learning pipelines. As an effective mesh extraction algorithm for UDFs, our method directly supports and enhances neural approaches for 3D reconstruction and generation. \n\nUDFs have recently gained significant attention in the AI and NeurIPS communities as a flexible representation for 3D shapes, especially in tasks involving neural implicit functions. Prior works (e.g., NDF, CAP-UDF, NeUDF, NU-NeRF, DreamUDF) demonstrate the advantage of UDFs in representing open surfaces, but their full potential, specifically for representing non-manifold structures, remains underutilized due to the lack of suitable mesh extraction algorithms.\n\nAlthough some methods such as DMUDF and NDC attempt to extract non-manifold geometry, they often introduce uncontrolled and excessive non-manifold artifacts, even in regions that are intrinsically manifold. In contrast, our method explicitly preserves manifold regions while correctly capturing non-manifold features, unlocking a unique capability of UDFs that was previously inaccessible.\n\nWe believe that our method has direct implications for learning-based 3D reconstruction. For example, NU-NeRF reconstructs nested transparent objects by combining multiple SDFs but suffers from discontinuities at non-manifold intersections due to the limitations of SDFs. Similarly, in 3D generation, methods such as TripoSF aim to produce models with rich internal structures, but the use of SDFs prevents mesh reconstruction at non-manifold junctions. Our method may inspire 3D AIGC work on generating non-manifold structures, either by extracting meshes from neural UDFs or, in the future, by attempting to integrate material interface (MI) prediction into neural pipelines.\n\nIn summary, we believe our work makes a foundational contribution to UDF-based shape modeling, which is highly relevant to current and emerging research directions in 3D learning. We hope that by presenting this work at NeurIPS, we can stimulate further research in this area and provide a missing tool for the community working on UDF-based 3D reconstruction and generation."}, {"review_id": "4NTdCMH2VM", "reviewer": "Reviewer_Tx5y", "summary": "To extract meshes from Unsigned distance fields (UDFs), the authors proposed a novel algorithm, MIND, to generate material interfaces directly from UDFs, enabling non-manifold mesh extraction from a global perspective. The effectiveness of MIND is demonstrated on different data sources including UDFs from point cloud reconstruction, multi-view reconstruction, and medial axis transforms.", "questions": "1.\tWhat is the N.A. in Figure 5?\n2.\tIn addition to chamfer distance, are there any other metrics to demonstrate the superiority of MIND?\n3.\tThe presented results are obtained on simple scenarios. Can the non-manifold be applied to more realistic and complex scenarios, such as medical image scenarios?", "limitations": "The potential applications of the proposed method should be discussed in more detail.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\nThe authors proposed MIND to extract no-manifold meshes directly from the UDFs. As they claimed, no previous method has effectively extracted non-manifold surfaces directly from UDFs. \n\nWeakness:\n1. The advantage of non-manifold surfaces compared to manifold surfaces should be discussed in more detail, including more realistic scenarios where manifold surfaces cannot work while non-manifold surfaces can.\n2. In the qualitative results of Figure 5, I would also suggest presenting the original images, which helps to determine which results are closer to the ground truth.\n3. In Table 2, I would suggest presenting the standard deviation of CD and conducting a statistical significance analysis.\n4. The authors only utilize CD for quantitative evaluation, which is not enough to demonstrate the performance of MIND.", "was_revised": true, "final_justification": "I believe the results of the standard deviation of CD and a statistical significance analysis are important to evaluate if there is a significant improvement in the performance. However, I didn't see additional results on them.", "rebuttal": "## In the qualitative results of Figure 5, I would also suggest presenting the original images, which helps to determine which results are closer to the ground truth.\n\nThanks for your suggestion. We will provide the original images in the revision.\n\n\n\n## What is the N.A. in Figure 5?\n\nIn this case, N.A. indicates that DMUDF fails to extract any mesh facets from the given UDF. \n\nSpecifically, DMUDF uses an octree-based structure to improve computational efficiency, but it relies on the UDF being accurate across the entire spatial domain. \nHowever, DEUDF, as a UDF learning method, focuses on accuracy near the surface and often produces unstable or noisy UDF values farther away. This inaccuracy leads the DMUDF octree to misidentify valid leaf nodes, resulting in complete reconstruction failure in large regions. As a result, no mesh can be generated for this case, and we mark it as N.A. in Figure 5 to reflect this failure.\n\n\n## In addition to chamfer distance, are there any other metrics to demonstrate the superiority of MIND?\n\nThe main advantage of MIND over previous methods lies in its ability to support non-manifold surface reconstruction. However, there is currently no standardized benchmark for quantitatively evaluating this capability. To partially address this, we incorporate geodesic distance comparisons in our experiments to help assess the quality and correctness of the extracted non-manifold structures.\n\n\n\n\n## The presented results are obtained on simple scenarios. Can the non-manifold be applied to more realistic and complex scenarios, such as medical image scenarios?\n\n\nYes, MIND can be applied to more realistic settings. In fact, we have tested our method using UDFs learned by NUDF on the Left Atrial Appendage (LAA) segmentation dataset, which contains anatomically complex structures and potential non-manifold features. We will provide the visual results in the revision."}]

Author rebuttal:

Meta-review: This paper proposes a novel method for extracting non-manifold meshes directly from Unsigned Distance Fields (UDFs).

The paper initially received one accept and three borderline-accept scores. Reviewers highlighted several strengths:
- Extending material interfaces to support both closed and open manifolds is a novel idea.
- Evaluation is comprehensive.
- Results demonstrate strong performance.

There were some concerns/questions raised, including the lack of an ablation study, clarification of differences from existing methods, limitations, and applicability to more complex scenarios. The authors addressed most of these concerns in their rebuttal. The final ratings are 2× accept, 1× borderline accept, and 1× borderline reject. Reviewer Tx5y suggested borderline reject due to the absence of standard deviation of CD and a statistical significance analysis, and these were provided during the rebuttal. Given this, the AC believes the merits of the work warrant acceptance. The authors are strongly encouraged to incorporate the promised updates in the final version.
Decision: Accept (poster)