Title: MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction
Venue: NeurIPS 2025
Accepted: yes
Keywords: Unsigned distance fields

neural implicit field

zero-level sets

non-manifold surface reconstruction

material interfaces
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

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.

1 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 a surface, enabling straightforward surface extraction via well-established methods such as Marching Cubes (MC) [1]. While recent adaptations of SDF [2-5] 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 a more flexible framework capable of representing a wide range of surface topologies, including

open and closed surfaces, non-manifold geometries, and shapes with complex internal structures [619]. However, this flexibility comes at a significant cost: the absence of sign information makes it 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 involves reconstructing local SDFs from UDFs using gradient-based estimation [6, 11, 20] or neural prediction [21] to approximate sign information and identify zero-level set 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] generalize dual contouring [24] to improve reconstruction quality, but they often introduce unintended non-manifold artifacts due to inconsistent topological handling. Mesh deformation methods, such as DCUDF [25, 26], improve robustness by iteratively shrinking an initial double-layered manifold surface to fit the target geometry. However, since the initial surface is 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 a 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.

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On the other hand, non-manifold structures are ubiquitous in many applications, such as anatomical modeling [28, 29], composite materials [30, 31], multi-phase fluids [32-35], and bubble simulations [36, 37]. These structures are 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 { F 1 , ..., F n } as shown in Figure 1(c).

Traditional MI representations are limited to closed surfaces, i.e., surfaces without boundaries. As illustrated in Figure 1, we define an enclosing envelope Ω 1 around the surface. The surface boundaries are extended slightly to intersect with Ω 1 to form MI partitions inside Ω 1 . The outside of Ω 1 is treated as background and assigned the label F 0 . This generalization allows us to deal with not only closed but also certain open non-manifold surfaces and to apply multi-label Marching Cubes methods, such as M3C [27], to reconstruct non-manifold meshes from such labeled partitions. Redundant surfaces, such as faces adjacent to the background, are removed.

However, MI is not a 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 (e.g., from CT images). In contrast, UDFs serve as a more universal

representation and have been widely adopted in many classic 3D reconstruction tasks, such as point cloud reconstruction [6-12], multi-view image reconstruction [13-16] and 3D generation [17-19].

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 a two-labeled field to distinguish between the two sides of a local surface patch using positive and negative signs. Second, we extend the local two-signed field into a global multi-labeled field, assigning unique labels to each side of a 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 to ensure both visual accuracy and topological coherence. We evaluate our method on a variety of datasets and UDF learning methods. Experimental results demonstrate that our approach generates clean meshes that accurately capture non-manifold structures, where existing methods often fail.

The main contributions of the paper are as follows:

We develop an algorithm for generating MIs from learned UDFs, enabling robust nonmanifold 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.

We introduce a novel algorithm that extends the local two-sided field-capable of distinguishing the two sides of local manifold patches-into a global multi-labeled field, enabling the differentiation of multiple sides of non-manifold surfaces.

We conduct extensive evaluations across diverse datasets and UDF learning methods. Experimental results demonstrate the capability of our method in extracting clean and accurate manifold and non-manifold meshes, outperforming existing techniques.

2 Related Works

2.1 Manifold Reconstruction

Recently, deep learning approaches have gained traction in surface reconstruction. These methods learn SDFs [39-49] 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 [1, 52], which inherently guarantee watertight manifold models. Extensions of SDFs to support open surfaces typically involve introducing additional constraints or masks [2-5]. 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 a promising alternative for representing surfaces with diverse topologies, including open surfaces, non-manifold geometries, and shapes with complex internal structures [6-11, 13-19, 53]. By discarding the sign term of SDFs, UDFs offer greater flexibility, enabling the representation of complex models, including non-manifold surfaces. However, most UDF-based methods primarily focus on open manifold surfaces, with limited exploration of non-manifold surface reconstruction. The primary obstacle lies in the lack of a robust mesh extraction algorithm tailored for non-manifold structures from UDFs.

Recent advancements have focused on extracting the zero-level sets from UDFs using modified Marching Cubes. Some methods [6, 11, 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-manifold structures, sampling point clouds from UDFs and applying non-manifold-specific methods [54] have been explored but suffer from low accuracy and robustness. Dual Contouringbased methods, such as NDC [22] and DMUDF [23], 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.

Existing non-manifold mesh extraction algorithms are predominantly applied in the context of material interfaces (MIs). MI represents a collection of regions where the target surface corresponds to 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 [32-35], where space is naturally segmented into distinct regions.Using the MI as input, multi-label algorithms, such as M3C [27], handle non-manifold surfaces by leveraging explicit material interface definitions. While effective, they require predefined region labels or arrangements, limiting their applicability.

In this paper, we aim to address the limitations of these approaches by introducing a 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.

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3 Method

In this work, we generate MIs from input UDFs to enable the extraction of non-manifold meshes from UDFs. As illustrated in Figure 2, our method consists of three key steps: In Section 3.1, we construct a local two-signed field to distinguish the two sides of manifold patches within the input UDF. In Section 3.2, the local two-signed field is extended to a 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-manifold surface meshes from the MI.

3.1 Local Two-Signed Fields

To generate the MI of the input UDF, we need to segment the 3D space into different partitions. As shown in Figure 2, 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 a surface S , given consistently oriented normals n x of points x ∈ S , we introduce the following indicator function w l S ( q ) to compute a side field for a query point q :

where ϵ is a small positive to avoid division by zero. Different from the generalized winding number, the region of integration is modified from the entire surface S to a local neighborhood N S ( q ) on S around the point q . This adjustment allows w l S to distinguish between the two sides of a local manifold using positive and negative signs.

Implementation Details Weextract a point cloud from the given UDF. Points are sampled randomly in space Ω 1 where the UDF values are equal to a threshold r 1 and these points are projected toward local minima, similar to the approach in [10]. The point cloud is then downsampled using uniform grid voxels to obtain a uniform initial point cloud P . Next, we apply [58] to compute oriented

normals for the points. Although [58] may result in flipped normals, the orientations are piecewise consistent, ensuring that most are oriented consistently. The discrete form of w l S ( q ) is,

We discretize the space into voxels and compute the side field only for the voxels o i inside Ω 1 , as points far from the surface are not of interest. Any voxel outside Ω 1 is considered background and assigned the label F 0 . w l S ( 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 or regions with flipped normals, w l S is not well-defined. These issues will be refined in the following Section 3.2.

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3.2 Global Multi-Labeled Fields

In this section, we generate the global multi-labeled distance field, which is able to distinguish all sides of a non-manifold surface, from the local two-signed side field. We cluster voxels based on the two signs of w l S by applying the 3D connected component labeling algorithm 2 . This algorithm assigns a label F i to each voxel that is connected and has the same sign (positive or negative). As a result, voxels within Ω 1 are split into a set of partitions { R k } . However, non-manifold or normal flipping regions, where three or more partitions coincide, are scarcely possible to be properly divided only by the two signs of w l S . As shown in Figure 3, 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 R e k and the remaining voxels by R r k . For the voxels in all the connected components of R r k , we assign different new labels F k to different connected components of R r k . Each voxel in R e k should be labeled by one of the labels of F k . The goal is to minimize variations in neighboring labels of R e k . Therefore, we minimize the following energy for labeling:

Here, f ( o i ) represents the to be solved label assigned to voxel o i , f s ( o i ) denotes the label assigned to voxels in R r k , 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

invariant. Occasionally, R k may be so small that R r k and F k are empty sets. In such cases, we omit the constraint. Equation (3) can be solved using α -expansion [59].

After refinement, the partitions ensure that the two sides of a non-manifold belong to different partitions. However, over-segmented partitions may exist, as shown in Figure 3, which are unavoidable in the two-signed field near non-manifold edges. These over-partitions should be merged. Otherwise they would lead to 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, Ω 2 , by extracting an iso-surface at value r 2 ( r 2 < r 1 ) from the UDF. This gives us the relation S ⊂ Ω 2 ⊂ Ω 1 . If two partitions are separated by S , their boundary voxels should lie within Ω 2 . Conversely, if two partitions are not separated by S , most of their boundary voxels should be outside Ω 2 , but still within Ω 1 -Ω 2 . As illustrated in Figure 3, through these simple tests, we can effectively merge redundant partitions, ensuring that different sides of a non-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 at the midpoint of each cube edge, we use the value of w l S to determine the intersection points, enhancing accuracy. We do not generate the face associated with the background label F 0 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 Ω 2 are removed.

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However, the accuracy of w l S remains limited by discretization. To address this limitation, we refine the extracted mesh M by optimizing its alignment with the input UDF as shown in Figure 4. Inspired by DCUDF [25], we fine-tune M by minimizing its UDF values for improved accuracy while incorporating a Laplacian regularization term to maintain the mesh's shape and prevent face folding. Unlike DCUDF, our mesh M contains non-manifold edges, where traditional Laplacian computation is not well-defined. For a point p m on a non-manifold edge, using all adjacent points to compute the Laplacian fails to prevent face folding, as illustrated in Figure 5. 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 p i ∈ M , the Laplacians are computed separately in each group of adjacent faces. For example, for a point on the non-manifold edge of a T-shape, there are 3 groups of adjacent faces and 3 Laplacian terms. We optimize the following loss function to refine the mesh,

where f ( · ) denotes the UDF values and π ( p i ) is the new location of point p i after optimization. S denotes the set of signs and M s is the sub-mesh whose faces border on the sign s . N s ( p i ) denotes the 1-ring neighboring points of p i in M s . The first term, f ( π 1 ( p i )) , drives the points p i toward the local minima of the UDF. The second Laplacian term prevents the triangular face from folding.

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4 Experimental Results

4.1 Experimental Setup and Hyperparameters

We normalize 3D models to fit within [ -0 . 5 , 0 . 5] 3 and use a bounding box of [ -0 . 6 , 0 . 6] 3 to contain the UDFs. For calculating the local two-signed field, we sample 1 million points on the r 1 level set and optimize their positions to align with the local minima of the UDF. The resolution is set to 256 3 , resulting in a voxel size of 0.0046. The voxel size for point cloud downsampling 3 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 r 2 = 0 . 01 to generate a continuous Ω 2 . To ensure Ω 1 is larger than Ω 2 , r 1 is set to 0.05. We erode the local two-signed field 2 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 Ω 1 -Ω 2 is three times greater than the number of voxels within Ω 2 . A more detailed experiment of hyperparameters can be found in Section A of appendix.

We use M3C [27] to extract meshes, implemented in Dream3D 4 . 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 in our paper, most of them correspond to the resolution and exhibit generalizability across different types of learned distance fields. All results are tested on a single NVIDIA V100 GPU.

4.2 Comparisons

Baselines To the best of our knowledge, no 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 algorithms, including DCUDF [25], and DMUDF [23]. While DCUDF uses double-layered manifold meshes to approximate non-manifold structures, DMUDF is capable of generating non-manifold edges. To assess the topological correctness of the extracted meshes, we compute geodesic distances, which are highly sensitive to topological features. Specifically, we use the heat method [60] with a 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 We learn UDFs from unoriented point clouds using CAPUDF [6], LevelSetUDF [7], and DEUDF [8], respectively. The results are shown in Figure 6, with non-manifold edges highlighted in red. We compare our method with DMUDF and DCUDF.

DMUDF [23], a Dual Contouring variant, is capable of generating non-manifold edges. However, the process of generating non-manifolds in DC is often uncontrolled, resulting in a 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 a specific leaf node, DMUDF relies on a key criterion based on the UDF value at the node's center point. This approach is highly sensitive to UDF accuracy, making it prone to failure in the presence of noise or inaccuracies in the UDF. Such issues can cause the octree subdivision process to terminate prematurely. As 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

LevelsetUDF

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result in significant missing regions in DMUDF's output when a node's center point is far from the vicinity of the target surface. DCUDF [25] approximates the target non-manifold surfaces using a 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 as a geometrical metric. Table 1 presents the results on the ShapeNet-Car [62] dataset and DeepFashion3D [63] dataset. The visualization results of ShapeNet-Car dataset are shown in Figure 7, where our visual results are the best.

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 our method and compare it with baselines on UDFs generated by NU-NeRF [43] on 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 a post-processing step to remove these redundant components, it creates discontinuities between the inner and outer meshes.

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To address this, we combine the two SDFs 5 to a 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 8, 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 8. NeUDF employs MeshUDF [20], a gradient-based Marching Cubes, for mesh extraction from learned UDFs. However, this approach fails in non-manifold regions due to the lack of a 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 to zero, leading to complete reconstruction failure for transparent objects. DCUDF addresses this limitation by extracting non-zero level sets, allowing it to 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-manifold surfaces. This highlights the robustness and versatility of our approach compared to existing methods.

UDFs Induced from Q-MDF [64] Non-manifold structures frequently appear in medial axes. QMDF [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 a double-layered manifold mesh. Consequently,

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this approach fails to preserve the non-manifold characteristics of medial axes. By utilizing MIND, we extract high-quality, single-layered non-manifold medial axes, as demonstrated in Figure 9.

Limitations We use α -expansion [59] to label voxel grids, which is time-consuming. 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 α -expansion computation effectively reduces costs. Another alternative is to use dilation instead of alpha expansion, which has a time cost independent of the number of labels but yields an approximate solution. On the other hand, our approach requires an erosion operation, which may inadvertently remove small or thin MI regions and lead to missing facets, as shown in Figure 10.

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5 Conclusions

In this paper, we introduce MIND, a 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 a broader range of scenarios. Our experimental results across various types of UDFs demonstrate the effectiveness of MIND in generating MIs for accurate nonmanifold mesh reconstruction. In its current form, our implementation generates MI from pre-learned 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.

Acknowledgments and Disclosure of Funding

This project was partially supported by the National Key R&D Program of China (2023YFB3002901), the Research Projects of ISCAS (ISCAS-JCMS-202303, ISCAS-ZD-202401, ISCAS-JCZD-202402, ISCAS-JCMS-202403), 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, we use a resolution-dependent voxel size to downsample the point cloud. As Figure 11 shows, a smaller voxel size does not affect the result but introduces a larger computational overhead. Conversely, if the voxel size is set too large (e.g., 0.01), the point cloud becomes too sparse and holes appear in the reconstructed model. Our r 1 and r 2 values are also set according to the resolution to maintain them within proper ranges. As shown in Figure 12, moderate changes in these parameters are acceptable, but excessive adjustments can cause problems. Though a large r 1 does not introduce issues beyond computational overhead, an overly small r 1 (e.g., 0.03) could cause the erosion step to delete all regions, leading to reconstruction failure. An excessively large r 2 (e.g., 0.02) can lead to insufficient region merging, whereas an overly small r 2 (e.g., 0.0025) can result in unnecessary merging.

0.002

0.005

0.0075

0.01

r

1

= 0

.

1

r

1

= 0

.

075

r

1

= 0

.

05

r

1

= 0

.

04

r

1

= 0

.

03

r

2

= 0

.

02

r

2

= 0

.

015

r

2

= 0

.

01

r

2

= 0

.

0075

r

2

= 0

.

0025

N.A.

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 as intersections between transparent objects and overlapping thin plate structures. These configurations represent challenging cases for signed distance fields to represent in practical scenarios. For point cloud reconstruction and medial axis transformations, we present additional results in Figure. 14 and Figure. 15, demonstrating the versatility of our approach. We also collected some more complex data to further illustrate the robustness of our method, as shown in Figure 16.

C Failed Case

As illustrated in Figure 17, the two sides of the non-orientable surface are indistinguishable, resulting in the absence of a well-defined MI. Consequently, our method fails to generate MIs for the surface, leading to artifacts in the extracted mesh.

Reference image

Sample point cloud

NU-NeRF

DCUDF

Ours

Non-manifold edges

Reference image

Sample point cloud

DCUDF

Ours

DEUDF

Sample point cloud

DCUDF

Ours

Sample point cloud

DCUDF

Ours

N.A.

N.A.

Sample point cloud

Ours

Ours

Sample point cloud

Ours

Ours

Geodesic distance

Non-manifold edge

Geodesic distance

Non-manifold edge

(a)

(b)

(c)

(d)

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Peer reviews:
comments: 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.

STRENGTHS AND WEAKNESSES:
Strength:
The 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. 

Weakness:
1. 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.
2. 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.
3. In Table 2, I would suggest presenting the standard deviation of CD and conducting a statistical significance analysis.
4. The authors only utilize CD for quantitative evaluation, which is not enough to demonstrate the performance of MIND.

QUESTIONS:
1.	What is the N.A. in Figure 5?
2.	In addition to chamfer distance, are there any other metrics to demonstrate the superiority of MIND?
3.	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?

LIMITATIONS:
The potential applications of the proposed method should be discussed in more detail.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nThe 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).\n\nQUESTIONS:\nThe 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.\n\nLIMITATIONS:\nYes, limitations discussed, though in supplementary. No broader impacts", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nstrengths:\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)\n\nQUESTIONS:\n1. 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?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nThe 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.\n\nQUESTIONS:\nWhy 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.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-05"}