High Resolution UDF Meshing via Iterative Networks
Authors: Federico Stella
Nicolas Talabot
Hieu Le
Pascal Fua
Venue: NeurIPS 2025 poster ()
Keywords: unsigned distance fields
udf
meshing
surface extraction
neural implicit representations
Primary area: applications
TL;DR: We extract meshes from unsigned distance fields at high resolution, mitigating the long-standing problem of missing surface portions

Abstract: Unsigned Distance Fields (UDFs) are a natural implicit representation for open surfaces but, unlike Signed Distance Fields (SDFs), are challenging to triangulate into explicit meshes. This is especially true at high resolutions where neural UDFs exhibit higher noise levels, which makes it hard to capture fine details.

Most current techniques perform within single voxels without reference to their neighborhood, resulting in missing surface and holes where the UDF is ambiguous or noisy. We  show that this can be remedied by performing several passes and by reasoning on previously extracted surface elements to incorporate neighborhood information. Our key contribution is an iterative neural network that does this and progressively improves surface recovery within each voxel by spatially propagating information from increasingly distant neighbors. Unlike single-pass methods, our approach integrates newly detected surfaces, distance values, and gradients across multiple iterations, effectively correcting errors and stabilizing extraction in challenging regions. Experiments on diverse 3D models demonstrate that our method produces significantly more accurate and complete meshes than existing approaches, particularly for complex geometries, enabling UDF surface extraction at higher resolutions where traditional methods fail.

High Resolution UDF Meshing via Iterative Networks
Federico Stella', Nicolas Talabot', Hieu Le², Pascal Fual
CCVLab, EPFL
UNC Charlotte
"nle40@charlotte.cee
Abstract
Unsigned Distance Fields (UDFs) are natural implicit representation for open surfaces but, unlike Signed Distance Fields (SDFs), are challenging to triangulate into explicit meshes. This is especially true at high resolutions where neural UDFs exhibit higher noise levels, which makes it hard capture fine details.
Most current techniques perform within single voxels without reference to their neighborhood, resulting in missing surface and holes where the UDF is ambiguous or noisy. We show that this can be remedied by performing several passes and by reasoning previously extracted surface elements to incorporate neighborhood information. Our key contribution an iterative neural network that does this and progressively improves surface recovery within each voxel by spatially propagating information from increasingly distant neighbors. Unlike single-pass methods, approach integrates newly detected surfaces, distance values, and gradients across multiple iterations, effectively correcting errors and stabilizing extraction in challenging regions. Experiments on diverse 3D models demonstrate that our method produces significantly more accurate and complete meshes than existing approaches, particularly for complex geometries, enabling UDF surface extraction at higher resolutions where traditional methods fail.
Introduction
Implicit Neural Representations [35, 12, 26] have become powerful tools to accurately model objects whose topology is priori unknown and without being bound to a specific mesh resolution. Those based on Occupancy Fields [23] or Signed Distance Functions (SDFs) [27] are best at handling watertight surfaces. They can be used represent open surfaces by wrapping a thin volume around them, but this is less than ideal. Unsigned Distance Fields (UDFs) offer more effective alternative [6, 44, 46, 30, 45, 11, 40] and are used by many surface reconstruction methods [20, 21, 19]. In typical scenario, a neural network is used to parametrize the field, which is then converted into an explicit mesh for downstream tasks through a meshing process. There are many algorithms to do this conversion well when the field features sign changes to signal surface locations [18, 15, 32, 29]. However, there are no such sign changes in the UDF case and the field is expected to be exactly zero at the surface location.
Most current approaches meshing UDFs [46, 41, 14, 36] rely on Marching Cubes or Dual Contouring- like algorithms that operate on the vertices of individual voxels to recover the sur- face that may or may not traverse them. However neural UDFs are notoriously noisy [13, 36, 14), which makes it hard to retrieve the correct surface. Counterintuitively and contrary to SDFs increasing the meshing resolution retrieve finer surface details actually worsens the problem, as shown in the results section (Fig. 5). This is because, at high resolutions, UDF values often become noisier or ambiguous within a voxel, and these local, single-pass methods lack the necessary context to infer the surface reliably, resulting in poorly recovered geometry. As shown in Fig. when the neural UDF fails to reach sufficiently low values, hole appears in the reconstructed surface. This
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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GT Mesh
True UDF
Neural UDF
MeshUDF [13] NSD-UDF [36] DMUDF [41] Ours - iter. 1
Ours - iter. 2 Ours iter.
Figure I: Avoiding holes in plane cockpit. (Top) Compared to the ground-truth UDF of plane, approximate neural UDF may fail reach zero, shown in white, the true surface location. This clear in the UDF detail shown in the upper right corner, where the two white areas are disconnected. This yields disconnections and holes in the reconstructions, especially high resolutions. (Bottom) This causes holes in the surfaces reconstructed by current methods. By leveraging neighboring surfaces, our iterative method properly recovers the cockpit nevertheless.
particularly apparent around the planes's 's cockpit, as shown in the upper right corner of the figure where existing methods do not reliably detect surface, even though there is local minimum region. Thus, looking beyond single voxels is necessary, attempted in [5, 13]. However, these attempts rely on basic propagation heuristics or a simple increase of the receptive fields and still fail high resolutions, also shown in the results section.
In this paper, argue that, to recover the missing parts and fill the holes, meshing models should incorporate information from previously extracted surface elements, which requires several consecutive extraction passes. To meet this challenge, we introduce iterative refinement approach. Given a voxel traversed by surface, it progressively improves the accuracy of the surface recovery by incorporating information previously obtained from increasingly distant voxels. Thus, instead of extracting surfaces in single pass, we improve the mesh over multiple iterations, where each step integrates newly detected surfaces, distance values, and gradients from neighboring cells.
In extensive experiments on diverse datasets, we show that our spatial propagation helps correcting error,, stabilizing surface extraction, and refining surface localization, particularly where the UDF is ambiguous or noisy, that is, enabling high-resolution meshing where single-pass methods would fail. Thus, contribution is novel recursive approach to meshing UDFs that gives much better results than earlier ones at high resolutions.
2 Related Work
Signed and unsigned distance fields are now in widespread use to represent 3D surfaces, which are typically parameterized by latent vector that decoded by deep network [23, 27, 6]. Shapes not tied specific resolution, but only to the representational power of the deep network in use. Neural signed distance fields (SDFs) are limited to watertight shapes but are relatively easy mesh, whereas unsigned distance fields (UDFs) can represent open surfaces. They used in volume rendering, shape reconstruction from multi-view and shape generation with a variety of techniques [20, 21, 19, 7]. but they are much harder to mesh.
Triangulating Signed Fields. Marching Cubes (MC) [22, 18] and Dual Contouring (DC) [15] are widely used to mesh signed fields by detecting sign transitions within voxels of a 3D grid. MC interpolates vertex positions along cell edges, while DC places them inside cells and optimizes their locations. Deep-learning adaptations, such as Neural Marching Cubes (NMC) [4] and Neural Dual Contouring (NDC) [5], improve on the classical methods by eliminating the need for manually defined rules or accurate field gradients, respectively. FlexiCubes [32] yields impressive performance on neural SDFs used for shape optimization while McGrids [29] improves the scalability of surface extraction at high resolution. In all methods increasing the resolution, the number of points used, typically produces more detailed meshes at higher computational cost. However, as they rely on sign changes, none of these methods is directly applicable to UDFs.

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Triangulating Unsigned Fields. Meshing neural unsigned distance fields (UDFs) is more difficult than meshing signed ones because the surface is assumed be where the field reaches zero, as opposed to where it crosses from positive to negative values. In the latter case, small field value errors may slightly shift the surface location whereas, in the former, it may result in the surface being missed altogether and undesirable holes appearing in the reconstruction, as in Fig. 1.
NDF [6] uses a ball-pivoting algorithm to mitigate this problem. Unfortunately, its reliance on dense point clouds and expensive processing takes hours per mesh and makes it impractical. Methods such as MeshUDF [13] and CAP-UDF [44, 46] assign pseudo-signs to the field values by comparing gradients so that MC can be used, but they are subject to artifacts, especially on complex geometries. MeshUDF partially conditions its pseudo-signs on previously computed voxels by defining a specific woxel-exploration order, but it does so in single pass and with heuristic that targets simple shapes such as garments. DCUDF [14] extracts an é-level set using MC, refines it by minimizing loss function, and cuts it to a single thin surface using a min-cut algorithm [2]. It produces smooth surfaces but requires much manual tuning, long processing times, while sometimes failing to properly eut the inflated surface. While the method refines the vertex locations with an optimization procedure, the mesh extraction is still carried out in a single pass. In NSD-UDF [36], a neural network predicts pseudo-signs starting from local UDF values and gradients, which can be meshed using SDF-like triangulation methods such as MC and DualMesh- UDF [41]. However, all these methods struggle at high resolutions on neural UDFs, where gradients and field values can become very noisy. This interferes with the proper generation of pseudo-signs, surface cuts, or dual vertices, depending on the specific method being used. This can yield inconsistencies and holes in the reconstructed surfaces, which our iterative approach is designed to prevent.
Since DC is popular alternative to MC, it has also been adapted to work with UDFs. DualMesh- UDF [41] prunes grid cells via a UDF-based threshold and refines vertices using a DC-like quadratic equation. While preserving sharp features, it relies on hand-crafted filtering rules that can produce holes and require manual tuning. This tuning can be partially avoided by using [36] for pre-processing. However the approach still struggles at high resolutions when there is noise. Unsigned Neural Dual Contouring (UNDC) [5] uses a 3D CNN to predict dual vertex locations and connectivity. Training the network requires heavy data augmentation and ignores gradient information, limiting the method's accuracy on neural UDFs [41, 36].
Iterative Refinement. Recursive refinement techniques for network predictions have been demon- strated across many domains [24, 28, 37, 33]. These approaches use the surrounding context to improve predictions [31, 9]. proving especially effective for tasks such as delincation [34, 10], human pose estimation [25], semantic segmentation [42], and depth estimation [8]. These methods have inspired us to develop the first-ever iterative approach to UDF meshing.
Mitigating noises in UDFs. Several approaches have been proposed to learn less noisy UDFs. Zhou al. [44, 46] enforced parallel level sets near surfaces to improve learning from sparse point clouds. Fainstein et al. [11] use hyperbolic scaling and second-order differentiation to reduce the noise gradients and ensure the differentiability of the field. Zhao et al. [43] used anshor-based 3D position features to enhance UDF predictions, aiding single-view garment reconstruction. Wang et al. [39] predicted pseudo-signs from surface gradients for meshing, while Venkatesh et al. [38] leveraged surface orientation for better local geometry. However, precise UDF predictions remain challenging, as existing methods struggle to climinate holes and discontinuities in meshed surfaces.
3 Method
A neural UDF can typically be written as
Us :
R
x R" + R+
(I)
x
where Us is implemented by deep network. x is point 3D space, and should be the distance from x to the closest points on the surface S corresponding to the n-dimensional latent vector z that controls the shape of The difficulty with this formulation is that if Us is not accurate, Us(x, x) might not reach zero at places where it should, resulting in unwarranted holes in the surface reconstruction. Since unsigned fields are not differentiable everywhere, they pose a parametrization challenge, resulting in noisy representations [13, 14, 36]. Similarly, the gradients of Us, which are
3

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Initial state
1st
iter
2nd iter
Output
Input
none
none
none
none
none
nome
none
none
none
none
none
UDF grad
none
none
none
none
none
none
none
current state
Iterative Network
none
none
none
none
Figure 2: Iterative Network. Our model iteratively refines cell configurations. The input consists of the UDF values and gradients at the vertices of the target cell, as well as the current estimated sign configurations of the target and neighboring cells. The surface within a given cell, shown in green, is progressively improved by enforcing consistency with its neighbors.
crucial for meshing [13, 44, 41, 36], can become very noisy when operating at high resolutions, also resulting in reconstruction failures.
Yet, gradients remain accurate further from the surface and there are still reliable cues in parts of the surfaces that are correctly modeled. This should be exploited to overcome the above-mentione difficulties. To this end, we propose an iterative approach that, at each pass, is conditioned on the surface extracted at the previous pass. By looking beyond single voxels over multiple passes, our method is trained to correct local inconsistencies while preserving the global scene structure. This yields better and more complete surface reconstructions, especially at high resolutions.
3.1 From UDF to Triangulated Mesh
At the core of our approach is a per-cell neural network that incorporates neighboring information and refines predictions iteratively. As new information is aggregated, the network progressively improves decisions, reducing noise and enhancing surface extraction for more complete and reliable reconstructions. We first describe its basic architecture and then the iterative refinement process.
Network Architecture. Given Us of Eq. 1, we query it for UDF values and gradients on a regular grid. We then group the values in cubic cells and feed them to a neural network fo, parametrized by 0, whose task is output a pseudo-sign configuration for the corners of the input cell. As in [36), we use a fully connected feed forward network with 2 = 128 outputs, representing a one-hot encoding of the possible pseudo-sign configurations, up complete sign symmetry in the cell.
As shown in Fig. 2, this network takes as input not only the UDF values and gradients at the vertices of the target cell but it also incorporates the current estimated sign configurations of the target and neighboring cells, allowing the model to make new predictions based on its earlier ones, which provides a spatial context. We provide all the architectural details in the supplementary.
Iterative Refinement. To refine the predictions and enforce global consistency, the network is run iteratively. This sets up a dynamic process that is trained to reinforce correct predictions, reducing the impact of local noise. Conditioning the network on its previous iterations helps the model retrieve the surface in regions where it previously failed due to noisiness or ambiguity.
More specifically, we set the sign configurations for the first iteration to be zero, which signals the absence of prior information. Note, however, that an all-zero vector is different from the "empty cell" configuration, which is a one-hot vector. This makes the network output predictions based only on the local UDF's and gradient values. In subsequent iterations, we feed the current output back as input. We train the network with a uniformly random number of iterations, with an empirically-determiin maximum of 5 additional iterations after the first pass. As a loss function, we use the cross- eross-yntropy between the predicted pseudo-signs and the ground-truth signs for all the cells every iteration, making the back proppagtaon process go through all the iterations.
Formally, the i-th iteration output for < i < 6, surface S and cell e is written
ys.c fo (Us(c), VUs(C), ((x
(i)
(i-1)
(1-1)
y V.N ys.c
(2)
d'NN
yscc = 10,0, O0.,.....))
(0)

---

where a is the sigmoid function, is the concatenation operator, N: is the set of cells sharing face with e, including itself, S. is the initial input to the network and (s(c) is resolution-normalize UDF, computed by dividing the input UDF by the cell size. For every shape S in the training dataset and at every epoch, the loss function is taken to be
C. ΣE
S.s.
where C' the cross entropy, is a random number between 1 and and GTs(c) is the ground-truth sign configuration. We observed that, without the sigmoid activation and the randomized number of iterations, the process converges poorly, or even not at all (see supplementary).
To increase robustness to noise, we augment the training values with Gaussian noise. We write
Us(c) + Us(c) (1+ ((0,)())))), VUs(c) + VUs(c) * (1+N(000x)).
(4)
where e is a grid cell and ax is typically set to 1.
Meshing. As in NSD-UDF [36], the final output of our pipeline a pseudo-SDF, that a UDF in which the grid cell corners have been assigned pseudo-signs so they can be triangulated using existing methods. We use Marching Cubes [18] for its ease of use or DualMesh-UDD [41] for its precision.
3.2 Speeding up the Process.
Algorithms such as MeshUDF [13] and NSD-UDF [36] use manually-defined resolution-dependee thresholds that ignore cells that too far from the surface and, thus, reduce the computational complexity of the algorithm. While this works well at lower resolutions, the high level of noise at higher resolutions makes this process error-prone, resulting in missing regions in the final mesh. Instead, we filter out cells whose vertices have UDF value equal or above the clamping threshold of the neural UDF, set to be 0.1 in our experiments. In practice, this eliminates 85% of the cells at 256 resolution, with no impact on the final result. For subsequent iterations, since the network outputs probability distribution over the sign configurations, we can interpret the highest probability as the confidence of the network. We can then conservatively filter out additional cells whose confidence is extremely high (> 0.999). As can be seen Tab. la, this substantially reduces the computational cost, making it comparable to that of the other baselines given in Tab. 1b, without accuracy loss compared to meshing all cells.
Table 1: Filtering and meshing times. (a) Median L.2 Chamfer Distance x x00 with 2M sample points (CD), Image Consistency (IC) and model inference times are reported at varying grid resolu- tions on an auto-decoder [27] trained on ShapeNet [3] cars. The times were measured on an NVIDIA A100 GPU, Notice that our filtering strategies put the proposed pipeline in the same range existing methods, without impacting its accuracy.
(a) Our filtering strategies speed up the method, maintaining the accuracy within run-to-run variance.
Res.
Filtering
CD
IC t Inference time J
Without filtering
5.26
89.2
7m
256
Low confidence
5.24
89.2
1.5m
UDF 0.1 and low confidence
5.24
30s
Without filtering
8.91
88.9
Ih
512
Low confidence
8.87
88.9
7m
UDF 0.1 and low confidence
8.88
88.9
2.5m
(b) Approximate UDF query and total meshing times at resolution 256. DCUDF makes multiple UDF queries at every iteration, making it difficult to measure the exact query time.
Time [CAP [46] MeshUDF (13) DCUDF [14] NSD [36] UNDC [5] DMUDF [41]
Ours
Query
Total
3.5m
35s
25m
35s
30s
20s
Im
5

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4 Experiments
4.1 Datasets and baselines
We test our method on five different 3D categories, including garments from MGN [T]: cars, chairs, and planes from ShapeNet [3]; and natural scenes from the 3DScene dataset [47]. using four different neural UDF architectures. For garments, cars, chairs, and planes, we train a traditional auto-decoder following [27, 36]. To showcase the capabilities of our method on downstream tasks and more precise single-shape neural architectures, we perform surface reconstruction from point clouds by training CAP-L [46]' on 3D scenes and cars, and DiftUDF [11] on cars. In the supplementary material, we provide additional results using softplus- pofpllus-based auto auto-decoder and meshing results obtained from ground-truth UDFs. We use 300 garments and the first 20 samples each for cars, chairs, and planes. As the MGN garments are simpler and exhibit less variety than the other shapes, we use lower resolution for them. For 3D scenes, we use three scenes from the official CAP-UDF [46] repository".
We divide the baselines into two groups, those that rely on Marching Cubes (CAP-UDF [46], MeshUDF [13], DCUDF [14), NSD-UDF [36]) and those that Dual Contouring (UNDC [5], DualMesh-UDF [41], NSD-UDF [36]). Notably, DCUDF [14] and DualMesh-UDF [41] have been shown be sensitive to parameter choices. We report results obtained using both the default parameters and those that we manually tuned, denoted as "-T". Due to implementation constraints, DualMesh-UDD and methods that depend on it use a resolution one pixel higher than the others, which we still include in the same tables. UNDC [5] failed at high resolution due to the method's VRAM requirements. DCUDF [14] failed on certain shapes, yielding invalid metrics; these cases are excluded, making its results not directly comparable. Following official recommendations we also evaluate DCUDutTT-ocut, a variant without the cutting step that produces double-layered meshes, on cars. All meshing methods are run without post-processing to ensure fair comparison.
4.2 Metrics
To compare extracted meshes to ground-truth surfaces, we compute three metries: the L2 Mesh Chamfer Distance (CD) between the meshes, computed with 2M sample points as a two-way point-to- mesh distance; the Image Consistency (IC) [13], which is the product of IoU and the cosine similarity of normal maps rendered from eight viewpoints; and the F1 score [4, 5], also computed with 2M sample points, which measures the portion of the surface within an error threshold of 0.003 from the ground-truth surface. We report the median of these metrics. It has been found to be more robust to outliers [36] than the mean, which we report in the supplementary for completeness along with the standard deviation.
4.3 Comparing against other methods
In Tab. 2a, 2b and Fig. 3, we compare method against state-of-the-art ones using four auto- decoders on four datasets, spanning from low to high resolutions. Our method consistently out- performs all baselines at high resolutions (2563 and 5123) complex shapes such as cars, chairs, and planes, which are the most prone to suffer from the UDF issues discussed at the beginning of Section 3 and depicted by Fig. 1. This is particularly visible in the three bottom rows of Fig. 3, where our method is the only one able to recover the front of the car, the legs of the chair and the cockpit of the plane. DCUDF [14] yields the smoothest meshes overall, at the cost of losing details and sometimes entire portions of the surface, as shown in Fig. 3, unless the cut operation is avoided, resulting in double surfaces. While previous comparisons [14, 36] have shown CAP-UDF [46] to be often be less accurate than other methods at low resolutions, we notice that the trend is reversed at higher resolutions. There, it retrieves surface portions missing from other basclines. MeshUDF [13] and DDF [36] can outperform it at high resolutions, but only when their filtering thresholds are removed, as shown in Tab.
At lower resolutions the missing surface problem is less pronounced, and thus iterative refinement does not provide significant advantages. To illustrate this, we present examples of 3D chair meshed
We refer the learning architecture of CDP-UDF as CAP-L. to distinguish it from the meshing method introduced in the same paper. which we employ as baseline.
'The repository contains five scenes, but "Copyroom" and "Lounge" produced bad metrics across all methods due inconsistent normalization, they have been excluded.

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Table 2: Triangulating auto-decoder-basee Neural Unsigned Distance Fields. Median L2 Mesh Chamfer Distance x10 with 2M sample points (CD), Fl score (FI) and Image Consistency (IC) are reported at varying grid resolutions. The best results are in bold. MGN denotes halved resolution for our MGN experiments due to the lower complexity of the shapes. UNDC failed at resolution 512 due to its large GPU memory requirements.
(a) Marching Cubes-based methods.
MGN []]
Shape cars
[3] IC
ShupeNet chairs [3]
ShupeNet planes [3]
Res.
Method
CD
FI f
IC1
CD
4
F1
f
CD J
F1 f
IC 1
CD
F1
IC
CAP-UDF [46]
16.2
69.4
79.4
53.9
53.3
83.2
378
50.9
70.3
14.0
69.5
80.6
MeshUDF [13]
2.45
82,9
94.1
11.3
57.7
88.6
7.43
67.6
88.0
6.82
74,6
81,0
DCUDF [14]
13500
2.50
2.76
6580
7.74
14.7
17000
15.9
13.9
1880
27.6
24.5
128
DCUDE-T [14]
90.8
2,86
87.3
50.3
58.0
87.3
214
64.1
82,9
144
68.8
77.2
DCUDF-T-nocut [14]
11.4
61.7
89.4
N MC [36]
1.34
83,9
94.7
6.79
59.6
88.5
6.11
67.8
88.1
3.82
79.0
84.8
Ours + MC
2.04
81.9
94.1
5.64
59.2
88.9
3.68
66.7
88.4
3,00
78.5
84,8
CAP-UDE [46]
1.66
86.8
91.8
34.0
61.2
87.6
114
70.5
82.0
5,50
83.7
85.4
MeshUDF [13]
0.958
89.7
95.0
13.6
62.3
88.6
27.8
72.9
87.3
3.47
85.8
85.2
256
DCUDF [14]
14400
4.76
3.71
346
$2.6
78.2
3530
49.9
54.3
27.9
84.7
82.0
DCUDE-T [14]
4,63
86.8
95.4
347
52.6
78.2
3560
50.0
54.3
47.3
80.4
78.7
DCUDF-T-nocut [14]
$2.0
58,9
82.3
NSD-UDF+ MC [36]
0.808
90.0
62.0
10.9
72.3
86.2
2.91
87.3
86.0
Ours MC
0.878
88,9
94.9
5.23
65.0
89.2
5.14
72.9
88.8
1.84
88.7
87.0
CAP-UDF [46]
0,872
90.6
94.6
31.8
61.7
87.5
63.9
71.7
82.0
5.94
87.5
86.2
McshUDF [13]
0.798
90.6
94.8
82.7
$7.0
81.7
378
61.5
65.7
12.6
88.1
84.6
DCUDF [14]
4.37
88.3
91.1
223
$6.5
84.2
2950
55.0
70.1
48.7
85.5
82.2
512
DCUDF-T [14]
4.38
88.2
91.1
223
56.5
84.2
2000
55.0
70.1
63.0
85.4
81.3
DCUDF-T-nocut [14]
43.1
60.4
85.6
NSD-UDF MC [36]
0.784
90.8
94.8
56.9
58.8
83.8
295
64.7
75.7
10.0
89.4
85.1
Ours MC
0.722
90.6
94.8
8.84
65.6
88.9
8.76
74.5
87.2
2.37
90.9
87.1
(b) Dual Contouring- based methods.
MGN [i]
ShapeNet [3] IC
ShapeNet chairs
ShapaNet planes [3]
Res.
Method
CD.
F1 1
IC1
CD
F1 f
CD
F1
1C11
CD 4
F1
IC
UNDC [5]
1.09
87.1
94.1
13.5
61.7
86.4
29.9
69.4
81.9
2.50
82.0
86.1
DunlMesh-UDH [41]
216
68.1
68.4
952
34.4
45.5
7930
12.1
9.08
112
74.3
76.1
128
DualMesh-UDF-TT [41]
0.806
89.9
95.4
5.56
63.5
89.5
5.34
75.1
89.1
1.96
84.3
87.5
NSD-UDF + DualMesh-UUD [36]
0.760
90.4
95.0
6.34
65.7
89.1
5.50
72.8
89.2
2,08
87.1
86.6
Ours DualMesh LDD
0.787
90.5
94,9
4,80
66.2
89.7
3.39
72.8
89.8
1.56
87.7
88.2
UNDC [S]
0.931
89.1
91.5
82.4
52.3
71.4
293
54.2
57.8
11.6
83,6
80.7
SaalMMssh-UDDP [41]
176
66.3
66.4
8-46
34.0
45.1
8280
12.4
9.26
105
77.9
76.0
256
MuulMesh-UDF-- [41]
0.722
91.2
95.1
10.6
64.3
87.0
22.8
72.2
84.1
2.43
88.2
87.0
NSD-UDF + Dun [36]
0.671
91.0
94.6
10.5
64.9
87.2
14.6
70.7
84.4
2.78
88.9
85.6
Ours DualMesh LDF
0.662
91.2
94.7
5,48
65.7
88.8
4.97
71.9
86.4
1.87
90.0
87.5
UNDC [S]
2.39
84.8
82.8
DuuiMesh-UDDR [41]
167
63.7
63.9
870
32.5
43.0
8190
11.8
9.07
111
77.6
74.2
512
DunlMesh-UDF-TT [41]
0.827
90.2
93.2
37.8
58.2
79.3
72.7
63.7
72.5
4.77
89.0
84.0
NSD-UDF + DUd [36]
0.787
89.7
92.5
60.5
57.5
79.9
296
62.5
68.0
9.95
87.6
83.3
Ours DualMesh-UDF
0.726
89.7
92.8
9.65
63.0
85.6
10.1
70.4
81.9
2.51
90.1
85.8
at resolutions of 1283, 256", and 5123 in Fig. 5, comparing one of the most accurate methods, NSD-UDF [36], with approach. As shown, lower resolutions NSD-UDF reconstructs good surfaces, leaving less room for improvement, however it fails to recover many surface regions at 2563 and especially at 512 resolution, whereas method handles these cases more effectively. Similarly, our method does not show significant advantages on the MGN dataset, where the shapes are less complex and nearly all methods achieve high accuracy without missing large portions of the surface.
We also observe that, while the pscudo-signs of NSD-UDF partially mitigate the need for tuning DualMesh-UDE when used in conjunction with it, our pseudo-signs are more robust and consistently outperform both NSD-UDF and the tuned DualMesh-UDD as shown in Tab. 2b.
Comparing primal and dual methods, we notice that dual ones tend to be more accurate at lower resolutions, while primal ones have an edge at higher resolutions. Note that, while achieving very good CD scores on MGN at high resolution, dual methods tend to create many holes in the reconstructed meshes, as can be seen the top row of Fig. 3. This does not impact the Chamfer Distance much due to the small size of these holes, but it affects the Fl and IC scores that are better in MC-based methods. Notice also that most primal methods show significant blockiness artifacts at high resolution, including pipeline paired with Marching Cubes, common issue with currently
7

---

GT
CAP-UDE
MeshtiDF
DCUDE-T DCUDF-T NSD-UDD
Ours
UNDC
DMUDE-T NSD-UDE
Ours?
Figure 3: Qualitative comparison with existing methods (auto-decoders). Surface meshing results of neural UDFs with all methods at resolution of 512 (and 256 for MGN). UNDC failed at resolution 512 due to high GPU memory requirements. f indicates that the method is combined with DMUDF.
Table 3: Neural Unsigned Distance Fields from point clouds. L2 Mesh Chamfer Distance x10-a with 2M sample points (CD), Fl score (FI) and Image Consistency (IC) are reported at varying grid resolutions. Median scores reported for cars, for scenes due the low numher of samples. The hest results are in bold.
CAP-L scenes [46]
CAP-L cars [46]
DifUUF cars [1]]
Res.
Method
CD
F1
ICT
CD
F1
IC f
CD 4
f
IC 1
CAP-UDE [46]
68.0
83.8
6.71
MeshUDF [13]
4,40
68.2
84,5
9.83
45.4
85.7
9.02
59.7
86.7
128
DCUDF-T [14]
279
59.7
84.0
45.5
41.4
85.5
32.7
49.6
89.6
DCUDF-T- WEDDF-T-mouul [14]
8.47
47.2
88.3
12.5
$6.9
90.2
NSD-UDF + MC [36]
3,34
69.8
86.7
8.14
47.1
86.4
4.18
65.7
87.7
Ours MC
3.44
69.3
85.3
7.03
48.3
86.8
5.46
62.3
87.4
CAP-UDE [46]
3.65
70.1
86.1
7.51
48.0
86.6
3.72
67.9
86.7
Mesht/DF [13]
3.42
69.6
86.3
8.65
47.5
86.1
5.18
65.9
87.2
256
DCUDF-T [14]
4.75
69.9
84.6
31.1
45.5
85.7
25.5
58.3
86.4
DCUDE-T-nocut [14]
9,58
47.9
86.0
5,56
87.7
NSD-UDF + MC [36]
3,30
70.3
86.3
8.76
47.9
86.3
3.63
70.0
86.9
Ours MC
71.4
CAP-UDF [46]
3,57
70.5
86.1
8,11
48.1
86.4
4,60
67.1
84.4
MeshUDF [133]
69.9
84.5
47.6
3.83
DCUDF-T T [14]
140
68.9
83.3
31.5
45.4
85.8
17.2
60.1
84.3
512
DCUDE-T-nocut [14]
84.8
5.53
87.1
NSD-UDF + MC [36]
3,72
70.0
84.0
9.85
47.3
85.9
5.63
66.0
82.0
Ours + MC
3.08
71.8
86.8
7.82
49.8
86.6
3.03
71.7
88.1
known architectures for neural UDFs. DCUDF and dual methods reduce this problem thanks to their optimization procedures, but they show more missing surfaces compared primal methods. Smoothing and mesh-repair algorithms can be used nevertheless to mitigate this in all methods, but they not applied here to better evaluate the direct output of each method.
In Tab. and Fig. 4, we show additional experiments using two single-shape neural UDF architectures trained on point clouds: CAP-L [46] and DiffUDF [11]. For 3D scenes we used the 100 points/m² setting from the CAP-UDF [46] paper, using the provided data. For cars, we sample 10k noise-free points per shape following the CAP-UDF protocol. Both architectures are trained using default parameters from their respective repositories. The results follow similar trends as in the auto-decoder experiments: our method achieves higher accuracy than the baselines, especially at high resolutions. Additional DC-based results and experimental details are included in the supplementary material.
4.4 Importance of Correct Thresholding
As described in Sec. 3.2, a correct filtering strategy crucial to keeping the computational costs under control when meshing neural UDFs at high resolution. MeshUDF [13] and NSD-UDF [36] rely on filtering out high UDF values to speed up the computation, which can be far from lossless at high resolutions. Removing such thresholds can help the algorithms to better retrieve surfaces at high
8

---

GT
CAP-UDE
MeshtIDF
DCUDET DCUDE--Taect NSD-UDE
Curs
DMUDE
NSD-UDF
Ours!
Figure 4: Qualitative comparison with existing methods (reconstruction from point clouds). Surface meshing results of neural UDFs resolution of 512. Top: CAP-L 3D scenes. Middle: CAP-L
car. Bottom: DiffUDF cars. indicates that the method combined with DMUDE
128
256
512
GT
NSD-UDF [36]
Ours
Figure 5: Meshing at different resolutions. While NSD-UDF [36] retrieves most of the surface well low resolution, it struggles higher ones. contrast, our method, recovers the surface well all resolutions. We use Marching Cubes with both methods.
Table 4: Removing thresholds existing methods. Median 1,2 Chamfer Distance x10 with 2M sample points (CD 4) varying grid resolutions, best results in bold. TThresholds removed. "Resolution halved.
Res.
Method
MGN
Cars
Chairs
Planes
Res.
Method
MGN
Cars
Chairs
Planes
MeshUDF
0.958
13.6
27.8
3.47
MeshUDF
0.798
82.7
378
12.6
McshUDFf
1.97
8.01
6.41
3.73
McshUDF
0.919
9.66
20.1
2.73
256
NSD+MC
0.808
10.2
10.9
2.91
512
NSD+MC
0.784
56.9
295
10.0
NSD+MCI
0.808
8.87
6.54
2,86
NSD+MCi
0.766
23.3
28.9
4.49
Ours&MC
0.878
5.23
1.84
Ouss+MC
0.722
8.84
8.76
2.37
resolution, but this is insufficient by itself. Tab. 4, computed the auto-decoder experiments, shows that there is a noticeable improvement at high resolutions, but the results are still not as good as those of our iterative pipeline. MeshUDF can become less accurate resolution 256 due to artifacts introduced in regions of the space with high UDF values, which its heuristic is not designed to handle. In contrast, our method is robust all such perturbations.
Table 5: Mesh refinement iterations. Median L2 Chamfer Distance x 10 with 2M sample points (CD L) varying grid resolutions, showing increasing precision over iterations most cases. *Resolution halved.
128
256
512
MGN
1,46
1.53
1.73
1,98
0.814
0.811
0.834
0.857
0.869
0.878
0.748
0.716
0.719
Cars
7.47
6.85
606
3.68
5.65
5.65
6.69
6:78
5.69
5.44
5.31
5.24
11.2
18.2
9.63
9.18
8.98
8.88
Chairs
491
4.45
3,88
3.78
3.77
3,66
5.56
5.48
5.32
5.19
5.15
5.15
10.9
10.4
9.55
9.43
9.97
8.87
Planes
3.69
3,47
3.10
3.08
3,03
2.70
2.28
2.04
1.88
1.85
3.43
2.87
2.47
2.38

---

Iter. 1
3
5
6
GT
Iter. 6
GT
Figure 6: Meshing iterations. Intermediate results the iterations. Propagating information across cells helps fill gaps and retrieve missing surfaces. See the car front and the chair leg. We show the fully reconstructed shapes on the right.
4.5 Mesh Evolution over Successive iterations
In Tab. 5 and Fig. 6, we show the evolution of the meshes over several iterations of our scheme on auto-decoder-basee UDFs. The meshes progressively refined and the missing regions filled, with the Chamfer Distance decreasing in most cases, especially at higher resolutions and in complicated shapes such cars, chairs and planes. The only partial exception to this trend occurs in the MGN dataset, where the mesh is already very accurate after the first iteration and remains so during the following ones at high resolutions. At lower resolution, such 64, especially for simple shapes like garments. The problems described in Fig. do not arise, lessening the usefulness of an iterative scheme. We also observe that our pipeline often produces more accurate meshes than the baselines already during the first iteration, as shown in Fig. and by comparing results in Tab. and 4. This is mainly due the more robust training of our network compared to NSD-UDF [36] and thanks to the asbsence of heavy thresholds during meshing.
the opposite behavior,
5
Limitations
Due to its iterative nature, our pipeline is naturally slower than single-pass or heavily thresholded approaches. However, the system's speed can be improved by reducing the number of iterations, which comes with tradeoff in accuracy as shown in Tab. 5, or by filtering cells more aggressively, Furthermore, as shown in Tab. 1b, querying input UDFs and gradients often constitutes significant portion of inference time, an operation performed only once in our iterative pipeline. As result, the additional iterations in our approach have comparatively small impact on the overall computation time, which remains in the ballpark as those of the fastest baselines.
For simpler shapes, such as garments, methods specifically designed prioritize topology accuracy, such as MeshUDF, may sometimes be more suitable. Moreover, while allowing high resolution surface extraction, our method can still produce artifacts in the form of irregular boundaries and small holes, as visible in Figs. 3 and 6. Post-processing algorithms can help with this, but future work should focus on improving in these aspects.
6 Conclusion
Our iterative approach to meshing neural UDFs achieves state-of-the-art accuracy and robustness, enabling surface extraction for complex shapes at high resolutions. By refining surfaces over multiple iterations, it addresses the challenges posed by noisy distance fields, which can create severe problems for heuristic-based methods. We believe this represents paradigm shift in using neural surface localization to capture the complex interplay between neural distance fields and reconstructed surfaces far from trivial task.
Looking ahead, to improve high-resolution surface extraction on UDFs key directions include optimizing computational efficiency, exploring adaptive iteration strategies, and improving topology preservation. End-to-end learning for unsigned distance fields and meshing remains critical frontier, bringing closer to seamless, high-fidelity 3D reconstruction across diverse applications.
10

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7 Acknowledgements
This work was funded in part by the Swiss National Science Foundation.
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A.1 Complete quantitative results
For the sake of completeness, we report in Tabs. A.3a, A.3b, A.4a, A.4b, A.5a, A.5b, A.6a and A.6b the mean results on the datasets and methods used in the main paper, alongside their respective standard deviations. We also report the results DC-based methods on point cloud reconstruction from CAP-L [46] and DiffUDF [1I] in Tab. A.2. We observe that the trends are consistent with the median results shown in the main paper, with our method outperforiing all baselines at high resolutions complex shapes, and competing closely with existing methods lower resolutions and on simpler shapes. The standard deviations computed on our method are also consistently lower than the baselines at high resolution, while remaining competitive at lower resolutions, showing that our method is also more robust to shape variations compared to existing basclines. As in the main tables, notice that UNDC [5] failed reconstruct meshes at high resolution due the method's VRAM requirements. DCUDF [14] failed to reconstruct some of the shapes in the experiments, producing unbound metrics. We discard such shapes from the reported results of DCUDF, which means that its numbers are not directly comparable to the other baselines.
A.2 Implementation details and other ablation studies
Table A.1: Number of additional training iterations. Median Image Consistency (IC 1) of the last iteration resolution 512. *Resolution is halved.
Max training iter.
MGN"
Cars
Chairs
Planes
I iter.
94.9
88.5
86.2
87.0
3 iter.
94.9
88.4
86.0
86.8
5 iter.
94.8
88.9
87.2
87.1
7 iter.
94.9
88.5
85.9
86.5
Our network architecture consists of 2 fully connected hidden layers, with 1024 nodes each, and an output layer with 128 outputs. The input layer accepts UDF values and gradients at the 8 cell corners, making up 32 inputs. Additionally, 128 inputs per cell are needed to enable multiple iterations. We consider the current cell and the 6 cells that share a face with it, for a total of * 128 additional inputs, which brings the total number of input nodes to 928 and the total number of trainable weights to around 2.1M. Each layer, except for the final one, is followed by a leaky ReLU activation function with negative slope of 0.01. The output layer is followed by a sigmoid activation before being used as input for the next iteration, and by a softmax function for the cross entropy loss. The network is trained using the Adam optimizer [16] with a learning rate of 5 10-4 for 50 epochs.
The learning rate is lower than in [36], with more epochs. We have found this helps our iterative process converge better. For training, we use the first 80 watertight shapes from ABC [17] sampled at resolution 128", yielding around 5.5M training cells. As mentioned the method section of the main paper, we limit the number of additional training iterations to 5. In Tab, A. we provide ablation study showing that training the network with a single additional pass already achieves good results, with 5 iterations achieving the best. Using even more iterations did not bring measurable benefits. The training takes around 2 hours on an NVIDIA A A100-40G GPU.
As an ablation, we also trained the network without the noise augmentation described in the method section of the main paper. The method presented in this work achieved a median Mesh Chamfer Distance x10- of 5.64, 5.23 and 8.84 at resolutions 1283, 256 and 512 respectively, using the UDF auto-decoder trained on ShapeNet [3] cars in Section 4.3 of the main paper. Without noise augmentation, the same experiment achieved 8.01, 12.5 and 47.8 respectively, showing that the noise augmentation is crucial to achieve good performance in practical scenarios.
A.3 Training convergence
In the method section of the main paper we state that our pipeline applies a sigmoid function to the network outputs before using them as input for the next iteration. We have experimentally found that, when using an identity activation (i.e. direct input) and training with only one iteration, the network goes from an IC of 87.0 on ShapeNet [3] cars at resolution 512 to 88.6, however it starts diverging
14

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Table A.2: Neural Unsigned Distance Fields from point clouds (DC-based methods). L.2 Mesh Chamfer Distance x10 3 with 2M sample points (CD), Fl score (FI) and Image Consistency (IC) are reported at varying grid resolutions. Median scores are reported for cars; mean for scenes due to the low number of samples. The best results are in bold. UNDC failed at resolution 512 due to its large GPU memory requirements.
CAP-L scenes [46]
CAP-L cars [46]
DiffUDF cars [11]
Res.
Method
f
IC
CD
IC1
CD L
F1
UNDC [5]
3.34
69.7
84.4
7.85
49.4
85.5
4,46
59.1
87.6
DualMesh-UDD [41]
53.5
63.4
69.5
9.44
50.4
85.6
6.03
62.3
84,9
128
NSD-UDF + DualMesh-UDF [36]
33,6
69.8
84,5
5.49
52.4
87.2
3.07
68.2
88,2
Ours + DualMesh-UDF
33.6
70.0
84.4
5.35
52.8
87.3
3.68
65.3
88.1
UNDC
7.85
69.1
76.9
7.77
48.5
84.2
6.84
56.1
80,9
DualMesh-UUDe [41]
50.4
63.0
68.3
8.51
49.2
84.9
5.01
61.9
83.1
256
NSD-UDF DualMesh-UDr [36]
34,3
68.9
83.4
6.74
49.7
86.5
2.72
72.3
88.3
Ours + DualMesh-UUD
220
49.9
79.6
6.35
50.6
86.9
2.89
70.0
88.5
UNDC [5]
DualMesh-UDE [41]
51.7
59.8
61.8
9.26
46.3
83.5
5.07
59.4
79.4
512
NSD-UDF+ + DualMesh-UDF [36]
35.2
66.5
77.9
7.69
47.0
85.7
3.35
69.6
85.6
Ours + DualMesh-UDF
34,0
68.6
82.8
7.81
48.2
86.5
2.6
73.3
88.4
after that. Using a softmax activation, which helps normalizing the otherwise unbound network outputs, the training converges, but the network does not produce significant improvements iterations, going from an IC of 87.3 to 87.5 after two iterations. Using a sigmoid activation, instead, showed more steady improvement 88.9 after an additional one. However, training it with more than one iteration did not show significant improvements. Using a random number of training iterations, instead, helped the network to converge until 5 iterations, achieving similar IC scores but better CD scores (9.90 x 10-5 vs 8.84 x 10-5), as shown the main paper, signifying an overall similar accuracy but better surface retrieval capabilities at high resolutions.
iterations, going from 87.6 to 88.5 after one iteration, and
A.4 Auto-decoder training
For our auto-decoder experiments we used the traditional auto-decoder architecture proposed in DeepSDF [27]. The input meshes are rescaled and centered within a [-1, 1Js volume, and during the data preparation phase, training points are sampled. For each mesh, 20k points are uniformly sampled within the volume, while 400k points are sampled near the surface. To obtain the surface points, 200k points are first uniformly distributed on the surface, and then small amounts of Gaussian noise are added. Gaussian noise with mean of and standard deviation of /0.005 applied to the first 200k surface points, and noise with a mean of and standard deviation of /0.0005 is added the remaining 200k points. The auto-decoder network consists of 12 layers, each with 1024 hidden nodes and ReLU activations, and latent codes of size 512. is trained using LI loss, without regularization or Fourier encoding, for 10k epochs with a batch size of 16. To focus the network's 's capacity on the surface, the UDF clamped 0.1. The Adam optimizer [16] used with learning rates of 0.0005 for the model and 0.001 for the latent codes, with learning rate decay applied at epochs 1600 and 3500 by factor of 0.35.
A.5 Different auto-decoder UDF architecture
To test the robustness of our method to different UDF architectures, we trained an auto-decoder
with a different architecture: using a softplus activation function and Eikonal loss with weight of 0.1, with the rest as in the section above. We show the results on ShapeNet [3] cars in Tab. A.7, along with the highest-scoring baselines from the main experiment. While all methods achieved slightly better performance compared to the ReI. architecture, the same conclusions apply. Our method outperforms the tested baselines, particularly so at high resolutions, while also achieving lower standard deviations across the dataset.
15

---

Table A.3: Triangulating auto-decoder-based Neural Unsigned Fields using Marching Cubes-based method. L2 Mesh Chamfer Distance x10 with 2M sample points (CD), Fl score (F1) and Image Consisteney (IC) are reported at varying grid resolutions. The best results are in bold. DCUDF failed to mesh some of the shapes, but its numbers are reported nonetheless. *Resolution is halved for experiments with MGN due to the lower complexity of the shapes.
(a) Mean results.
MGN [I]
ShapeNet cars [3]
ShapeNet chairs [3]
ShapeNet planes [3]
Res.
Method
CD
F1
IC
CD
F1
IC
CD |
Fl 1
IC
CD
Fl
IC
CAP-UDF [46]
19.7
68.2
78.6
71.7
49.5
81.8
518
51.3
68.9
19.5
68.1
79.0
MeshUDF [13]
2.79
82.0
93.3
11.9
57.9
88.7
21.8
68.0
88.7
19.4
73.5
81.0
128-MC
DCUDF [14]
14100
3.40
3.84
8000
10.6
13.7
22700
14.4
16.8
2900
28.9
24.3
DCUDF-T [14]
116
3.04
86.6
66.5
55.4
86.8
2720
65.2
78.2
902
69.4
78.8
DCUDF-T-nocut [14]
14.4
60.9
89.2
NSD-UDF MC [36]
1.55
82,9
94,1
9,40
59,9
88.5
17.7
68.7
88.5
4.72
78.0
84.5
Ours + MC
2.26
80.8
93.4
6.79
59.5
88.9
7.27
67.8
89.5
3.49
77.6
84.8
CAP-UDF [46]
3.23
85.4
91.2
58.8
86.2
223
78.5
8.95
83.2
85.0
McshUDF [13]
1.16
88.2
94.5
17.1
61.1
88.2
67.1
69.8
85.4
4.83
85.2
85.1
256-MC
DCUDF [14]
18200
5.17
4.12
1090
50.6
75.1
7900
50.7
55.3
278
82.4
80.2
DCUDET [14]
5113
75.0
7840
55.3
80.1
77.9
DCUDF-T-nocut [14]
68.4
56.4
80.7
NSD-UDF + MC [36]
0.973
88.7
94.8
14.7
61.2
87.6
53.7
69.8
85.4
3.81
86.9
85.2
Ours MC
L.02
87.6
94.4
7.26
63.1
89.0
10.6
70.6
89.3
2.64
88.2
86.6
CAP-UDF [46]
2.14
89.1
94.1
48.6
611.2
86.4
202
67.9
79.3
8,94
87.3
85.5
MeshUDF [13]
1.18
89.3
94.4
136
54.4
78.8
799
57.5
64.2
21.2
87.4
83.4
512-MC
DCUDF
49.4
85,8
88.8
478
52.9
80.2
7510
55.7
63.8
199
84.1
81.0
DCUDE-T [14]
32.8
85.9
88.9
478
52.9
80.2
7380
55.9
64.2
284
83.2
79.9
DCUDE-T-Rocut [14]
61.4
58.5
84.7
NSD-UDE MC
1,08
89.5
94.4
80.8
56.8
82.0
394
62.9
71.2
13.4
88.2
83.8
Ours + MC
0,880
89.3
94.4
12.3
63.4
88.2
36.6
71.6
86.5
3.31
90.1
86.5
(b) Standard deviation for each metric, computed across the dataset.
MGN [T]
ShapeNet cars
[3]
ShapeNet chairs [3]
Shape planes [3]
Res.
Method
CD
F1
IC
CD
Fl
IC
CD
Fl
IC
CD
Fl
IC
CAP-UDF [46]
12.1
7.83
3.46
51.9
12.2
5.69
649
15.4
14.7
21.3
5.63
3.45
MeshUDF [13]
1.28
7.9
2.34
5.21
12.1
2.22
30.3
13.9
5.58
27.4
5.54
2.56
DCUDFF [14]
561
0.901
5560
16.0
7.45
128-MC
DCUDF-T [14]
169
1.30
3.97
57.6
11.4
4.28
5020
14.0
17.6
1400
6.72
6.79
DCUDE- [14]
9.59
11.1
2.49
NSD-UDF MC [36]
0.817
7.87
1.91
5.24
12.2
2.33
28.0
13.7
5.64
2.87
6.10
2.28
Ours MC
0.872
7.75
2.09
3,16
11.7
1.92
8.55
13.4
4.93
1.49
6.02
1.89
CAP-UDF [46]
4.83
7.23
2.37
40.8
12.6
4.46
220
15.9
12.7
7.44
5.32
3.03
MeshUDF [13]
0.733
6.78
1.56
11.7
11.6
2.64
74.9
14.3
8.51
4.18
5.51
2.41
DCUDF [14]
12700
2.22
1.86
3250
14.0
15.2
9500
17.7
19.9
664
8.45
6.52
256-MC
DCUDE-T [14]
12.5
7.00
1.68
3250
14.0
15.1
9440
17.6
19.9
1440
8.70
7.70
DCUDF-T-nocus [14]
51.9
12.3
7.02
NSD-UDF + MC [36]
0.636
6,78
1.45
10.3
11.8
2.79
68.9
14.4
8,36
3.04
5.80
3.13
0.557
6.55
1.46
3.91
14.0
5.12
2.06
CAP-UDF [46]
3.97
6.78
1,80
4016
12.4
4.19
217
13.8
12.2
7.65
4.03
3.20
McshUDF [13]
1.30
6.63
1.42
115
12.9
8.34
964
16.3
17.8
20.0
5.30
4.67
512-MC
DCUDF [14]
362
10.2
7.60
989
14.7
12.8
9890
19.0
22.0
537
8.35
4.99
DCUDE- [14]
219
9.98
7.33
989
14.7
12.8
9950
19.0
22.5
774
8.53
5.93
DCUDF-T-nocul [14]
47.4
12.4
5.51
NSD-UDE MC
1.09
6.66
1.48
65.7
12.8
6.40
442
15.1
15.8
11.3
5.08
4.38
Ours MC
0.563
6.49
1.27
8.41
11.2
2.48
48.5
12.7
7.55
2.83
4.08
2.73
A.6 Additional figures
We show here additional qualitative results of our method compared the baselines. In Fig. A.1 we show an additional example at different resolutions compared to the NSD-UDF [36] baseline: the shapes look similar at low resolutions, but at 256 and 512 the baseline cannot retrieve large portions of the surface.
In Fig. A.2 & A.3 we show the same shapes as in Fig. 3 of the main paper, but with different resolutions. In Fig. A.4, A.5 & A.6 we show additional shapes at all tested resolutions, As observed
16

---

Table A.4: Triangulating auto-dccoder-based Neural Unsigned Fields using Dual Contouring- methods. L2 Mesh Chamfer Distance x10 with sample points (CD), Fl score (F1) and Image Consistency (IC) are reported at varying grid resolutions. The best results are in bold. UNDC failed at resolution 512 due to high GPU memory requirements, "Resolution is halved for experiments with MGN due to the lower complexity of the shapes.
(a) Mean results.
MGN
ShapeNet
[3]
ShapeNer chairs [3]
ShapeNet planes [3]
Res.
Method
CD
FI
IC1
CD J
F1 1
IC1
CD)
FI
IC
CD)
F1
IC
UNDC
1.26
86.1
86.0
66.8
78.8
3.82
81.8
DualMesh-UDDFPe [41]
[120
61.1
60.9
1600
33.0
42.8
12400
15.0
13.0
341
72.4
72.3
128-DC
DualMesh-UUDDe [41]
0.39
88.7
94.9
7.45
62.6
89.4
19.1
71.4
88.7
2.91
83.3
87.3
NSD-UDF DualMesh-UDDi [36]
0.901
89.2
94.5
8.60
63.9
89.1
17.3
70.2
88.3
3.12
85.9
86.5
Ours DuaiMesh-UDF
0,904
89.2
94.5
5.89
64.2
89.7
7,28
70.1
89.8
2.21
86.7
88.0
69.0
50.9
DualMesh LDF [41]
993
60.0
59.0
1440
33.3
42.6
11900
15.2
13.0
155
76.
72.5
256-DC
DualMesh-UDD-1
NSD-UDF DualMesh-UDF [36]
0.838
89.5
94.3
15.6
61.8
87.0
56.0
68.3
82.4
3.72
88.3
85.4
Ours DualMesh-UUDD
0.806
89.5
94.4
7.57
63.5
88.5
12.5
69.2
86.7
2,66
89.3
87.3
UNDC
DualMesh LDF [41]
948
58.4
57.1
1560
32.2
41.1
12400
14.7
12.2
172
75.6
70.6
512-DC
UDF-T
NSD-UDF DualMesh-UDF [36]
1.13
88.2
91.9
86.3
54,3
77.8
412
58.4
63.9
13.8
86.7
82.1
Ours DualMesh-UDF
0.899
83.2
92.3
13.5
61.0
85.1
38.9
67.1
80.1
3.47
89.0
85.2
(b) Standard deviation for each metric, computed across the dataset.
MGN [i]
ShapeNet cars [3]
ShapeNet chairs
[3] IC
ShapeNet planes [3]
Res.
Method
CD
Fl
IC
CD
F1
IC
CD
F1
CD
Fl
IC
UNDC [5]
0.651
6.80
1.43
11.6
12.0
3.26
94.4
15.5
11.2
3.33
5.77
2.69
DualMesh-UDF [41]
2470
25.6
25.4
995
10.8
12.2
128-DC
DualMesh-UDE-TG [41]
0.561
6.51
1.36
4.17
10.5
2.10
29.3
13.5
5.94
2:58
5.34
1.94
NSD-UDE DualMesh-UiD [36]
0.546
6.48
1.50
5.14
11.4
2.21
27.2
13.3
5.55
2.76
4.96
2.33
Ours DualMesh UDF
0.517
6.47
1.43
2.92
11.0
1.87
9.04
13.2
4.48
1.40
4.88
1.95
UNDC [5]
1.25
6.80
2.41
97.7
11.9
9.59
716
17.6
16.1
21.1
6.89
5.63
DualMesh-tIDF [41]
11.9
9.85
256. IXC
DualMesh. UDF-T [41]
0.673
6.49
1.31
9.94
10.7
3.12
72.3
13.6
8.97
2.96
3.96
2.39
SUD-UDFF+ DualMesh-UDF [36]
Ours DualMesh-UDP
0,516
6.81
1.26
4.21
11.1
2.22
15.9
13.0
4.98
2.57
4.08
2.30
UNDC [5]
11.3
9.36
6.95
DualMesh-UDF [41]
2080
26.0
25.6
12.5
14500
11.6
267
9.88
11.7
512-DC
DualMesh. UDF-T [41]
1.36
7.14
2,51
38.5
11.5
5.96
221
13.6
14.3
6.87
4.94
3.93
NSD-UDF DualMesh-UDF [36]
1.18
7.48
2.92
7.41
14.9
5.2
4.83
Ours DualMesh. UDP
0.616
7.48
2.54
9.32
11.4
3.03
49.6
12.3
7.63
2.83
4.36
3.10
in the main paper, existing methods retrieve most of the surface at lower resolutions, leaving less room for improvement, whereas higher resolutions method shows significant advantage. In Fig. A.7, we show the meshing on the CAP-L 3D scene [46] used in Fig. 4 of the main text in greater size better appreciate the details, egg, the base of the statues.
17

---

128
256
512
GT
NSD-UDF UDF [36]
Ours
Figure A.1: Meshing different resolutions, additional examples. While NSD-UDF [36] retrieves most of the surface well at low resolution, it struggles at higher ones. In contrast, our method, recovers the surface well all resolutions. We Marching Cubes with both methods.
GT CDF-UDF MeshUDF DCUDF-T DCUDF NSD-UDE
Ours
UNDC
DMUDF-T NSD UDF
Ours
Figure A.2: Qualitative comparison at resolution 256. Surface meshing results of auto-decoder- based neural UDFs with all methods resolution of 256 (and 128 for MGN). indicates that the method is combined with DMUDF. The shapes are the same in the main text.
GT
CAP-UDF
MeshUDF DCUDE-T DCCDF NSD-UDE
Ours
UNDC
DMUDE-T NSD-UDE
Ours!
Figure A.3: Qualitative comparison at resolution 128. Surface meshing results of auto-decoder- based neural UDFs with all methods at resolution of 128 (and for MGN). indicates that the method is combined with DMUDE. The shapes are the same as in the main text.
18

---

Table A.5: Neural Unsigned Distance Fields from point clouds (MC-based methods). Mesh Chamfer Distance x10 with 2M sample points (CD), Fl score (FI) and Image Consistency (IC) are reported at varying grid resolutions. The best results are in bold.
Mcan results.
CAP-L scenes
[46]
CAP-L cars [46]
DiffUDF cars
[1]]
Res.
Method
CD 4
FI F
IC1
CD 4
F1
IC
CD 4
F1
IC1
CAP-UDF [46]
4.27
68.0
83.8
11.4
48.5
85.3
7.96
60.1
86.2
MeshUDF [13]
4.40
68.2
84.5
11.9
49.7
86.1
9.52
61.4
87.0
DCUDE-T [14]
279
59.7
84.0
131
45.0
83.7
99.4
53.2
87.0
128-MC
DCUDF-T-nocut [14]
10.7
51.3
87.6
15.3
58.6
90.2
NSD-UDF MC [36]
3.34
69.8
86.7
11.1
51.7
86.3
4.86
66.0
87.8
Ours + MC
3.44
69.3
85.3
9.76
51.8
86.8
6.65
63.6
87.5
CAP-UDF [46]
3.65
70.1
86.1
10.1
53.4
86.4
4.04
69.0
86.6
McshUDF [13]
3.42
69.6
86.3
10.2
52.3
86.1
5.61
66.8
87.5
DCUDF-T [14]
4.75
69.9
84.6
42.1
50.7
84.7
106
63.8
84.6
256-MC
DCUDF-T-nocut [14]
12.0
53.1
85.7
6.37
68.8
87.1
NSD-UDF [36]
3.30
70.3
86.3
11.5
86.
3.85
70.6
86.7
Ours + MC
3.07
71.4
86.6
9.93
54.0
86.8
4.23
69.2
88.0
CAP-UDF [46]
3.57
70.5
86.1
10.8
53.8
86.2
4.87
69.3
84.0
MeshUDF [13]
4.49
69.9
84.5
10.9
52.7
85.7
4.25
68.8
86.2
DCUDE-T [14]
140
68.9
83.3
37.0
50.9
85.0
727
61.8
78.3
512-MC
DCUDF-T-nocut [14]
13.5
51.5
84.4
6.64
68.2
86.4
NSD-UDF MC [36]
3.72
70.0
84.1
12.3
52.5
85.6
5.92
67.1
81.1
Ours + MC
3.08
71.8
86.8
10.5
54.1
3.48
71.9
87.8
(h) Standard deviation for each metric, computed across the dataset.
CAP-L scenes [46]
CAP-L cars [46]
DiffUDF cars
[11]
Res.
Method
CD
Fl
IC
CD
F1
IC
CD
F1
IC
CAP-UDF [46]
1.98
19.9
2.43
4.71
12.2
3.07
3.88
11.2
2.53
McshUDF [13]
1.38
20.1
1.42
5.77
13.9
3.13
5.23
13.4
2.97
DCUDF-T [14]
385
20.1
6.53
318
12.9
5.91
109
12.0
5.37
128-MC
DCUDF-T-nocul [14]
5.37
12.6
3.06
12.5
12.5
1.65
NSD-UDF MC [36]
1.67
20.8
2.20
6.91
14.2
3.31
3.54
12.6
2.69
Ours MC
1.67
20.0
1.8
6.26
13.3
2.75
5.29
12.1
2.30
CAP-UDF [46]
1.91
21.1
1.94
6.65
14.4
3.46
2.35
12.6
3.41
McshUDF [13]
1.79
21.3
2.03
5.65
14.9
3.48
3.06
13.3
2.78
DCUDF-T [14]
3.71
21.8
2.99
46.7
15.5
4.38
202
14.3
7.80
256-MC
DCUDF-T-nocut [14]
6.85
15.2
4.13
3.66
13.4
3.40
NSD-UDF+ MC [36]
1.76
21.5
2.63
7.27
15.1
3.69
2.47
13.0
3.56
Ours + MC
1.60
20.3
2.04
6.63
14.4
3.11
3.31
11.9
2.24
CAP-UDF [46]
1.98
21.3
2.44
7.26
15
3.64
3.14
14.2
5.29
MeshUDF [13]
3.38
21.5
3.45
6.35
15.3
3.94
2.46
13.3
3.30
DCUDF-T [14]
191
21.3
4.07
28.2
15.3
4.21
1310
15.8
12.2
512-MC
DCUDF-T-nocut [14]
7.45
15.3
5.10
3.78
13.5
3.57
NSD-UDF MC [36]
2.07
21.1
3.21
7.66
15.4
4.07
3.95
15.6
7.05
Ours + MC
1.63
20.4
2.54
6.99
15.0
3.48
2.15
12.4
2.73
19

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Table A.6: Neural Unsigned Distance Fields from point clouds (DC-based methods), 1.2 Mesh Chamfer Distance x10 with 2M sample points (CD), Fl (FI) and Image Consistency (IC) reported at varying grid resolutions. The best results are bold. UNDC failed resolution 512 due its large GPU memory requirements.
(a) Mean results.
CAP-L
scenes
[46]
CAP-L.cmm cars
[46]
Dif cars
[1]]
Res.
Method
CD
F1
IC1
CD
F1
IC
CD
F1
IC
UNDC
3.34
69.7
84.4
12.7
52.3
84.8
4.76
60.9
87.6
DualMesh-UDF [41]
53.5
63.4
69.5
11.3
54.0
85.0
5.77
62.5
84.3
128-DC
NSD-UDF + DualMesh-UDF [36]
33.6
69.8
84,5
7.01
56.0
87.0
3,51
68.3
88.3
Ours DualMesh-UDF
33.6
70.0
84.4
6.73
56.2
87.2
4.37
66.7
88.2
UNDC [5]
7.85
69.1
76.9
9.89
52.9
83.9
17.5
58.3
81.2
DualMesh-UDF [41]
50.4
63.0
68.3
10.8
53.2
84.3
5.43
61.1
82,5
256-DC
NSD-UDF + DualMesh-UDF [36]
34.3
68.9
83.4
8.42
54.0
86.2
3.08
71.5
87.7
Ours DualMesh-UDF
220
49.9
79.6
7.95
54.6
86.7
3.36
70.4
88.3
UNDC [5]
DualMesh-UDF [41]
51.7
59.8
61.8
11.4
50.6
83.1
5.69
58.2
79.0
512-DC
NSD-UDF + DualMesh-UDF [36]
35.2
66.5
77.9
10.1
51.7
85.4
3.99
68.8
Ours DualMesh-UDF
34.0
68.6
82.8
9.15
52.5
3.05
87.9
(b) Standard deviation for each metric, computed across the dataset.
CAP-L scenes [46]
CAP-L cars [46]
DiffUDF cars (11]
Res.
Method
CD
F1
IC
CD
IC
CD
IC
UNDC [S]
2.55
20.2
3.97
13.4
13.0
3.27
2.22
13.1
2.14
DualMesh- UDF [41]
35.7
18.9
7.07
6.58
13.8
4.27
2.77
13.7
3.42
128-DC
NSD-UDF + DualMesh-UDE [36]
42.8
17.6
0.739
3.98
13.1
2.88
2.04
11.7
2.14
Ours + MhalMeshhUDDR
43.0
17.3
0.803
3.70
12.8
2.60
3.02
11.8
2.00
UNDC [5]
8,26
21.8
9.61
5.38
14.4
3.88
30.5
10.3
1.65
DualMesh- SHalMesh-UDFii [41]
35.7
19.5
7.01
6.34
14.7
4.60
2.66
13.9
3.16
256-DC
NSD-UDE + DualMesh- UDF [36]
43.3
18.6
0.403
4,82
14.3
3,51
1.96
12.5
2.82
Ours + DualMesh-UDF
243
28.1
6.58
4.43
14.0
3.11
2.34
12.0
2.17
UNDC [S]
DualMesh-UDF [41]
35.0
19.9
8.32
6.45
14.6
4.86
2.68
13.5
3.03
512-DC
NSD-UDF + DualMesh- UDF [36]
42.3
18.6
2.04
5.74
14.7
4.04
2.50
14.0
3.80
Ours + DualMesh-UDF
43.2
18.2
0.0709
5.05
14.6
3.53
1.89
12.4
2.86
Table A.7: Triangulating Softplus-based auto-decoder. L2 Chamfer Distance x10 with 2M sam- ple points (CD), Fl score (F1) and Image Consistency (IC) reported varying grid resolutions the ShapeNet [3] cars dataset. The best results are in bold.
Median Fl f
Mean Fl
Std
Res.
Method
CD
IC
CD
IC
CD
F1
IC
CAP-UDF [46]
60.9
52.5
80.7
69.2
49.9
80.1
56.6
10.5
4.51
MeshUDF [13]
8.06
61.4
10.0
61.3
88.6
6.40
2.17
NSD-UDF + MC [36]
5.95
64.9
88.6
7.69
63,5
88.7
5.13
11.9
2.26
128-MC
Ours MC
4.80
64.0
89.0
5.85
63.1
89.1
3.53
11.3
1.94
CAP-UDF [46]
23.7
65.2
86.8
30.0
63.9
23.9
12.3
3.96
MeshUDF [13]
13.4
67.9
88.4
15.1
66.3
88.3
10.4
11.7
2.56
NSD-UDF + MC [36]
8.63
69.3
88.3
10.4
66.7
88.0
8.94
11.9
2.57
256-MC
Ours MC
4.95
70.4
89.6
6.28
68.2
89.3
4.69
11.3
1.89
CAP-UDF [46]
23.8
67.3
87.2
30.3
65.8
86.4
24.6
12.6
3.97
MeshUDF [13]
58.3
62.3
77.9
69.5
59.6
77.4
45.2
13.2
7.15
NSD-UDF + MC [36]
21.2
68.0
85,8
24.6
65.0
84.8
19.9
12.8
4.44
512-MC
Ours MC
8.83
71.4
88.9
10.7
68.7
88.7
9.25
11.6
2.37
20

---

CAP-UDF
MeshUDF
DCUDE-T DoCDF-nocut NSD-UDF
Ours
UNDC
DMUDE-T NSD-UDF
Ours?
Figure A.4: Additional qualitative comparison at resolution 512. Surface meshing results of
auto-decoder-based neural UDFs with all methods at resolution 512 (and 256 for MGN). UNDC failed at resolution 512 due to high GPU memory requirements. indicates that the method is combined with DMUDE.
CAP-UDF MeshUDF DCUDE-T DCUDF-nocut NSD-UDF
Ours
UNDC
DMUDE-T NSD-UDF
Ours
Figure A.5: Additional qualitative comparison at resolution 256. Surface meshing results of auto-decoder-basee neural UDFs with all methods at resolution 256 (and 128 for MGN). indicates that the method is combined with DMUDF.
CAPAIDF MeshUDF DCUDE-T DCUDF-nncul NSD-UDE
Qurs
UNDC
DMUDE-T NSD-UDE
Ours?
Figure A.6: Additional qualitative comparison at resolution 128. Surface meshing results of auto-decoder-basee neural UDFs with all methods at resolution of 128 (and 64 for MGN). indicates that the method combined with DMUDE.
21

---

GT
CAP-UDF
MeshUDF
DCUDF-T
NSD-UDF
Ours
DMUDF
NSD-UDF
Ourst
Figure A.7: Meshing of 3D scene from CAP-L [46]. Surface meshing results of the "Burghers" scene with all methods at resolution of 512. UNDC failed at resolution 512 due to high GPU memory requirements. indicates the method is Dual Contouring- otherwise is Marching Cubes- based.
A.7 DoubleCoverUDD [14] tuning and min-cut
To achieve better results with DCUDF [14] compared its default parameters, we have run the algorithm 3 times per experiment and per resolution, with different parameters, and we have selected the best run in each scenario. Additionally, in Fig. A.8, we present the meshing results of DCUDF [14] on UDFs from different models on cars, both with and without the final min-cut step, at resolutions of 128 and 512. Without the min-cut, more surfaces are retained, though they are double-layered. Moreover, the overall meshing quality deteriorates at higher resolutions, following the trend observed for the other baselines.
A.8 Meshing ground-truth UDF
Although method is designed to handle imperfect UDFs, also evaluate it true UDFs computed directly from ground-truth meshes to verify that it does not introduce unwanted artifacts. We report results the ShapeNet [3] cars dataset in Tab. A.8 (top), and visualize several triangulations at a resolution of 512 in Fig. A.9. As observed, our method does not introduce significant artifacts; however, as expected, multiple iterations provide no benefit in this setting.
In the same table, we also compute the number of holes as surface boundaries, similarly to the description provided by DCUDF [14], resolution 512. We report the average. We notice that the original meshes have a large number of boundaries because they contain multiple detailed components and inner structures. None of the methods faithfully recovers the correct mesh topology. Methods that rely directly on MC triangulation, such as CAP-UDF [46], NSD-UDF+MC [36] and Ours+MC, tend to suffer from micro-holes and gaps between some of the faces. MeshUDF uses heuristic specifically designed to reduce this behavior and connect as many portions of the surface as possible, explaining the lower number of holes. DCUDF-T [14] starts from an inflated mesh so it generally tends to have fewer holes. Simple postprocessing steps can be applied to all methods to improve the final mesh quality. We take as an example the first of ShapeNet Cars (object 15545ee544773338555b4eeeee
and we apply Trimesh-bast based postprocessing (fill small holes, merge close vertices, remove spurious faces), showing that methods improve.
22

---

Auto-decoder cars
CAP-L cars [46]
DifTUDF [11]
GT
with min-cut
128
without min-cut
with min-cut
512
without min-cut
Figure A.8: DoubleCoverUDD min-cut. Comparing reconstructions of DCUDF [14] with and without the min-cut step at resolution 128 (middle) and 512 (bottom).
23

---

G1
SSD-UDE [36]
Ours
Figure A.9: Triangulating ground-truth UDE Surface meshing results on the ground-truth UDF in comparison NSD-UDF [36]. Our method does not introduce significant unwanted artifacts.
Table A.8:
Triangulating ground-truth UDFs. Results are reported on the ShapeNet [3] cars dataset, using the true UDF computed from the mesh. We compare against NSD-UDF + MC [36] at multiple resolution with the Median L2 Chamfer Distance x10 with 2M sample points (Chanfer-Distance) and against all MC-based methods with the average number of holes, as surface boundaries at resolution 5 512(urb of holes). For the latter, we also report results on the first car of the dataset, before and after post-processing the mesh
(a) Chamfer-Distance
Res.
Method
128
256
512
NSD-UDF MC [36]
1.34
0.230
0.0300
Ours + MC at iter.
1.36
0.244
0.0294
Ours MC at iter.
1.40
0.231
0.0300
(b) Number of holes resolution 512
ShapeNet cars [3]
Car
(before post- post-process.)
Car (post-processed)
GT'
783
1552
CAP-UDF [46]
10024
13265
2125
MeshUDF [13]
428
997
240
DCUDF-T [14]
6
DCUDF-T-nocut [14]
2.65
2
NSD-UDF+MC [36]
8280
8885
1387
Ours+MC
9284
9808
1604
24

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31


Reviews:
[{"review_id": "amnQQ9rZtH", "reviewer": "Reviewer_Ypj2", "summary": "This paper addresses the problem of mesh extraction from neural unsigned distance fields (UDFs). Its main contribution is an iterative technique that leverages neighborhood information from the marching cubes grid to refine surface extraction through multiple passes of a neural network. The approach is shown to perform well on complex and high-resolution shapes.\n\nThe method builds upon NSD-UDF, with significant overlap in the methodology section; which would benefit from further polishing. This raises the question of how incremental the contribution is, especially since the main novelty (iterative refinement scheme) is introduced without any theoretical justification. This should be clearly acknowledged in the introduction.", "questions": "[Figure 5] Why do the reconstructions appear voxelized? Please clarify.\n\nSince the proposed method does not depend on the UDF being represented by an INR,  how does it perform when applied to the ground-truth UDF?\n\nMost of the reconstructed surfaces shown are low in detail. Can the method be applied to more detailed models, such as the Thai Statue and the Asian Dragon?\nNote that these cases would require marching cubes at a resolution higher than 512×512.\n\nRegarding the augmentation term. It appears to be a design choice inherited from NSD-UDF, which showed that this factor improves reconstruction quality. However, given the introduction of a refinement step in the current method, I am curious whether this term is still necessary or beneficial.\nFinally, I was also curious about the dataset split. Did the authors divide the data into training and validation sets and report results only on the validation set? If so, could they clarify how this split was performed?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nThe claim in [L45] that meshing models should incorporate information from previously extracted surface elements is compelling. The evaluation confirms that the proposed iterative refinement improves reconstruction quality. However, the paper lacks a theoretical explanation for why this approach works.\n\nThe authors conduct extensive experiments demonstrating improved reconstructions compared to the state of the art.\n\nWeakness:\n\n[L21] The paper cites DeepSDF as a primary motivation for using SDFs in INRs. However, a more accurate motivation involves the use of the Eikonal equation for regularization. Missing references include:\n- Sitzmann et al., Implicit Neural Representations with Periodic Activation Functions, NeurIPS\n- Gropp et al., Implicit Geometric Regularization for Learning Shapes, ICML\n- Novello et al., Exploring Differential Geometry in Neural Implicits, Computers & Graphics\n- Fainstein et al., DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling, CVPR\n\nThe sentences in [L28–30] and [L33–34] appear redundant and should be revised for clarity.\n\n[L35] “worsens the problem, as shown in the results section” — Please indicate the exact section number or figure that supports this claim.\n\n[Figure 1] This figure needs refinement. Consider showing the full 3D model with zoom-ins to improve clarity. Also, please include the ground-truth mesh for comparison. \n\n[Section 3.2] This section appears to be mostly implementation details.", "was_revised": true, "final_justification": "I have carefully reviewed the rebuttal, and the authors addressed most of my comments. Therefore, I will maintain my positive score.\nIf the paper is accepted for publication, I strongly recommend that the additional experiments, important comments, and missing references be incorporated into the paper and supplementary material.", "rebuttal": "> **Q1**: Iterative refinement scheme is introduced without any theoretical justification.\n\n**A1**: We agree that a theoretical foundation would strengthen the work. However, providing a mathematical proof for the convergence of the iterative refinement over noisy neural fields is extremely challenging, as it involves complex interactions between spatial context, prediction dynamics, and network behavior - none of which is fully understood in existing literature, to the best of our knowledge. For example [8] compares it to denoising autoencoders, this would be an interesting direction. However, our approach is grounded in prior work where similar iterative strategies have proven effective in structured prediction tasks. We hope the strong empirical results (Table 2, Figure 3 and 4) help support its value in this setting. \n\n***\n\n> **Q2**: Contribution over NSD-UDF?\n\n**A2**: While our method builds on NSD-UDF, we believe the shift from a single-pass to an iterative, context-aware refinement process is a meaningful advancement, particularly at high resolutions. As shown in Figure 1 and 3 and Table 2, the iterative passes help recover surfaces that NSD-UDF misses. That being said, we will make sure to more clearly highlight where our method extends NSD-UDF and where it introduces new ideas.\n\n***\n\n> **Q3**: The paper cites DeepSDF as a primary motivation for using SDFs in INRs. However, a more accurate motivation involves the use of the Eikonal equation for regularization with missing citations.\n\n**A3**: Thank you for the suggestion and the papers which we will happily cite. However, we would like to clarify that our contribution is focused on meshing from already trained UDFs, not on learning or regularizing them. As such, the Eikonal equation - which is typically used during UDF training - is not directly relevant to our method. While DeepSDF and related works provide context for using distance fields in INRs, our approach is agnostic to the training objective and instead addresses the challenge of surface extraction at inference time. Nevertheless, we provide results on a network trained with Eikonal loss in section A.5 of the supplementary.\n\n***\n\n> **Q4**: Redundancy in [L28–30] and [L33–34].\n\n**A4**: We agree. L28-30 should be removed.\n\n***\n\n> **Q5**: [L35] “worsens the problem, as shown in the results section” — Please indicate the exact section number or figure that supports this claim.\n\n**A5**: This is particularly visible in Figure 3 and A.1, in which the extraction of NSD-UDF gets worse with increasing resolution. A similar phenomenon happens to most of the other methods as well, and can be seen by comparing the same shape across different resolutions in figures A.2 to A.6. We will clarify this in the manuscript.\n\n***\n\n> **Q6**: [Figure 1] This figure needs refinement. Consider showing the full 3D model with zoom-ins to improve clarity. Also, please include the ground-truth mesh for comparison.\n\n**A6**: Thank you for the suggestion. We agree that including the full shape as well as the ground truth would improve the figure. We will update the paper accordingly.\n\n***\n\n> **Q7**: [Figure 5] Why do the reconstructions appear voxelized? Please clarify.\n\n**A7**: We purposefully did not apply any post-processing or smoothing algorithm, and we rendered the shapes in Blender using non-smoothed normals, which contribute to making the shapes appear voxelized. We did this to faithfully show the output of each meshing algorithm. This could be mitigated with post-processing and using different rendering techniques. The only naturally non-voxelized extraction method, in our testing, has been DCUDF, thanks to its optimization procedure.\n\n***\n\n> **Q8**: Since the proposed method does not depend on the UDF being represented by an INR, how does it perform when applied to the ground-truth UDF?\n\n**A8**: That is a good point. We did test the method with clean UDFs, and it works well in that setting. However, since there is no neural noise in that case, the iterative refinement offers little to none additional benefit. We include here the median results on ground-truth ShapeNet cars, comparing the first itearation with the last one, and we will clarify this in the revision. CD is $\\times 10^{-5}$.\n\n| GT ShapeNet Cars | CD ↓ (128) | CD ↓ (256) | CD ↓ (512) |\n|------------------|------------|------------|------------|\n| Ours iteration 1        | 1.36       | 0.244      | 0.0294     |\n| Ours iteration 6        | 1.40       | 0.231      | 0.0300     |\n\n***\n\n> **Q9**: Most of the reconstructed surfaces shown are low in detail. Can the method be applied to more detailed models?\n\n**A9**: We believe the perceived low detail is mostly due to the choice of examples, which may not have fully showcased the complexity present in the dataset. In fact, categories like ShapeNet cars and chairs do contain highly detailed structures, and we will include more representative examples to better highlight our method's performance. Additionally, we have extended our evaluation to more complex cases from the 3D Scene dataset, trained with the learning part of CAP-UDF in order to encode more details than in the scenarios shown in the paper, with quantitative results shown at the end of the rebuttal for reviewer EmVW, to further demonstrate the method's applicability to high-detail models.\n\n***\n\n> **Q10**: Regarding the augmentation term. It appears to be a design choice inherited from NSD-UDF, which showed that this factor improves reconstruction quality. However, given the introduction of a refinement step in the current method, I am curious whether this term is still necessary or beneficial. \n\n**A10**: Thank you for the question. Yes, we found it remains important. The augmentation (Eq. 4) helps the network learn robustness to noisy gradients and values, which are still present in early iterations. Removing it led to slower convergence and worse performance in our tests, as shown below. We appreciate the opportunity to clarify this design choice and we will add this ablation to the supplementary. CD is $\\times 10^{-5}$.\n\n| Auto-dec ShapeNet Cars    | CD ↓ (128) | CD ↓ (256) | CD ↓ (512) |\n|---------------------------|------------|------------|------------|\n| Ours+MC (as in paper)     | 5.64       | 5.23       | 8.84       |\n| Ours+MC (no augmentation) | 8.01       | 12.5       | 47.8       |\n\n***\n\n> **Q11**: Finally, I was also curious about the dataset split. Did the authors divide the data into training and validation sets and report results only on the validation set? If so, could they clarify how this split was performed?\n\n**A11**: The pipeline has been trained on watertight ABC shapes, and has been tested exclusively on open shapes that belong to different datasets, to ensure that there is no overlap between training and testing. \n\n\n## References\n[8] Durasov N. et al., Enabling Uncertainty Estimation in Iterative Neural Networks, ICML, 2024"}, {"review_id": "ft3ljmkgKz", "reviewer": "Reviewer_YYpx", "summary": "The paper introduces an iterative scheme to compute pseudo-signs for Unsigned Distance Fields (UDF) mesh extraction. The core idea is to progressively refine the result by taking into consideration the previous interaction pseudo-signs, UDF values and gradients.", "questions": "No additional questions.", "limitations": "Yes, they are described in Section 5.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "To be honest, I don't see noticeable flaws in the paper, so I will focus on the strengths.\n\n## Strengths\n\n* Excellent motivation. The problem and the reasons why it exists are clearly described. The claims are properly stated and are sound.\n\n* Contextualization is done well. The differences in comparison with related work are discussed in detail. The authors present confident knowledge in the neural UDF literature.\n\n* Good writing. The paper reads well and is easy to follow. The math notation is also good.\n\n* Experiments provide an excellent overview of how the area deals with mesh extraction. The results are adequate for the claims: a method designed to work well on high resolutions, avoiding the noise generated by the difficult of achieving true zeros at the trained UDF.\n\n* About the method itself, its design makes sense. The iterative nature is aligned with the idea of considering the current neighborhood while computing the pseudo-signs. This seems to be a good alternative to analytic approaches, such as computing curvature, for example, which would also provide neighborhood analysis but would be influenced by gradient existence on discontinuities at the surface. I also liked the efforts into making it faster and more robust to noise. Being an iterative procedure, ensuring it has comparable running times to other SOTA methods is important for it to be considered as a viable choice. Noise robustness is also very important because of the focus on high-resolution reconstruction. The worries of the authors are on-point with the necessities of the problem at hand. \n\n## Current assessment\n\nI am not completely familiar with all the current neural UDF literature. I have reviewed a few papers on recent conferences in the subject, but I am more familiar with SDFs. It is possible that my rating decreases in case reasonable important flaws are pointed by the other reviewers. If that is not the case, I recommend acceptance.", "was_revised": true, "final_justification": "I acknowledge reading the rebuttal message and reflecting about the points raised by the other reviewers. I decide to maintain my rating, the paper was an interesting reading and deserves publication in my opinion.", "rebuttal": "We sincerely thank the reviewer for the thoughtful and encouraging feedback. We are especially grateful for the comments highlighting the clarity of the writing, the relevance of the motivation, and the soundness of the method design.\n\n> “Excellent motivation... confident knowledge in the neural UDF literature... good writing... results are adequate for the claims”\n\nWe appreciate these remarks, and we are glad the motivation and problem setup came across clearly. It was important for us to position the work carefully within the existing literature and articulate why high-resolution UDF meshing remains a challenging and underexplored problem.\n\n> “The iterative nature is aligned with the idea of considering the current neighborhood... a good alternative to analytic approaches.”\n\nThank you for this insight. We agree that iterative refinement offers a practical and robust alternative to curvature-based or analytic neighborhood methods, especially when gradients may be unreliable near surface discontinuities. We are also glad the design considerations around runtime and noise robustness resonated — these were key goals in making the method not only effective but also practical.\n\n> “I am not completely familiar with all the current neural UDF literature”, my rating may adjust based on other reviews.\n\nWe completely understand, and we appreciate your openness. We hope the additional responses and clarifications across reviews help to confirm the soundness of the contribution. We are of course receptive to any further concerns that may be raised and we will gladly address them in revisions.\n\nThank you again for the constructive and thoughtful review."}, {"review_id": "ZGqyOlChdY", "reviewer": "Reviewer_EmVW", "summary": "This paper presents a new approach for meshing neural Unsigned Distance Fields (UDFs) at high resolution, which are typically more difficult to triangulate than Signed Distance Fields due to the lack of sign changes near the surface. The proposed method introduces an iterative refinement strategy: instead of performing surface extraction in a single pass, the network operates over multiple iterations, progressively improving local predictions by integrating surface information from neighboring voxels. At each iteration, the network predicts pseudo-sign configurations for the vertices of a voxel using UDF values, gradients, and surrounding context. This iterative propagation scheme enables the recovery of finer surface details, closes holes, and stabilizes extraction in noisy or ambiguous regions. The approach is tested across diverse 3D datasets and resolutions, demonstrating improved robustness over existing methods.", "questions": "see weaknesses", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The proposed method tackles a well-known challenge in high-resolution UDF meshing by introducing a conceptually simple yet powerful idea: iterative correction based on spatial propagation. This naturally complements the limitations of single-pass algorithms and effectively exploits structure within the field. The design of the network is well-explained and integrates neighboring context without needing complicated geometry-specific heuristics. Additionally, the method is robust to noise and generalizes across multiple datasets and resolutions, showcasing the practicality of the approach for real-world high-resolution meshing tasks.\nSeveral points, however, could be clarified further. First, the approach currently uses a fixed maximum number of iterations (up to 6), selected empirically. Could the authors provide insights into whether an adaptive stopping criterion might be beneficial, or whether performance saturates early? Second, while the filtering strategy for removing high-UDF cells is described, it's unclear whether the model remains robust under different UDF scales or UDFs learned from different network architectures—some discussion on generalizability across UDF sources would be helpful.Third, some related work such as “Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection” could be cited for completeness.", "was_revised": false, "final_justification": "", "rebuttal": "> **Q1**: Why is a fixed number of iterations used, and could an adaptive stopping criterion improve the method?\n\n**A1**: Thank you for raising this interesting point. We used a fixed maximum of 6 iterations for simplicity and ease of training, and found that performance tends to saturate after 5–6 passes (see Table 4 and A.3). That said, an adaptive stopping criterion is an interesting direction. We observe that simpler shapes indeed do not require full cycle and can be stopped early to save computation. This can be seen in Table 4, where cars, chairs and planes always benefit from additional iterations, whereas garments, due to their simplicity, only benefit at high resolution. It remains an interesting direction for future work. We also experimented with a per-cell stopping criterion based on output confidence scores, but it did not improve the results.\n\n***\n\n> **Q2**: Is the model robust to UDFs with different value scales or learned from different architectures? Some discussion on generalizability across UDF sources would be helpful.\n\n**A2**: This is a great question. Our current approach includes resolution normalization of the UDF values (Sec. 3.1), which helps maintain robustness across scales, and assumes that the shapes lie in a $[-1,1]^3$ cube. It can be used also with non-normalized (or differently normalized) shapes by re-normalizing the UDF values after grid sampling, which is what we did in the experiments with the UDF training pipeline of CAP-UDF [1] (see below), since it is not trained on a $[-1,1]^3$ cube. Our method is designed to operate on any pre-trained UDF and does not depend on the specific architecture or training objective used. In fact, we only trained a single network on 80 shapes of the ABC dataset and tested this network on various datasets including two auto-decoders architectures (ReLU-based, in the main paper, and Softplus-based, in the supplementary) trained on MGN, ShapeNet cars, chairs and planes, as well as CAP-UDF [1] networks trained on ShapeNet cars and 3D Scene point clouds in the new experiment shown below. However, we recognize that UDF quality and noise levels can vary across sources and architectures, and we will include a discussion of this in the final version to acknowledge the scope and limitations of the current evaluation.\n\n***\n\n> **Q3**: Some related work such as “Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection” could be cited for completeness.\n\n**A3**: We would be happy to. Thank you for the suggestion.\n\n***\n\n## Surface extraction from a different UDF architecture\n\n*Note: CAP-UDF [1,3] defines a UDF architecture and training as well as a meshing algorithm. To avoid confusion, we refer here to the learning part as CAP-UDF-L, and to the meshing part as CAP-UDF-M, which has been referred to as CAP-UDF in the manuscript.*\n\nWe train CAP-UDF-L [1] networks following the official code repository on the point clouds provided by the authors: 2 cars from ShapeNet, which are not part of our other experiments, using 10k points as described in [1]; and 5 scenes from 3D Scene [2], using the 100 $points/m^2$ scenario described in [1]. These networks are trained differently than the ones used in our other experiments, have a different normalization, and are not auto-decoders, providing insights about the performance of our pipeline in a very different scenario.\n\nWe found that Copyroom and Lounge from 3D Scene produced very bad metrics across all methods due to a seemingly inconsistent normalization, skewing the means, so we excluded them from the table below. We compare Marching Cubes-based methods using the same metrics as the main paper. CD is $\\times 10^{-5}$. Since the number of shapes/scenes is low, we report mean metrics instead of median.\n\nOn cars, which are learned using a relatively dense input point cloud, most methods perform relatively well at resolution 128 and 256, with NSD-UDF and our own pipeline closely competing. At 512 a similar scenario as in the main paper arises, with the competing methods sometimes losing accuracy compared to their scores at 256. We also confirm the trend noticed in the main paper regarding the behavior of CAP-UDF-M (LL219-221), which has been often found less accurate than competing methods, but we find that it performs better at higher resolutions.\n\n\n| ShapeNet cars | CD ↓ (128) | F1 ↑ (128) | IC ↑ (128) | CD ↓ (256) | F1 ↑ (256) | IC ↑ (256) | CD ↓ (512) | F1 ↑ (512) | IC ↑ (512) |\n|---------------|------------|------------|------------|------------|------------|------------|------------|------------|------------|\n| CAP-UDF-M       | 7.67       | 66.0       | 88.9       | 2.05       | 74.9       | 90.5       | 1.93       | 76.0       | 90.5       |\n| MeshUDF       | 3.77       | 70.5       | 89.3       | 2.34       | 74.8       | 90.3       | 2.25       | 75.7       | 90.3       |\n| DCUDF-T       | 159        | 58.6       | 85.8       | 86.5       | 71.4       | **90.7**       | 112        | 70.3       | 88.6       |\n| NSD-UDF+MC    | **2.34**       | **72.8**       | **90.0**       | 2.05       | **75.8**       | 90.5       | 2.16       | 75.9       | 90.4       |\n| Ours+MC       | 2.43       | 71.3       | 89.8       | **1.86**       | 75.5       | 90.6       | **1.85**       | **76.3**       | **90.7**       |\n\nOn 3D Scene, containing complex and larger scale scenes, our iterative scheme is able to provide benefits already at resolution 256, confirming the findinds of the main paper.\n\n\n| 3D Scene - 100 | CD ↓ (128) | F1 ↑ (128) | IC ↑ (128) | CD ↓ (256) | F1 ↑ (256) | IC ↑ (256) | CD ↓ (512) | F1 ↑ (512) | IC ↑ (512) |\n|----------------|------------|------------|------------|------------|------------|------------|------------|------------|------------|\n| CAP-UDF-M        | 4.27       | 68.0       | 83.8       | 3.65       | 70.1       | 86.1       | 3.57       | 70.5       | 86.1       |\n| MeshUDF        | 4.40       | 68.2       | 84.5       | 3.42       | 69.6       | 86.3       | 4.49       | 69.9       | 84.5       |\n| DCUDF-T        | 279        | 59.7       | 84.0       | 4.75       | 69.9       | 84.6       | 140        | 68.9       | 83.3       |\n| NSD-UDF+MC     | **3.34**       | **69.8**       | **86.7**       | 3.30       | 70.3       | 86.3       | 3.72       | 70.0       | 84.0       |\n| Ours+MC        | 3.44       | 69.3       | 85.3       | **3.07**       | **71.4**       | **86.6**       | **3.08**       | **71.8**       | **86.8**       |\n\n\n## References\n[1] Zhou J. et al., CAP-UDF: Learning Unsigned Distance Functions Progressively From Raw Point Clouds With Consistency-Aware Field Optimization, PAMI, 2024\n\n[2] Q.-Y. Zhou and V. Koltun, “Dense scene reconstruction with points\nof interest,” ACM Transactions on Graphics (TOG), 2013.\n\n[3] Zhou J. et al., Learning Consistency-Aware Unsigned Distance Functions Progressively from Raw Point Clouds, NeurIPS, 2022"}, {"review_id": "Ll3M4bGWHu", "reviewer": "Reviewer_YyyE", "summary": "The authors present a framework that reconstruct the mesh from a learned unsigned distance field (UDF) network. Given a learned UDF network, this paper iteratively query the UDF network on a grid and enforces sign configuration consistency with its neighboring cells. Doing so helps close the holes due to UDF networks usually cannot reach true zero in their UDF predictions.", "questions": "I cannot accept the paper with an inherent unfair comparison. If the authors could demonstrate the UDF extraction results with more advanced UDF learning methods, and show that they exhibit better qualities over other UDF mesh extraction methods, I would reconsider my rating.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 2, "significance": 1, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n1. The authors present an improvement over various previous works. There is a catch though, see below.\n\n**Weaknesses**\n1. The authors use an autoencoder to learn the UDF field, and such choice is subject to serious question. For example in the teaser image (Figure 1), the authors claim that neural UDFs often fail to reach zero. While this is often the case, the quality of such learned UDF field should not be bad enough to fail to reconstruct the nosewheel of the aircraft. This brings the question of the intrinsic quality of the learned UDF in this paper. The authors follow the architecture of DeepSDF dating back to 2019. In recent years there have been multiple UDF learning methods -- CAP-UDF [1] (the learning part), GeoUDF [2], LevelsetUDF [3], DUDF [4], DEUDF [5], just to name a few. It is unclear whether the bad results (from CAP-UDF, DCUDF, etc) shown in this paper are the fault of the mesh extraction methods or the learned UDF field, and if the latter is the case, the comparison of the paper is unfair. While in supplementary material the authors present another UDF network setup (Section A.5), it is still an autoencoder.\n2. I am also very concerned about the authors' misrepresentation of other works. Specifically, the authors claim that GaussianUDF [6] also follows the autoencoder framework used in this paper to represent the UDF (L188; suppl. L46-47), which seems completely untrue -- their network follows NeuralUDF [7], which is a simple MLP with positional encoding. See their paper Section 4.1 \"Details\" \"The UDF $f$ ... 8-layer MLP with 256 hidden units ... apply positional encoding ...\"\n\n**Others**\n1. The paper heavily uses the term \"nerual UDF\", but since there is a well-known work literally named \"NeuralUDF\" [7], it only adds to the confusion.\n\n[1] Zhou et al. \"CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization\" (NeurIPS 2022 / TPAMI)\n\n[2] Ren et al. \"GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation\" (ICCV 2023)\n\n[3] Zhou et al. \"Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection\" (ICCV 2023)\n\n[4] Fainstein et al. \"DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling\" (CVPR 2024)\n\n[5] Xu et al. \"Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction\" (AAAI 2025)\n\n[6] Li et al. \"GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting\" (To appear in CVPR 2025)\n\n[7] Long et al. \"NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies\" (CVPR 2023)", "was_revised": true, "final_justification": "After multiple rounds of discussion and opinions from other reviewers I decided to raise my score to resolve the discrepancy between me and other reviewers. I am willing to accept the paper **conditionally** if the authors could:\n1. Demonstrate qualitative visualisations on GT UDF.\n2. Complete the experiments with DiffUDF and CAP-UDF backbones, and incorporate the qualitative & quantitative results to the main text.\n3. Demonstrate the results of DCUDF **without mini-cut**, and incorporate the qualitative visualisations to the main text.\n\nI would also encourage that the authors conduct experiments on watertight models for topology evaluations. The ground truth meshes from ShapeNet Cars is known to contain many fake holes. Therefore I suggest using watertight meshes for that.\n\nI thank the authors' passionate discussion and appreciate their efforts to defend their work.", "rebuttal": "Before addressing the reviewer's specific concerns, we would like to clear a potential misunderstanding. The review refers several times to our experiments as using an \"autoencoder\". This may simply be a typo or shorthand, but just to clarify: we actually use an auto-decoder framework, not an autoencoder. Specifically, our network learns a shape distribution from multiple training shapes using per-shape latent codes and a shared MLP - in the spirit of DeepSDF and subsequent works [4,5]. Thus, there is no encoder involved in our setup. This is a valid choice because auto-decoders remain a widely used and well-established approach [4,5,6,7] in shape modeling, particularly when the focus is on high-fidelity reconstruction and controllable latent space exploration. This has proven valuable in many applications such as interpolation between shapes, shape completion, generative modeling, or shape optimization - all of which commonly rely on mesh extraction, which is the focus of our work. We mention this only to avoid confusion, as autoencoders and auto-decoders differ significantly in architecture and training objectives. We appreciate the reviewer's detailed engagement with our method and hope this clears up some ambiguity. \n\n***\n\n> **Q1**: The authors use an autoencoder to learn the UDF field, and such choice is subject to serious questions. Why does the teaser (Figure 1) show such a poor reconstruction (e.g., missing nosewheel), given that neural UDFs, while often failing to reach zero, usually perform better?\n\n**A1**: We thank the reviewer for the question. The missing surface in Figure 1 showcases the more significant failure modes that we encountered in our experiments. Other less pronounced examples are visible in Figures 3-4-5, where smaller portions of the shapes are missing. More precise learning-based UDFs can indeed yield better shapes overall, but reaching a precise zero remains difficult, as also noted by the reviewer. So, we have shown a fairly extreme case for exposition purposes but similar situations are sure to arise, maybe to a less extreme extent or at higher resolutions. This is shown by Section A.5 of the supplementary material, which tests our pipeline on a more precise UDF. We also report additional results on an even more precise single-shape UDFs at the end of this rebuttal.\n\nOur intention is to highlight the challenge we deal with: at higher resolutions the UDF must be extremely precise near zero to localize the surface accurately, while the gradients become increasingly noisy near the surface. These factors together make high-resolution meshing particularly difficult  -  a key motivation for our iterative refinement scheme. We will clarify this more clearly in the revision and provide results from both auto-decoder and recent single-shape approaches for completeness.\n\n***\n\n> **Q2**: Does the paper rely on naive UDF learning methods (e.g., DeepSDF), and could more modern approaches (e.g., CAP-UDF, GeoUDF, DUDF) lead to better results?\n\n**A2**: Our choice to use a DeepSDF-style auto-decoder is motivated by its use both in prior works on meshing methods (like NSD-UDF, MeshUDF) and in prior works on surface representation [4,5,6,7], allowing for controlled and direct comparison of mesh extraction methods on a widespread scenario. That said, we agree that recent UDF learning methods (e.g., CAP-UDF, DUDF, GeoUDF) can offer improved field quality and smoother zero-level sets in certain applications. To address this, at the end of this rebuttal and in the rebuttal for reviewer EmVW, we provide the results on 2 ShapeNet cars and 3 complex scenes from 3D Scene using the CAP-UDF learning pipeline and the point clouds provided by its authors. We find that the results of Copyroom and Lounge are not correctly normalized, resulting in terrible metrics for all of the meshing methods we tested, so we remove them from the 5 originally provided 3D Scene scenes, to avoid skewing the mean metrics. We report results for all MC-based methods tested in the manuscript.\n\n***\n\n> **Q3**: If the bad results are because the UDF field is noisy, the comparison of the paper is unfair.\n\n**A3**: We respectfully but strongly disagree with this. Our method is a mesh extraction technique, and is agnostic to how the UDF is learned. All methods in our comparisons are evaluated using the exact same input UDF fields, ensuring a controlled and fair comparison focused purely on extraction performance.\n\nGiven that learning a perfect UDF is still widely regarded as an open challenge, it is crucial for a meshing method to perform robustly under realistic, imperfect conditions. In that light, the fact that our method consistently outperforms others even with noisy UDF inputs further demonstrates its effectiveness and practical utility.\n\nHowever we agree that the paper could be strengthened by additional results from single-shape UDF networks such as CAP-UDF, which we include at the end of this rebuttal and in the rebuttal for reviewer EmVW, as discussed above.\n\n***\n\n> **Q4**: The authors claim that GaussianUDF [6] also follows the autoencoder framework used in this paper to represent the UDF (L188; suppl. L46-47), which seems completely untrue.\n\n**A4**: The sentences in our manuscript (\"we train an autodecoder as in [DeepSDF, NSD-UDF, GaussianUDF]\" and \"we used the traditional autodecoder architecture proposed in DeepSDF and used also in [NSD-UDF, GaussianUDF]\") are wrong. We thank the reviewer for pointing it out and we will rewrite them to reflect what we meant. GaussianUDF does not use an auto-decoder, but it uses a ReLU-based MLP, which is the same network architecture that we also use. What we meant is that we train an auto-decoder as in DeepSDF and NSD-UDF, using a similar network architecture also used in recent UDF methods such as GaussianUDF to emphasize that, while introduced a few years ago, ReLU-based MLPs are still a popular choice for UDFs.\n\n***\n\n> **Q5**: The paper heavily uses the term \"nerual UDF\", but since there is a well-known work literally named \"NeuralUDF\", it only adds to the confusion.\n\n**A5**: Thank you for pointing this out. We used this term because it has been used in existing literature (DualMesh-UDF and NSD-UDF). To avoid ambiguity, we will revise the terminology in the paper to use clearer alternatives like \"learned UDF\" or \"MLP-based UDF\", and explicitly distinguish our usage from the NeuralUDF work.\n\n***\n\n## Surface extraction from CAP-UDF[1,3]\n\n*Note: CAP-UDF [1,3] defines a UDF architecture and training as well as a meshing algorithm. To avoid confusion, we refer here to the learning part as CAP-UDF-L, and to the meshing part as CAP-UDF-M, which has been referred to as CAP-UDF in the manuscript.*\n\nWe train CAP-UDF-L [1] networks following the official code repository on the point clouds provided by the authors: 2 cars from ShapeNet, which are not part of our other experiments, using 10k points as described in [1]; and 3 scenes from 3D Scene [2], using the 100 $points/m^2$ scenario described in [1]. We compare Marching Cubes-based methods using the same metrics as the main paper. Quantitative results are shown at the end of the rebuttal for reviewer EmVW.\n\nOn cars, which are learned using a relatively dense input point cloud, most methods perform quite well at resolution 128 and 256, with NSD-UDF and our own pipeline closely competing. At 512 a similar scenario as in the main paper arises, with the competing methods sometimes losing accuracy compared to their scores at 256. We also confirm the trend noticed in the main paper regarding the behavior of CAP-UDF-M (LL219-221), which has been often found less accurate than competing methods, but we find that it performs better at higher resolutions.\n\nOn 3D Scene, containing complex and larger scale scenes, our iterative scheme is able to provide benefits already at resolution 256, confirming the findings of the main paper.\n\n## References\n[1] Zhou J. et al., CAP-UDF: Learning Unsigned Distance Functions Progressively From Raw Point Clouds With Consistency-Aware Field Optimization, PAMI, 2024\n\n[2] Q.-Y. Zhou and V. Koltun, “Dense scene reconstruction with points\nof interest,” ACM Transactions on Graphics (TOG), 2013.\n\n[3] Zhou J. et al., Learning Consistency-Aware Unsigned Distance Functions Progressively from Raw Point Clouds, NeurIPS, 2022\n\n[4] Mello Rella E. et al., Neural Vector Fields for Implicit Surface Representation and Inference, IJCV, 2025\n\n[5] Zheng Z. et al., Deep Implicit Templates for 3D Shape Representation, CVPR, 2021\n\n[6] Takikawa T. et al., Variable Bitrate Neural Fields, SIGGRAPH 2022\n\n[7] Nam G. et al., 3D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Models, 2022"}]

Author rebuttal:

Meta-review: Strengths
* Well-motivated problem of improving the meshing of learned UDFs with inaccuracies
* Iterative refinement is a simple and sensible approach, as the authors state, "meshing models should incorporate information from previously extracted surface elements" (L45)
  * Specifically, the method builds on top of NSD-UDF for iterative, context-aware refinement

Weaknesses
* Could be viewed as an incremental extension to NSD-UDF (debatable, I do not think this is an issue)
* Some missing experiments (see below)

Under the condition that the authors will incorporate the discussions with the reviewers in the final revision, I would like to recommend accepting this paper. In particular, YyyE requested
* Demonstrate qualitative visualisations on GT UDF
  * Ypj2 also raised questions about applying the method to the GT UDF. While the authors stress that the method is meant to recover mesh on noisy UDFs, experiments on GT UDFs will help clarify the scope of the paper and verify that the method does not introduce new artifacts
* Complete the experiments with DiffUDF and CAP-UDF backbones, and incorporate the qualitative & quantitative results to the main text.
* Demonstrate the results of DCUDF without mini-cut, and incorporate the qualitative visualisations to the main text.

YyyE's suggestion on evaluating with watertight meshes is a good test of the topological consistency.
Decision: Accept (poster)