SurfelSplat: Learning Efficient and Generalizable Gaussian Surfel Representations for Sparse-View Surface Reconstruction
Authors: Chensheng Dai
Shengjun Zhang
Min Chen
Yueqi Duan
Venue: NeurIPS 2025 poster ()
Keywords: 3D Gaussian Splatting
feed-forward netowrk
surface reconstruction
Primary area: applications

Abstract: 3D Gaussian Splatting (3DGS) has demonstrated impressive performance in 3D scene reconstruction. Beyond novel view synthesis, it shows great potential for multi-view surface reconstruction. Existing methods employ optimization-based reconstruction pipelines that achieve precise and complete surface extractions. However, these approaches typically require dense input views and high time consumption for per-scene optimization. To address these limitations, we propose SurfaceSplat, a feed-forward framework that generates efficient and generalizable pixel-aligned Gaussian surfel representations from sparse-view images. We observe that conventional feed-forward structures struggle to recover accurate geometric attributes of Gaussian surfels because the spatial frequency of pixel-aligned primitives exceeds Nyquist sampling rates. Therefore, we propose a cross-view feature aggregation module based on the Nyquist sampling theorem. Specifically, we first adapt the geometric forms of Gaussian surfels with spatial sampling rate-guided low-pass filters. We then project the filtered surfels across all input views to obtain cross-view feature correlations. By processing these correlations through a specially designed feature fusion network, we can finally regress Gaussian surfels with precise geometry. Extensive experiments on DTU reconstruction benchmarks demonstrate that our model achieves comparable results with state-of-the-art methods, and predict Gaussian surfels within 1 second, offering a 100× speedup without costly per-scene training.

SurfelSplat: Learning Efficient and Generalizable Gaussian Surfel Representations for Sparse- Viewse-View Surface Reconstruction
Chensheng Dai; Shengjun Zhang, Min Chen, Yueqi Duan'
Tsinghua University
(dcs23, zhangsj23, (m22)mmmaall tsinghua. edu. en, duanyueqi edu,
NeuSuuf
20G5
Previous
35-
SurfelSplat
Interference Timetsecond)
(a) Visualization and performance of our framework
(b) Performance and runtime comparison
Figure I: Our method delivers state-of-the-ar surface reconstruction with ultra-fast inference speed. (a) Framework visualization: Given an image pair, our approach regresses Gaussian radiance fields capturing fine geometric details in just second. (b) Quantitative comparisons: Our method achieves superior reconstruction accuracy while maintaining the fastest runtime among existing approaches.
Abstract
3D Gaussian Splatting (3DGS) has demonstrated impressive performance in 3D scene reconstruction. Beyond novel view synthesis, it shows great potential for multi-view surface reconstruction. Existing methods employ optimization- reconstruction pipelines that achieve precise and complete surface extractions. However, these approaches typically require dense input views and high time consumption for per-scene optimization. To address these limitations, we propose SurfelSplat, a feed-forward framework that generates efficient and generalizable pixel-aligned Gaussian surfel representations from sparse-view images. We observe that conventional feed-forward structures struggle to recover accurate geometric attributes of Gaussian surfels because the spatial frequency of pixel-aligned primi- tives exceeds Nyquist sampling rates. Therefore, we propose cross-view feature aggregation module based on the Nyquist sampling theorem. Specifically, we first adapt the geometric forms of Gaussian surfels with spatial sampling rate-guided low-pass filters. We then project the filtered surfels across all input views ob- tain cross- view feature correlations. By processing these correlations through a
"qqual contribution Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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(a) Current Feed-F red--Forward Networks
(b) Correlated Image Regions Are Rotation-invarian
Input Images
Rumdered Nurmal
Rendered D Depth
Rendered Color
Parallel to Image Plane
Camera
Image
Undetermined
Surface
Figure Experimental Observation. (a) Current feed-forward networks generate geometrically inaccurate Gaussian radiance fields. (b) The correlated image regions of pixel-aligned Gaussian surfels exhibit rotation invariance, limiting the network's ability accurately infer surface orientations.
specially designed feature fusion network, we can finally regress Gaussian surfels with precise geometry. Extensive experiments on DTU reconstruction benchmarks demonstrate that our model achieves comparable results with stte-of-the-ane meth- ods, and predict Gaussian surfels within I second, offering 100x speedup without costly per-scene training.
1 Introduction
Reconstructing accurate surfaces from multi-view images remains fundamental challenge in computer vision. Previous methods focus on Multi Muew Stereo [1, 2] techniques to capture geometric details from multi-view images. Recent advancements of neural implicit representa- tions [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] have demonstrated significant progress recovering smooth and complete surface. However, these approaches typically struggle to extract precise surfaces in terms of sparse viewpoints. While following works [6. 7, 14, 15] have shown promise in sparse-view reconstruction, they generally require per-scene optimization with high time consumption. More recently, 3D Gaussian Splatting (3DGS) [16] has recently drawn increasing attention due to its rapid rendering speed and high visual fidelity. To enhance the surface alignment capabilities of Gaussian primitives, recent approaches [17, 18, 19, 20, 21] have modified the geometric shape of Gaussian representations better conform to actual surfaces. For instance, 2D Gaussian Splatting (2DGS) [18] transforms 3D Gaussian primitives into 2D Gaussian surfels to maintain improved view-consistent geometry. While 3DGS-bard based methods succeed in precise surface extraction, they tend overfit to the camera when presented with limited viewpoint information (i.e., as few as two images), resulting in geometric collapse.
To circumvent per-scene optimization while ensuring generalizable and efficient scene reconstruction, several feed-forward networks [22, 23, 24, 25, 26, 27, 28, 29] have been proposed to directly regress 3D Gaussian parameters from sparse-view input images. These approaches predict the depth map and appearance attributes of pixel-aligned Gaussian primitives from cross-view image features. Current feed-forwan frameworks achieve superior performance in fast and generalizable scene reconstruction intuitive approach to apply the current feed-forward
for novel view synthesis. Therefore. networks for parameter prediction of 2D Gaussian surfels. However, shown in Figure 2, typical methods such as MVSplat [24] fail to generate surfels with accurate geometry. where the normal vectors of surfels cannot be precisely recovered. The Gaussian surfels tend to orient parallel to image plane rather than aligning with actual surface geometry. As shown Figure 2(b), Gaussian surfels predicted by these networks only cover the area of single pixel. Consequently, the corresponding image regions relevant surfel attributes cannot provide sufficient supervisory information to accurately learn the covariance of Gaussian surfels.

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In this paper, we first analyze this phenomenon from the perspective of the Nyquist sampling theorem. Our key insight is that the failure to generate surface-aligned primitives is because the spatial frequency of pixel-aligned Gaussian surfels exceeds the Nyquist sampling rate, thus violating the fundamental signal processing principles. To trackle this challenge, we introduce SurfelSplat, a novel feed-forward framework to regress 2D Gaussian radiance field with precise geometry guided by Nyquist theorem. Our method dynamically modulates the geometric forms of diverse Gaussian surfels in the frequency domain and correlates pixel regions across multiple input views that effectively contribute to Gaussian geometric feature learning. We subsequently develop a feature aggregation network that leverages image features from these identified regions to enhance the original Gaussian image features, thereby yielding accurate Gaussian surfel representations with improved geometric fidelity. Our contributions summarized follows:
We propose SurfelSplat, a feed-forward framework that regresses 2D Gaussian surfels directly from sparse-view images for surface reconstruction.
We conduct detailed analysis of why current feed-forward frameworks fail generate geometricall--acuuaae Gaussian primitives and introduce Nyquist theorem-guided Gaussian surfel adaptations and feature aggregations achieve superior geometric properties of the scene.
Experimental results demonstrate the effectiveness of our method. SurfelSplat generates surface- aligned Gaussian radiance fields with high efficiency and accurate geometry.
2
Related Work
2.1 Neural Implicit 3D Representation
Neural Radiance Fields (NeRF) represent scenes through implicit radiance fields, with optimization processes dependent on volumetric rendering [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]. For surface reconstruction, NeuS [3] pioneered scene representation using implicit Signed Distance Functions (SDFs) [5, 11, 12, 50J. The inherent continuity of MLP-based SDFs ensures smooth and accurate extracted meshes. Subsequent research has enhanced performance in sparse-view settings: VolRecon [51] integrates multi-scale feature extraction with geometry-aware regularization to recover 3D surfaces from limited viewpoints; NeuSurf [6] combines differentiable rendering with adaptive surface extraction techniques, enabling high-fidelin recovery of complex geometries; and UFORecon [8] employs uncertainty- fusion optimization framework that leverages probabilistic feature correspondence and adaptive confidence weighting for robust surface reconstruction. However, the inherent complexity of volumetric rendering typically requires several hours of computation per scene.
2.2 Neural Explicit 3D Representation
Beyond neural implicit representations, 3D Gaussian Splatting (3DGS) has achieved remarkable progress in 31) scene reconstruction, delivering photorealistic rendering quality with high rendering speed [16, 52, 53, 54, 55, 56, 57, 58). Two primary approaches have emerged for accurate surface extraction. The first enhances primitives to better fit surfaces: SuGaR [17] models 3D Gaussians as 2D pieces by incorporating flat and signed-distance regularization terms; 2DGS [18] and Gaussian Surfels [19] transform 3D Gaussian primitives into 2D surfels, with 2DGS proposing depth and normal consistency constraints to align surfels more accurately with surfaces. The second approach combines implicit representations to guide 3DGS training: NeuSG [59] integrates NeRF and 3DGS to recover complex 3D surfaces through differentiable optimization that preserves both local details and global structure; GSDF [21] employs two-branch framework to simultaneously optimize SDF and Gaussian fields, allowing mutual enhancement to capture better geometric details. However, these methods require dense views to obtain smooth and complete surfaces due to the lack of scene data priors.
2.3 Generalizable Feed-forward Networks
The aforementioned optimization-basel approaches have demonstrated strong performance in 3D reconstruction tasks, yet they typically require expensive per-scene training. More recently, feed- forward networks have emerged as promising paradigm for generalizable 3D scene reconstruction.
3

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2D Caussion Radiance Fichle
Feature Aggregation Module
Depth Decoder
Overfit to Cameras
Backbone Image Encoder
92 14
Adaption Module
V/
Feature Decoder
Mygiist Theawen
f --ULNO,
Cross-view Feature Refinement
Prender
Surface Aligned Surfels
+
L geo
16 Rl
Rendered Color
Rendered Depth
Rendered Normal
Figure 3: Pipeline. Given an image pair, our method first extracts initial image features using a backbone image encoder. We then predict Gaussian features and depth maps of the scene. Since 2D radiance fields are geometrically inaccurate, we apply Nyquist theorem theorem-guides guided surfel adaptation to each surfel. In the feature aggregation module, we project the adapted surfels across views identify image regions containing relevant geometric information. After refining the image features with these related regions, we regress the Gaussian radiance fields again obtain accurate representations.
These models learn rich priors from large-scale datasets, enabling the reconstruction process to be accomplished through single feed-forward inference. pixeINeRF [47] pioneered a feature-based framework that leverages encoded features to render novel views. Building upon Gaussian primitives the fundamental representation, Splatter Image [22] and GPS-Gaussian [53] have achieved notable progress by predicting Gaussian parameters for object-level reconstruction, pixelSplat [23] further advanced this direction by regressing pixel-aligned Gaussian primitives, effectively incorporating epipolar geometry and depth estimation. MVSplat [24] enhances geometric quality by extracting cost volumes cross-view features, which facilitates fast and accurate depth prediction. However, existing feed-forward methods predominantly target 3D reconstruction tasks such novel view synthesis. Their potential for surface reconstruction where significantly higher precision in Gaussian primitives is remains largely unexplored.
3 Methods
We present SurfelSplat, feedforward framework for predicting 2D Gaussians with accurate geometric reconstruction, principled by the Nyquist sampling theorem (Figure 3). Our approach begins by predicting Gaussian centers and their associated attributes, followed by surfel adaptation module that optimizes Gaussian primitives in the frequency domain. We then introduce feature aggregation module that refines Gaussian representations by cxploiting cross-view feature correlations. These refined features are subsequently utilized to regress surface-aligned 2D Gaussian radiance fields. In Section 3.1, present comprehensive analysis of spatial frequency characteristics and sampling rates for Gaussian surfels. Section 3.2 details our Nyquist-guider surfel adaptation and image feature aggregation modules, along with their corresponding network architectures. Our SurfelSplat is illustrated in Algorithm
3.1 Sensitivity to Sampling Rates for Pixel-Aligned Gaussian Surfels
To overcome the limitations inherent in current pixel-aligned feedforward approaches, we initially examine the spatial sampling frequency within multi-camera systems and establish methodology for computing the spatial frequency of individual 2D Gaussian primitives.

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Algorithm SurfelSplat: Nyquist Srampling-Guiderr Gaussian Feature Aggregation
1: Input: Multi-view images I { j camera parameters P {P.) fa and fy
2: Output: Gaussian parameters {At Ik; Tb, Ck } for each primitive k
3: F + Pimage (I,P)
4: + L'unproj ( deeepts P(), fi + Pater (Pi) i == 1,2, 1. NN
5: for i + to N do
6: dk + prro (Gk, P.)
letu 7: Di (d
8: end for
9: VK & max 1
10: Glow + exp( u2 oR
9k
Gadapted
f- Gk @ g
20
20
FR. & Vproj (F, W,,PCC (F, gadaptedd
12: FFe Frefined (- Prefine (Fkco)
Fx
13: fg +- [8k, Tk: Ōk Cx] aattr (F freefined
3.1.1 Nyquist Sampling Theorem
The Nyquist Sampling Theorem [60] represents cornerstone principle in signal processing. For precise reconstruction a continuous signal from its discrete samples, the following criteria must be met:
The continuous signal must be sampling rate i must be at least twice the signal bandwidth:i 2 2v.
Nyquist Conditions
with bandwidth v, and the spatial
The Nyquist sampling theorem establishes the fundamental relationship between spatial signals and their corresponding sampling frequencies, In this work, we exploit the Nyquist criterion to learn local image features that significantly improve the reconstruction of fine- fineggriied geometric scene details.
3.1.2 Spatial Sampling Rates in Multi-Camee Systems
For a single-camera system, the sampling interval in the image plane is determined by the pixel area. When projected into 3D space, this sampling interval corresponds the area occupied on the surface manifold. For an image with focal lengths fz and f (expressed in pixel units), the sampling interval in screen space is unity. Consider unit area element d.Asy in screen space and its corresponding surface area coverage dAug- The sampling rate in 3D space can then be derived as:
dAwy
i samplinng
(1)
dAAv
The relationship between these two parameter spaces given by dAzy = dd du, where [J]
represents the determinant of Jacobian matrix: J OP (2.8)
8X camera 8x wodld, By evaluating
ax Kommonn 0X d(u,))
the spatial projection relationship that governs the projection process, we obtain the sampling frequency for given spatial primitive:
Laly d²
sampling
J
where d denotes the corresponding depth value. The detailed mathematical derivation is provided in the Appendix B.I. For multi-camera system, the spatial sampling frequency is computed across all cameras. We define the overall sampling frequency for Gaussian primitive pk: as the maximum frequency among all views:
i = max (px) -
where represents the number of cameras and V, denotes the visibility function. the primitive visible to the i-th camera, V, returns 1, otherwise O. Specifically, our choice of using the maximum sampling frequency as the overall frequency (Equatton 3) is motivated by Equation 7 of Mip-Splattin [54]. The key insight of Mip-Splatting is that for accurate reconstruction, need to ensure that each
5

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3D Gaussian primitive satisfies the Nyquist sampling criterion for at least one camera view where visible. This because if primitive can be accurately reconstructed from least one view, have captured its essential geometric information.
3.1.3 Spatial Frequency 2D Gaussian Primitives
Given a spatial surfel, the spatial frequency can be calculated through spatial Fourier transform derivation [G(k) Since the Gaussian function contains over 95% of its energy within #2 standard deviations, when considering a Gaussian with two standard deviations as the surfel size, we can obtain the frequencies along the tangent vector directions t, and t, in the 2D Gaussian surfel via [Gtt)) and (G(t.)), respectively. The detailed derivation can be found in Appendix B.2.
Consequently, along the t. direction, the frequency is w., 2 (and analogously, we 2 for the t direction). Accounting for the 2 periodic normalization of the Fourier transform, the spatial frequency of the Gaussian primitive along each tangent vector can be expressed as:
Vu
(4)
ST
T
For Gaussian primitives that fail to satisfy the Nyquist criterion, the spatial signal cannot be perfectly reconstructed. In such cases, the network tends predict spatial parameters (e.g., covariance) with considerable stochasticity, resulting in surfels that are misaligned with the actual surface geometry.
3.2 Surfel Prediction with Nyquist Theorem-Guided Feature Aggregation
Having established the methodology for calculating sampling rates and spatial primitive frequencies, we proceed to design modules that enable Gaussian primitive predictions to adhere to the Nyquist sampling criterion. Specifically, we perform Gaussian surfel adaptation in the frequency domain and employ cross-view feature aggregation to regress primitives with enhanced geometric detail fidelity.
3.2.1 Nyquist Theorem-Guider Gaussian Surfel Adaptation
We aim to constrain the maximum frequency of G& according to the spatial sampling rates. We propose an adaptive surfel adaptation module operating in the frequency domain. Specifically, we achieve this by passing 2D Gaussian primitives through adaptive Gaussian low-pass filter:
G Gadlapted (x) = (Gs 3 (x), gl (x) =
2
(5)
Here, is a scalar hyperparameter (default value is 1), and each Gaussian filter is designed according to the specific frequency bound i-- We then adaptively modify the transformation matrix the 2D Gaussian primitive Hadapted as the scaling matrix changes:
H adapeed
tu
SU
1+
t
Pk
R.S
R.Sadppe
adapted
P& 1
(6)
where Sqilapped is the adapted scaling matrix, and the transformation matrix H. H.plupied completely characterizes the 2D Gaussian representation, incorporating the effects the low-pass filter.
Theoretical Nyquist Criterion Verification Prior to adaptation, whether all primitives satisfy the Nyquist criterion cannot determined. After adaptation, the spatial frequency can be constrained by setting
DK
DR
SUT
Regardless of how the spatial sampling rates vary, the Nyquist criterion is consistently satisfied.
3.2.2 Nyquist theorem-Guided Gaussian Feature Aggregation
Gaussian Parameters Initialization Given N input images I (L. RNxHxWX3 and cor- responding camera parameters P (P.). P. K, [t first epipolar transformers to

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extract rough image features, and use cost volumes between perspective pairs to extract geometric interrelaioonshis. We then concatenate these features obtain our initial image features:
(T), == D initial (I), == {F,] R RNXx*HXC
(8)
where 4 Pnnitial is the image feature extraction backbone. In conventional feedforward frameworks, cross-view features are fed into two distinct regression networks & Pdepth and & Pattr to predict depth d and Gaussian attributes f; [S:, F2, 5s ca]:
d; deppth (F:) R #W M4 Mumproj (d,, P.) E R HWx3 Dattr E R HWHWXCoa XCater
where Vumproj denotes the unprojection process.
Cross-view Gaussian Feature Aggregation Given the frequency distribution in space, we perform Gaussian surfel adaptations for each primitive @ (x) = (G& @ ( Within our framework, we project 2D Gaussian primitives back to viewpoints extract the set of image features required for refinement. With lower frequency, primitives tend to occupy more pixels related to Gaussian
attributes regression. The image regions R2 associated with Gadapted defined by:
R (x (i,j) E 2² G
Gollppedd (i.j:m) e), R2 = U
(10)
where Gadapted (i. j:mm m) represents the Gaussian value of primitive gadapted splatted onto the m view pixel (i.
We can then identify image features associated with the geometric information of primitive G::
N
F C = (Fi(1.)). E R FE U 1=1
geo
(11)
1
Gaussian Prediction with Refined Feature As features in F are essential for accurate geometry learning of our Gaussian representation Gk. we implement feature refinement architecture with cross-attention transformations to enhance the initial image feature Fs. The query, key, and value composition is specifically designed enable cross-attention interaction for Gaussian primitive Gx PA & Am Q2 K, V):
Q= (Fx),
K hx
V = (v
(12)
We then employ standard feed-forward architecture in the transformer:
k
(FFN) + Fx
(13)
Finally, we predict gcometry-aware pixel-aligned 2D Gaussian primitives with the refined feature per [Frellned Gk C I+} using the same Gaussian head as in Equation 9;
view Fredined
f, [s,, r, o., c,]
T Patt a (Frelined)
E R JHHWWCC
(14)
3.3 Loss Design
Our loss function comprises two parts: rendering loss and geometric loss. The rendering loss Crender LRGB + ALPIPSCLPIPS employs mean square eπrr along with LPIPS loss. For geometric loss, we use depth and normal continuity functions to align surfels to the surface: Latign = E,wi( nf N). Furthermore, we incorporate depth and normal mean square error: Lyeo = Aatign Latign + Xaha + AnCn. Our complete loss function is formulated as:
L Lrender + Ayeo
(15)
4 Experiments
To demonstrate the effectiveness of our method, we conduct experiments on DTU benchmarks [61] and compare the reconstruction accuracy and evaluation efficiency with state-of-the-art methods. Additionally, we provide a detailed analysis of the geometric properties from the perspective of the Nyquist sampling criterion to further validate our approach. the ablation study, we analyze the effectiveness of each component of our method.
7

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UFORecon
NeuSurf
FatesGS
2DGS
Ours
GT images
Figure 4: Qualitative Comparison of Surface Reconstruction with Sparse Views on DTU Benchmarks.
4.1 Experimental Setup
Datasets.
We evaluate our method on the DTU dataset. DTU consists of 128 scenes, with 15 scenes designated for testing. We assess reconstruction accuracy using Destination Source (D2S) Chamfer Distance the evaluation metric. The investigated experimental setting is sparse-view reconstruction with input views. Input images are downsampled to a resolution 256 320 pixels.
Implementation Details. Our implementation is built upon the pixelSplat [23] framework. The training process consists of two stages: first, we train our model on RealEstate [62] for 300,000 iterations, followed by fine-tuning Equation 5 set to All experiments reported this paper were conducted on single NVIDIA RTX A6000 GPU using the Adam optimizer.
the DTU dataset for 2,000 iterations. The hyperparameter in
4.2
Comparisons
Sparse view surface reconstruction. As shown in Table 1, our SurfelSplat exhibits the best mean D2S reconstruction Chamfer distance (CD) performance compared to other state-of-the-an surface reconstruction methods. As illustrated in Figure 4, our method presents superior global geometry and exhibits enhanced surface details. In contrast to UFORecon [8], which only produce coarse global geometry, our method demonstrates improved global surface smoothness. We can also refine local details that would be ignored by methods like 2DGS [18], which delivers coarse and incomplete surfaces. Additional experimental results on the BlendedMVS [63] dataset are presented in Appendix C.4.
Efficiency. We conduct efficiency studies on all tested scenes for the sparse-view reconstruction methods mentioned above. As highlighted in Table 2, we compare the mean inference time DTU benchmarks. All experiments are conducted on the same device.
For neural implicit methods that require per-scene training, convergence requires significantly long training times. Neural explicit training methods greatly reduce training time consumptioon but still require approximately 10 minutes to obtain the Gaussian radiance fields. Most recent implicit methods have successfully compressed the inference time to the 1-minute level. However, our method shows the best efficiency with single feed-forward process that takes only seconds.

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Table The quantitative comparison results of Chamfer Distance (CDL) on DTU dataset. The best results are in bold, the second best are underlined.
ID
24
37
40
55
63
65
69
83
97
105
106
110
114
118
122
Mean
NeuS [3]
4.69
4.72
4.03
4.58
4.71
2.01
4.83
3.94
4.31
2.61
1.63
6,48
1.44
5.69
6,34
NeuSurf [6]
1.96
3.73
2.35
0.82
1.07
2.51
0.87
1.21
1.15
1.13
1.06
1.23
0,41
0.92
1.13
1.44
VolRecon [51]
1.41
3.24
1.76
1.43
1.66
2.25
1.42
1.81
1.54
1.26
1.52
1.53
0.99
1.54
1.75
1.67
UFORccon [8]
1.15
2.42
1.67
2.55
1.90
2.73
1.55
1.49
2.16
0.95
2.22
1.98
1.40
2.11
2.32
1.91
2DGS [18]
2.29
2.63
2.33
1.23
3.69
4.71
2.64
3.94
3.55
3.92
3.95
2.68
2.37
3.15
2.21
3.02
GausSurf [19]
4.22
5.69
4.32
3.98
4.93
2.81
4.67
5.52
4.98
3.61
4.11
5.43
2.98
3.66
4.55
4.36
FatesGS [64]
0.77
2.35
1.43
1.00
1.31
2.06
0.85
1.24
1.06
0.83
1.22
0.58
0.64
0.99
1.32
1.18
Ours
1.23
1.69
1.63
0.90
1.24
1.14
1.12
1.18
1.13
0.79
0.84
1.02
0.98
0.84
1.04
1.12
Table 2: Comparisons with recon-
struction efficiency.
Inpous
Method
Interference Time
NeuS
10
hours
NeuSurf
14
hours
Before
VolRecon
6045
seconds
UFORecon
100+s
seconds
2DGS
1020.5
minutes
GauSurf
240.2
hours
After
FatesGS
14.0.5
minutes
Ours
110.05
second
Figure 5: Visualization of Nyquist Theorem Verification
4.3 Experimental Nyquist Theorem Verifications
In Section 3.1, we analyze detail how to derive the Nyquist sampling rates and spatial frequency of Gaussian primitive. In our theoretical analysis, prove that our surfel adaptation module can adjust the spatial frequency within Nyquist thresholds. To further demonstrate the effectiveness of method, conduct experiments record the rendered depth maps and scale factor distributions from all tested scenes, and calculate the corresponding sampling rates and spatial frequencies. From the Nyquist criterion, we know that Mewrfel
evaluated scenes for Nyquist criterion verification. We
V& and V Ngguiiet Prampisng must satisfy
so we summarize the normalized frequency
PNnguiatt
ratio Meurfel across all Gaussian surfels.
DNuquese
As illustrated in Figure 6, we see that before surfel adaptation, almost all Gaussian primitives exceed the Nyquist threshold. The network cannot obtain sufficient information during the backprop- agation stage and thus is unable to recover precise geometry. After the surfel adaptation module, all Gaussian primitives fall within the Nyquist frequency boundary. As shown in Figure 5, the rendered normal maps before and after the surfel adaptation module show significant differences, which further validates our method.
4.4 Ablation Studies
To demonstrate the necessity and effectiveness of our proposed components, we conducted ex- periments on DTU evaluation scenes measure the impact of individual technical designs on reconstruction performance. The proposed modules are tested for ablation: the surfel adaptation module and the feature aggregation module, As shown in Table in addition the mean Chamfer Distance values, we also evaluate the normal rendering errors. For ground truth normal vectors, we utilize the normal maps provided by Gaussian Surfel [19]. We conduct experiments with 2 input views and render the normal maps the same views. The results demonstrate that removing any of the proposed modules results in different performance degradation, confirming the effectiveness of each proposed component.

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(a) Spatial Frequency Before daptions
(b) Spatial Frequency After A daptions
x
Gauesion Numiless
10000
8000
4000
4020
2000
0
5.0
0
0.5
Vsurfet / Dyyquist
Veurfet / Wyyquist
Nyquist Threshold
Nyquist Threshold
Figure 6: Nyquist Theorem Verification: (a) Before adaptation. most surfels exceed the Nyquist threshold, resulting in inaccurate geometry prediction. (b) After the adaptation module, all Gaussian primitives fall within the Nyquist threshold, ensuring accurate geometric feature learning.
Table 3: Ablation study of surfel adaption and feature aggregation module on DTU benchmarks.
Method
CD4
Normal MSE
w/o Adaption.
2.56
0.135
w/o Aggre.
1.96
0.115
Ours
1.12
0.060
5 Conclusion and Discussion
In this paper, we propose SurfelSplat to predict surface-aligned Gaussian surfel representations from sier images. To regress geometrically precise surfels, we apply Nyquist sampling criterion-guides surfel adaptation and feature aggregation modules to make the spatial frequency conform the frequency constraints. Experimental results demonstrate that our method generates Gaussian radiance fields with more precise geometry and higher efficiency.
Although SurfaceSplat outperforms prior works, it has limitations. Since predict pixel-aligned Gaussians for each view, the radiance fields are sensitive to image resolution. With higher resolutions such 1024 x 1024, over million Gaussian surfels would degrade both rendering and inference speed. Moreover, the unseen parts of the scene limit reconstruction performance, suggesting that generative models such as diffusion models could be introduced into our framework. Consequently. several promising directions remain to be explored.
We also acknowledge that the efficiency of our method benefits from the feed-forward architecture. However, integrating surface reconstruction effectively into feed-forward networks presents significant challenges: the orientations of Gaussian primitives cannot be correctly recovered due to insufficient spatial sampling frequency. To address this, we adopt surfel adaptation modules that enable each Gaussian primitive acquire adequate geometric information, guided by the Nyquist sampling theorem, thereby achieving geometrically fine Gaussian radiance fields within the feed-forward framework.
Acknowledgments
This work was supported in part by the Beijing Natural Science Foundation under Grant 1.252011, and by the National Natural Science Foundation of China under Grant 62206147.
10

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References
[1] Yao Yao, Zixin Luo, Shiwei Li, Tian Fang, and Long Quan. Mysnet: Depth inference for unstructured multi-view stereo. In Proceedings of the European conference computer vision (ECCV), pages 767-783, 2018.
[2] Yikang Ding, Wentao Yuan, Qingtian Zhu, Haotian Zhang, Xiangyue Liu, Yuanjiang Wang, and Xiao Liu. Transmvsnet: Global context-aware multi-view stereo network with transformers. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pages 8585-8594, 2022.
[3] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. arXiv preprint arXiv:2106. 10689, 2021.
[4] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. Advances in Neural Information Processing Systems, 34:4805-4815. 2021.
[5] Zehao Yu, Songyou Peng. Michael Niemeyer, Torsten Sattler, and Andreas Geiger. Monosdf: Exploring monocular geometric cues for neural implicit surface reconstruction, Advances in neural information processing systems, 35:25018 --0032, 2022.
[6] Han Huang, Yulun Wu, Junsheng Zhou, Ge Gao, Ming Gu, and Yu-Shen Liu. Neusurf: On- surface priors for neural surface reconstruction from sparse input views. In Proceedings of the AAAI conference artificial intelligence, volume 38, pages 2312-2320, 2024.
[7] Xiaoxiao Long, Cheng Lin, Peng Wang, Taku Komura, and Wenping Wang. Sparseneus: Fast generalizable neural surface reconstruction from sparse views. In European Conference on Computer Vision, pages 210-227. Springer, 2022.
[8] Youngju Na, Woo Jae Kim, Kyu Beom Han, Suhyeon Ha, and Sung-Eui Yoon. Uforecon: gener- alizable sparse-view surface reconstruction from arbitrary and unfavorable sets. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5094-5104, 2024.
[9] Jiaming Sun, Yiming Xie, Linghao Chen, Xiaowei Zhou, and Hujun Bao. Neuralrecon: Real- time coherent 3d reconstruction from monocular video. In 2021 IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), 2021.
[10] Yiming Wang, Qin Han, Mare Habermann, Kostas Daniilidis, Christian Theobalt, and Lingjie Liu. Neus2: Fast learning of neural implicit surfaces for multi-view reconstruction. 2023 IEEE/CVF International Conference on Computer Vision (ICCV), 2023.
[11] Haoyu Wu, Alexandros Graikos, and Dimitris Samaras. S-volsdf: Sparse multi-view stereo regularization of neural implicit surfaces. 2023 IEFE/CVF International Conference on Computer Vision (ICCV), 2023.
[12] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. In Proceedings of the 35th International Conference on Neural Information Processing Systems, 2021.
[13] Zhaoshuo Li, Thomas Müller, Alex Evans, Russell H. Taylor, Mathias Unberath, Ming- Yu Liu, and Chen-Hsuan Lin. Neuralangelo: High-fidelity neural surface reconstruction. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023.
[14] Luoyuan Xu, Tao Guan, Yuesong Wang, Wenkai Liu, Zhaojie Zeng, Junle Wang, and Wei Yang. C2f2neus: Cascade cost frustum fusion for high fidelity and generalizable neural surface reconstruction. In Proceedings of the IEEF/CVF International Conference Computer Vision, pages 18291-18301, 2023.
[15] Yixun Liang, Hao He, and Yingcong Chen. Retr: Modeling rendering via transformer for generalizable neural surface reconstruction. Advances neural information processing systems, 1462332-622351, 2023.

---

[16] Bernhard Kerbl, Georgios Kopanas. Thomas Leimkühler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph., 12 2023.
[17] Antoine Guédon and Vincent Lepetit. Sugar: Surface-aligned gaussian splatting for efficient
3d mesh reconstruction and high-quality mesh rendering. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 5354-5363, 2024.
[18] Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically accurate radiance fields. In ACM SIGGRAPH 2024 conference papers, pages 1-11, 2024.
[19] Pinxuan Dai, Jiamin Xu, Wenxiang Xie, Xinguo Liu, Huamin Wang, and Weiwei Xu. High- quality surface reconstruction using gaussian surfels. In ACM SIGGRAPH 2024 Conference Papers, pages 1-11, 2024.
[20] Zehao Yu, Torsten Sattler, and Andreas Geiger. Gaussian opacity fields: Efficient adaptive surface reconstruction in unbounded scenes. ACM Transactions Graphics (TOG), 43(6);1-13, 2024.
[21] Mulin Yu, Tao Lu, Linning Xu, Lihan Jiang, Yuanbo Xiangli, and Bo Dai. Gsdf: 3dgs meets sdf for improved rendering and reconstruction. arXiv preprint arXiv:2403. 16964, 2024.
[22] Stanislaw Szymanowicz. Chrisitian Rupprecht, and Andrea Vedaldi. Splatter image: Ultra-fast single-view 3d reconstruction. In Proceedings of the IEEE/CVF conference on computer vision 2024.
and pattern recognition, pages
[23] David Charatan, Sizhe Lester Li, Andrea Tagliasacchi, and Vincent Sitzmann, pixelsplat: 3d gaussian splats from image pairs for scalable generalizable 3d reconstruction. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 19457-19467, 2024.
[24] Yuedong Chen, Haofei Xu, Chuanxia Zheng, Bohan Zhuang, Mare Pollefeys, Andreas Geiger, Tat-Jen Cham, and Jianfei Cai. Mvsplat: Efficient 3d gaussian splatting from sparse multi-view images. In European Conference on Computer Vision, pages 370-386. Springer, 2024.
[25] Christopher Wewer, Kevin Raj, Eddy llg, Bernt Schiele, and Jan Eric Lenssen. latentsplat: Autoencoding variational gaussians for fast generalizable 3d reconstruction. In European Conference Computer Vision, pages 456-473. Springer, 2024.
[26] Botao Ye, Sifei Liu, Haofei Xu, Xueting Li, Mare Pollefeys, Ming-Hsuan Yang, and Songyou Peng. No pose, no problem: Surprisingly simple 3d gaussian splats from sparse unposed images. arXiv preprint arXiv:2410.242077 2024.
[27] Shengjun Zhang, Xin Fei, Fangfu Liu, Haixu Song, and Yueqi Duan. Gaussian graph network: Learning efficient and generalizable gaussian representations from multi view images. Advances in Neural Information Processing Systems, 37:50361-50388 2024.
[28] Shengji Tang, Weicai Ye, Peng Ye, Weihao Lin, Yang Zhou, Tao Chen, and Wanli Ouyang. Hisplat: Hierarchical 3d gaussian splatting for generalizable sparse-view reconstruction. arXiv preprint arXiv:2410.06245, 2024.
[29] Chuanrui Zhang, Yingshuang Zou, Zhuoling Li, Minmin Yi, and Haoqian Wang. Transplat: Generalizable 3d gaussian splatting from sparse multi-view images with transformers. AAAI, 2025.
[30] Ben Mildenhall, Pratul Srinivasan, Matthew Tancik, Jonathan Barron, Ravi Ramamoor- thi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 6561)999-106, 2021.
[31] Jiawei Yang. Marco Pavone, and Yue Wang. Freenerf: Improving few-shot neural rendering with free frequency regularization. 2023 JEFF/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023.
12

---

[32] Anpei Chen, Zexiang Xu, Fuqiang Zhao, Xiaoshuai Zhang, Fanbo Xiang, Jingyi Yu, and Hao Su. Mvsnerf: Fast generalizable radiance field reconstruction from multi-view stereo. In 2021 IEEF/CVF International Conference on Computer Vision (ICCV), 2021.
[33] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In ICCV, pages
2021.
[34] Christian Reiser, Songyou Peng, Yiyi Liao, and Andreas Geiger. Kilonerf: Speeding up neural radiance fields with thousands of tiny mlps. In ICCV, pages 14335-14345, 2021.
[35] Qiangeng Xu, Zexiang Xu, Julien Philip, Sai Bi, Zhixin Shu, Kalyan Sunkavalli, and Ulrich Neumann. Point-nerf: Point-based neural radiance fields. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022.
[36] Stephan J Garbin, Marek Kowalski, Matthew Johnson, Jamie Shotton, and Julien Valentin. Fastnerf: High-fidelity neural rendering at 200fps. In ICCV, pages 14346-14355, 2021.
[37] Tao Hu, Shu Liu, Yilun Chen, Tiancheng Shen, and Jiaya Jia. Efficientnerf efficient neural radiance fields. In CVPR, pages 12902-12911, 2022.
[38] Mijeong Kim, Seonguk Seo, and Bohyung Han. Infonerf: Ray entropy minimization for few-shot neural volume rendering. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022.
[39] Congyue Deng. Chiyu Max Jiang, Charles Qi, Xinchen Yan, Yin Zhou, Leonidas Guibas, and Dragomir Anguelov. Nerdi: Single-view nerf synthesis with language-guided diffusion as general image priors. In 2023 IEEE/CVF Conference on Computer Vision and Puttern Recognition (CVPR), 2023.
[40] Lingjie Liu, Jiatao Gu, Kyaw Zaw Lin, Tat-Seng Chua, and Christian Theobalt. Neural sparse voxel fields. NeurlPS, 13:15651-15663, 2020.
[41] Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger, Occupancy networks: Learning 3d reconstruction in function space. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019.
[42] Albert Pumarola, Enric Corona, Gerard Pons-Moll, and Francesc Moreno-Noguer D-nerf: Neural radiance fields for dynamic scenes. CVPR, pages 10318-10327, 2021.
[43] Linning Xu, Yuanbo Xiangli, Sida Peng, Xingang Pan, Nanxuan Zhao, Christian Theobalt, Bo Dai, and Dahua Lin. Grid-guided neural radiance fields for large urban scenes. In CVPR, pages 2296-8306.25 2023.
[44] Haithem Turki, Deva Ramanan, and Mahadev Satyanarayanan. Mega-nerf: Scalable construc- tion of large-scale nerfs for virtual fly-throughs. In CVPR, pages 12922-12931, 2022.
[45] Matthew Tancik, Vincent Casser, Xinchen Yan, Sabeek Pradhan, Ben Mildenhall, Pratul Srinivasan, Jonathan T Barron, and Henrik Kretzschmar. Block-nerf: Scalable large scene neural view synthesis. In CVPR, pages 8248 2244-8258, 8258, 2022.
[46] Haotong Lin, Sida Peng, Zhen Xu, Yunzhi Yan, Qing Shuai, Hujun Bao, and Xiaowei Zhou. Efficient neural radiance fields for interactive free-viewpoint video. In SIGGRAPII Asia, pages 2022.
[47] Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelnerf: Neural radiance fields from one few images. In CVPR, pages 4578 4587, 2021.
[48] Yuanbo Xiangli, Linning Xu, Xingang Pan, Nanxuan Zhao, Anyi Rao, Christian Theobalt, Bo Dai, and Dahua Lin. Bungeenerf: Progressive neural radiance field for extreme multi-scale scene rendering. In ECCV, pages 106- 122. Springer, 2022.
[49] Chen Gao, Ayush Saraf, Johannes Kopf, and Jia-Bin Huang. Dynamic view synthesis from dynamic monocular video. In ICCV, 2021.
13

---

[50] Zak Murez, Tarrence Van As, James Bartolozzi, Ayan Sinha, Vijay Badrinarayanan, and Andrew Rabinovich. Atlas: End-to-end 3d scene reconstruction from posed images. In European conference on computer vision, pages 414-431 431. Springer, 2020.
[51] Yufan Ren, Fangjinhua Wang, Tong Zhang, Mare Pollefeys, and Sabine Süsstrunk. Volrecon: Volume rendering of signed ray distance functions for generalizable multi-view reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16685-16695, 2023.
[52] Jonathon Luiten, Georgios Kopanas, Bastian Leibe, and Deva Ramanan. Dynamic 3d gaussians: Tracking by persistent dynamic view synthesis. In 2024 International Conference on 3D Vision (3DV), 2024.
[53] Shunyuan Zheng, Boyao Zhou, Ruizhi Shao, Boning Liu, Shengping Zhang, Liqiang Nie, and Yebin Liu. Gps-gaussian: Generalizable pixel-wise 3d gaussian splatting for real-time human novel view synthesis. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024.
[54] Zehao Yu, Anpei Chen, Binbin Huang, Torsten Sattler, and Andreas Geiger. Mip-splatting: Alias-free 3d gaussian splatting. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 19447-19456, 2024.
[55] Johannes L. Schonberger and Jan-Michael Frahm. Structure-from-mottine revisited. In CVPR, pages 4104-4113, 2016.
[56] Zhiwen Fan, Kevin Wang, Kairun Wen, Zehao Zhu, Dejia Xu, and Zhangyang Wang. Light- gaussian: Unbounded 3d gaussian compression with 15x reduction and 200+ fps. arXiv preprint arXiv:2311. 17245, 2023.
[57] Tao Lu, Mulin Yu, Linning Xu, Yuanbo Xiangli, Limin Wang, Dahua Lin, and Bo Dai. Scaffold- gs: Structured 3d gaussians for view-adaptive rendering. arXiv preprint arXiv:2312.00109, 2023.
[58] Kai Katsumata, Due Minh Vo, and Hideki Nakayama. An efficient 3d gaussian representation for monocular/mmlttivieew dynamic scenes. arXiv preprint arXiv:2311.12897 2023.
[59] Hanlin Chen, Chen Li, and Gim Hee Lee. Neusg: Neural implicit surface reconstruction with
3d gaussian splatting guidance. arXiv preprint arXiv:2312.0084 2023.
[60] Harry Nyquist. Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 47(2):117-644, 2009.
[61] Henrik Aanæs, Rasmus Ramsbøl Jensen, George Vogiatzis, Engin Tola, and Anders Bjorholm Dahl. Large-scall data for multiple-vie view stereopsis. International Journal of Computer Vision, 120:153 120:153-168, 2016
[62] Tinghui Zhou, Richard Tucker, John Flynn, Graham Fyffe, and Noah Snavely. Stereo magnifi- cation: Learning view synthesis using multiplane images. arXiv preprint 2018.
09817,
[63] Yao Yao, Zixin Luo, Shiwei Li, Jingyang Zhang, Yufan Ren, Lei Zhou, Tian Fang, and Long Quan. Blendedmvs: A large-scale dataset for generalized multi-view stereo networks. In Proceedings of the IEEE/CVE conference on computer vision and pattern recognition, pages 1790-1799, 2020.
[64] Han Huang, Yulun Wu, Chao Deng, Ge Gao, Ming Gu, and Yu-Shen Liu, Fatesgs: Fast and accurate sperse-view surface reconstruction using gaussian splatting with depth-feature consistency. arXiv preprint arXiv:2501.04622, 2025.
[65] Hanspeter Pfister, Matthias Zwicker, Jeroen Van Baar, and Markus Gross. Surfels: Surface elements as rendering primitives. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pages 335-342, 2000.
14

---

[66] Jianyuan Wang, Minghao Chen, Nikita Karaev, Andrea Vedaldi, Christian Rupprecht, and David Novotny. Vggt: Visual geometry grounded transformer. Proceedings of the Computer Vision and Pattern Recognition Conference, pages 5294-5306, 2025.
[67] Shuzhe Wang, Vincent Leroy, Yohann Cabon, Boris Chidlovskii, and Jerome Revaud. Dust3r: Geometric 3d vision made easy. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20697-20709, 2024.
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Appendix
A Preliminaries
A.1 Surfels: Surface Elements
Surface elements, commonly referred as surfels, constitute point-based representation paradigm for modeling three-dimensional surfaces without explicit connectivity information. Originally intro- duced by Pfister et al. [65], surfels have emerged a powerful alternative traditional mesh-based representations in various surface reconstruction applications.
A surfel is formally defined as tuple:
,,,,
(16)
where:
P E I denotes the 3D position vector of the surfel
n E represents the unit normal vector (S² being the unit sphere in IR,)
specifies the radius (or size) of the surfel
R3 R+ encodes color information (optional)
. a E Rt indicates the confidence or uncertainty measure (optional)
Each surfel can be geometrically interpreted local surface approximation, typically visualized as a oriented disk centered at p with radius r and orientation defined by n. Collectively, set of surfels 81; -. 82, &N forms discrete sampling of the underlying continuous surface M.
A.2 2D Gaussian Splatting
2D Gaussian splatting (2DGS) has demonstrated remarkable efficacy achieving accurate and smooth surface extraction. Each 2D Gaussian primitive represents tangent plane in 3D space characterized by three key parameters: a central position Рæ. two orthogonal tangential vectors t, and t.. and scaling vector (su. s.) that determines the covariance of the 2D Gaussian primitive.
The normal vector of the surfel is computed as tu tu X t.. The rotation matrix defined as R (t,,, to, tw] E RR333, while the scaling vector is arranged into diagonal scaling matrix 33x3 with its last diagonal entry set to zero.
point P in world space on the 2D Gaussian surfel pk is defined in the local tangent space and parameterized by:
P(u, Pk + sytuu + spt,v H(u, u. 1,
(17)
H = tu t,t 0
p
RS Pk
(18)
0
0
where H E 1 denotes the homogeneous transformation matrix. For a point (u, v) on the tangent plane, its Gaussian value defined by: ((u) = =exp 2 2
In this paper, adopt the 2D Gaussian primitive the fundamental surfel representation. The surfel attributes mentioned in Equation 16 can be mapped as follows: the center p corresponds to the central position pæ; the normal vector is defined by t, t,; the radius is represented by the scaling vector s = (su, sw); and the color e and uncertainty a correspond to the spherical harmonic coefficients and opacity, respectively.
A.3 Spatial Fourier Transform
The Spatial Fourier Transform (SFT) provides a framework for analyzing spatial frequency compo- nents in multidimensional signals. For continuous function fxx) where E Rdd represents spatial coordinates in a d'dimensiionll space, the SFT is defined as:
F(f(x)) = F(k) = f(x)e ikx
(19)
23

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where w E IR' denotes the spatial frequency vector and is the imaginary unit. Correspondingly, the inverse SFT is expressed as:
(F(K) = f(x)= = J F(k)e 2kx
(20)
A.4 Basic Assumptions on the surface manifold
In the main body of our paper, the real signal we aim to recover is the 3D surface manifold of the scene. However, we only have access to discrete image observations of this continuous 3D signal. And 2D) Gaussian surfels are our chosen representation to approximate this surface.
Specifically, model the real signal using collection of 2D Gaussian primitives (following the foundation established by 2DGS [18] and Gaussian Surfels [19]). The problem of reconstructing the surface from discrete 2D sampling is thus reformulated reconstructing the Gaussian primitives from the 2D image data.
B
Mathematical Derivations
B.1 Spatial Sampling Rates in Multi-Camera Systems
In this paper, we provide a comprehensive derivation of the spatial sampling rates for a single-camera system. Intuitively, the spatial sampling interval in image space unity, and the width and height of the sampling area times larger than the spatial sampling interval of the image space. Therefore, fa
we can readily derive the sampling frequency as
d
dAgu J.. where Specifically, the spatial sampling rate Psampling determined by Psampling dAu.v denotes the Jacobian matrix of the projection process. The projection process can be characterized by the following Jacobian matrix:
OP image (2,
Ox oameroo
@Xworld Ou, v)
(21)
0X OXaamera
OX
woold
First, point in camera space Xe derived from its corresponding point in world space X through the transformation: X = R.X - t.
Subsequently, project Xe onto the image plane, establishing the relationship between the point on the image plane x and Xe:
fa X + Cxr Ye
(22)
Sa Tc
Cy
The corresponding Jacobian matrix can then be calculated as:
05 Or Oxc =
Le Xx
J2x3 = ax OXc 0x
Ze
R
(23)
Zc
0
fy
Yo
Zo
where Ze represents the depth value D(x, v) the corresponding image coordinates. Analogously, the inverse transformation yields:
+
u-cx aze du
w- cx aZc fx dh
0x 8Xc
R. OXc R.
fo
Jax2 aXc O(u.)) u)
0 Fx O2c
8ZG
+
p --cy a2c
(24)
o(u, v)
dec
Ot
The overall Jacobian matrix is obtained through composition:
1 +
02c
dZg
fz
0
Xo
J
fz
J
Zc
0
fg
20
1
Yo
RRT
bZc Bh
cu azc.
due
+
82c
Cy DZc
de
0
Z
(25)

---

Therefore, at point (x, y) on the image plane, the sampling rate for single-camert system is:
samplligg = |J] fxfy
(26)
d?
where d (x, y)- The overall sampling rate for Gaussian primitive Ps is given by:
Dn max ([V: (
(27)
where represents the number of cameras and V, denotes the visibility function.
B.2
Spatial Frequency of 2D Gaussian Primitive
Given a spatial geometry with an analytic mathematical expression, the spatial frequency can be computed through the Spatial Fourier Transform (SFT).
The three-dimensional Fourier transform of a 2D Gaussian basis element is given by:
- gs
((k)
(u, u) - (P& + sutuu + s,t, P
(28)
Since the Gaussian primitive is confined to the tangent plane, the integral can be simplified to two-dimensional parameter space:
u² + v²
g(k) Su8,6 ik-p
exp
tosstt koo) du du
(29)
Applying the two-dimensional Gaussian integral formula:
S c - dudu 2
2
(30)
where a = sutu k and b = sotu k. Substituting these values yields:
S (t. k)² + (t k)²
g(k) = S ik cxp
(31)
2
The spatial frequency spectrum of a 2D Gaussian surfel is therefore determined by:
(G(K) = 8. exp (- 2
tz + 22 t,,)
(32)
2
We define the projection of the wave vector k onto the tangent vector t, the spatial frequency that direction. Since the Gaussian function contains over 95% of its energy within +22 standard deviations, when considering a Gaussian of two standard deviations the effective surfel size, the spatial frequency the direction of tu can be determined by the following condition:
2 (k- t. ) + s (k t²)² 22 k t.
(33)
Thus, we obtain t, k 2. Consequently, in the direction of tw. the angular frequency is Wi = t,, k 2. (and analogously, w. 2 for the t, direction).
Accounting for the 2x normalization convention of the Fourier transform, the spatial frequency the Gaussian primitive along each tangent vector can be expressed as:
Vu
(34)
ST
C More Implementation Details and Experiments
C.1 Network Design
In the initial feature extraction network & Pimage. we implement a cross-view epipolar transformer and DINO feature backbones to extract preliminary image features F. Subsequently, we employ the depth prediction network &aeph to regress per-view depth maps from the above image features. For the Gaussian feature prediction head &aur we utilize 2D convolutional network. The feature refinement network p is implemented via cross-attention network as described in the original paper.
25

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GT images
Ours
FatesGS
2DGS
UFORecon
Figure 7: Visual comparison of 2-view reconstruction on BlendedMVS dataset.
C.2 Baselines
We compare method with SOTA methods with categories. i. Neural implicit methods: NeuS [3], VolRecon [51], UFORecon [8], NeuSurf [6]. ii. Neural Explicit methods: 2DGS [18], GausSurf [19], FatesGS [64].
C.3 Training Strategy
To progressively extract Gaussian features, we implement two-phase curriculum learning- based training framework. During the initial phase, we leverage diverse scene datasets such as RealEstate104 [62]. Subsequently, in the refinement phase, we fine-tune the model on test sets from datasets such DTU [61] that contain ground truth depth and surface measurements, thereby enhancing the precision of depth estimation and the characterization geometric details.
C.4 Experiments on BlendedMVS
We conduct experiments the BlendedMVS dataset [63] and visualize the qualitative results in Figure 7. Given a pair of images, our method exhibits consistent stable performance across all tested scenes after fine-tuning. In contrast, methods such as UFORecon [8] cannot maintain consistent performance across different scenes and may produce significant geometric collapse in certain scenarios. FatesGS [64] and 2DGS [18] achieve stable performance, but they tend to suffer from insufficient geometric consistency and fail to converge to a complete and smooth surface.
C.5 Experiments on Novel View Synthesis
As shown in Figure 8, we further evaluate our approach through novel view synthesis experiments on the DTU dataset. Given a pair of input images, we synthesize intermediate viewpoints between the provided views and assess the quality of the generated novel views. We compare our method's visual fidelity against pixelSplat [23] and MVSplat [24]. To ensure fair comparison, we fine-tune all baseline methods the DTU training dataset and evaluate their performance on the designated
26

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Input images
pixelSplat
MV Splat
Ours
GT images
Figure 8: Visual comparison novel view synthesis on DTU dataset.
test scenes. As demonstrated in Figure 8, our method achieves superior novel view synthesis quality compared existing approaches. This improvement can be attributed to our method's ability to capture fine-grained geometric details that are not preserved by alternative techniques.
C.6 More Experimental Details
We constrain the Gaussian primitives to be either fully transparent fully opaque, rather than semi- transparent. Consequently, the opacity attributes of 2D) Gaussian Surfels are set to values approaching either 0 facilitate clean surface extraction. The time consumption statisties reported in this paper represent the average inference time. The meshing process requires additional computational resources. On our hardware configuration, the meshing process consumes approximately 30 seconds.
D Broader Impacts
The proposed Gaussian feed-forward network approach for fast surface reconstruction carries several notable societal implications. First, the acceleration of reconstruction processes may democratize access to high-quality 3D modeling capabilities across resource snourcc-constrained environments, potentially reducing technological disparities between well-funded research institutions and those with limited computational infrastructure. We also recognize the environmental impact dimension. While our method reduces computational requirements per reconstruction task, the aggregate environmental effect depends on whether this efficiency leads to reduced energy consumption conversely, to increased utilization through rebound effects. Future work should quantify these energy consumption patterns to better understand the net environmental impact.
E Limitations and Future Works
Camera Pose Configuration. It is challenging for our approach to predict credible depth when input views only have small overlap regions. Our training data is relatively limited. We pretrain
27

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method on Re10K dataset (about 10,000), and subsequently perform fine-tuning on the DTU dataset. Methods such as VGGT [66] and Dust3R [67] demonstrate robust depth prediction capabilities across wide range of camera configurations, benefiting from extensive training data (more than 1,000,000) with explicit depth regularization. 'he generalizability our method is not enough.
Efficiency. The cost-volume techique predicts depth by computing correspondence between pairs of images, which indicates that processing images requires computational operations. Additionally, our methodology directly combines Gaussian groups derived from different viewpoints to construct scene representations, resulting in redundant representations particularly in overlapping regions where similar Gaussian primitives are predicted from multiple source images. Besides, the pixel-aligned Gaussians are sensitive the resolution of input images. For high resolution inputs, e.g. 1024 1024, we generate over I million Gaussians for each view, which will significantly increase the inference and rendering time. The consumption of computational resources and time grows rapidly with more views or higher resolutions.
28


Reviews:
[{"review_id": "AwBShz6EYQ", "reviewer": "Reviewer_Wk3j", "summary": "The authors propose SurfaceSplat, a feed-forward approach for multi-view surface reconstruction using 2D Gaussian surfels that is fast and improves on the state-of-the-art. They observed a problem with conventional feed-forward approaches where the geometric attributes of Gaussian surfels were not accurately recovered. Specifically, the normal vectors often oriented parallel to the image plane instead of aligning with the actual surface, because their spatial frequency exceeded Nyquist sampling rates.\n\nThus, they propose a Nyquist theorem-guided Gaussian surfel adaptation module to constrain the maximum frequency of the Gaussian surfels to fall within Nyquist thresholds. The theoretical analysis for the surfel adaptation module is provided, demonstrating its ability to adjust frequencies, and its effectiveness is then experimentally verified. The results show that these Nyquist constraints significantly improve depth estimation and normal rendering performance in feed-forward networks.", "questions": "**Considering the weaknesses in motivation:**\n- What are the main references for the networks that presented the issues mentioned in line 50?\n- Can the authors provide a concrete example?\n\n**Considering the weaknesses in efficiency:**\n- Why is your method so fast? What improvements in your frequency modeling also improve speed?\n- What is the difference in speed between your approach and pixelSplat (the backbone used)?\n\n**Considering the weaknesses in the results:**\n- If feed-forward networks are the motivation for the authors' solution, why are they not featured in the experiments?\n- Could the proposed solution be used as an add-on to previous methods?", "limitations": "The motivation for the problem should be better presented, as well as the contributions. The authors make claims that are not fully justified throughout the text.\n\nAdditionally, the text needs an overall improvement, starting with the references and the figures.\n\nMore detailed examples of the effect of the frequency constraint and the effects of hyperparameters in the ablation studies would add strength to the paper.\n\nMore datasets and baselines would improve the paper's contributions.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# **Strengths**\n\n**Sparse Views**\n\nThe paper directly tackles the challenging problem of reconstructing accurate surfaces from sparse-view images. The authors extend feed-forward networks to 2DGS and solve the inherent issues caused by these with frequency-based constraints on the Gaussian centers. \n\n**Frequency-Based Constraint for Gaussian Surfels**\n\nThe introduction of Nyquist theorem-guided Gaussian surfel adaptations and feature aggregations is a technically sound approach to address the inherent geometric inaccuracies observed in prior feed-forward Gaussian radiance fields. The ablation study effectively validates the contribution of these modules to improved geometry and overall performance.\n\n**Robustness and Detail**\n\nThe method is shown to deliver \"superior global geometry and exhibits enhanced surface details,\" demonstrating improved global surface smoothness compared to competitors like UFORecon and FateGS.\n\n___\n\n# **Weaknesses**\n\n**Motivation**\n\nThe related work section does not include a subsection on feed-forward networks, and in the introduction (2nd paragraph), it is not clear which papers present the issue and/or motivate the problem.\n\nIf the problem is the 2DGS-like structure in feed-forward networks, which networks are the authors referring to? Is the solution just an add-on to previous models? If so, the claim of a new feed-forward framework is not valid.\n\nAdditionally, Figure 2 does not help to clarify this. In line 46, there is no reference to the networks that exhibit the problem shown in Fig. 2(b), and there is no concrete example of the issue. For instance, an image generated by one of the methods would be a clearer representation of the problem.\n\n**Efficiency**\n\nThe authors do not detail why their method achieves such a significant speed-up in inference. There is a comparison of efficiency against other methods, but how the speed was obtained is not clear. It seems that the speed comes from the fact that the authors use pixelSplat for their work's backbone, but they should not have claimed this as their own contribution. At least, it is not clear; there is nothing in their approach that accelerates inference.\n\nAgain, considering the efficiency of the method, in my opinion, the speed computations are not a fair comparison. The authors are comparing methods that require training from scratch, including the training time, against feed-forward methods that simply render the image. Even in the FateGS paper, the authors make that distinction.\n\n**Results**\n\nThe authors only show results on the DTU dataset in the paper. They do not include results from BlendeMVS in the main paper—at least the quantitative results should have been included—and do not consider other, more complex datasets like Mip-NeRF 360.\n\nSince the main motivation comes from solving a problem for feed-forward networks, the authors' evaluation is very limited. The authors follow the common practice of evaluating sparse views against explicit networks, while only comparing their method with FateGS, which is a feed-forward approach.\n\n**Text and Figures**\n\nReferences should not be grouped. They should be placed near where the paper is cited. Especially in the introduction and related work, the authors cite all the papers in the first sentence, and then the rest of the paragraph has no citations, making it hard to follow.\n\nSome wording and examples are unusual, and there are a few typos. For example:\n* \"Verification\" instead of \"Proof\" when proving the Nyquist Theorem Criterion.\n* \"Our key insight is that the failure to generate surface-aligned primitives is because the spatial frequency...\" - The phrase \"is because\" is redundant.\n* In Table 2: \"Interference\" should be \"Inference.\"\n* The graph in Figure 1 has an inverted y-axis.", "was_revised": true, "final_justification": "After careful consideration of the authors' rebuttal and the significant work they've put in, I am increasing my score to reflect my confidence in the paper. They have provided a thorough justification of their approach and have committed to several key changes for a clearer presentation. Specifically, their clarifications on the efficiency claims and backbones, along with new experimental results that fully validate their claims, have resolved my previous concerns. I am increasing the grade towards acceptance.", "rebuttal": "## 1. Motivation \n### 1.1 Inadequate introduction to Feed-Forward networks\nWhile we listed several feed-forward networks in line 38 of the Introduction, we acknowledge that recent progress in this area deserves more comprehensive coverage. \nFeed-forward models [1,2,3,4] learn powerful priors from large-scale datasets, so that 3D reconstruction and view synthesis can be achieved via a single feed-forward inference. These networks extract image features using an image encoder from multi-view input and regress pixel-aligned Gaussian primitives through depth and feature decoders. In the final version, we will add a dedicated subsection in Related Work to thoroughly introduce current feed-forward networks for generalizable 3D scene reconstruction. Specifically, we will analyze works including pixelSplat [1], MVSplat [2], HiSplat [3], and NoPoSplat [4], and so on. \n\n### 1.2 Unclear presentation of the motivation\nThe issue we address is a common limitation across previous feed-forward networks such as pixelSplat [1], MVSplat [2], HiSplat [3], and NoPoSplat [4], and the example in Figure 2 is from MVSplat [2]. We apologize for the unclear citation placement. We summarize our key motivations as follows:\n\nExisting feed-forward Gaussian networks reconstruct 3D scenes by predicting pixel-aligned Gaussian primitives, focusing on high-quality novel view synthesis. \nWhile these methods can achieve photorealistic renderings, we observe that the predicted Gaussians are parallel to the image plane rather than aligned with the actual surface geometry. As shown in Figure 2(a), we render the normals of MVSplat [2], which predicts similar normal directions for all Gaussians.\nFor further demonstration, we evaluate current feed-forward networks [1,2,3,4] on DTU benchmarks and report the mean Chamfer distance, MSE loss and **the covariance of normal**.\nAs shown in Table A, the high normal loss and small covariance of normal directions further confirm our findings.\n\nHowever, primitive orientation is critical for surface reconstruction. In Figure 2(b), the supervision is not sufficient to recover the attributes of such high-frequency pixel-aligned Gaussians given the sparsity of the observations.\nAs evidenced in Table B, randomizing the predicted orientations of our network causes a 1.09dB PSNR drop while degrading reconstruction geometry on mean CD by 2.91. \nAccording to Nyquist's sampling theorem, we must operate at lower spatial frequencies to correctly predict Gaussian primitive orientations. This restriction in spatial sampling frequency for recovering Gaussian signals has also been noted in Mip-Splatting [5], which primarily addresses aliasing in multi-resolution rendering as a per-scene optimization framework.\n\n\n**Table A Evaluation of feed-forward networks on the DTU dataset**\n| | Normal Loss | Normal Covariance | Mean CD $\\downarrow$ |\n|---|---|---|---|\n| pixelSplat [1]|  0.141 | 0.023 | 10.53 |\n| MVSplat [2]| 0.135 | 0.055 | 4.89 |\n| HiSplat [3]| 0.125 | 0.079 | 4.11 |\n| NoPoSplat [4]| 0.138 | 0.028 | 6.63 |\n| Ours | 0.060 | 0.540 |  1.12|\n\n**Table B Rendering quality on Re10k and surface reconstruction on DTU**\n| | PSNR $\\uparrow$ |SSIM $\\uparrow$| LPIPS $\\downarrow$|Mean CD $\\downarrow$|\n|---|---|---|---|---|\n|Ours| 26.39|0.869 | 0.128|1.12 |\n|Ours with random Gaussian orientations | 25.31| 0.825| 0.223| 4.03|\n\n### 1.3 Is the solution just an add-on to previous models?\n\nWhile previous methods [1,2,3,4] directly regress Gaussians from the parameter prediction head, we introduce a circuit process to restricts the frequency by surfel adaptations and feature aggregation, which both are guided by the Nyquist sampling rates.\nWe follow MVSplat [2] to construct our backbone image encoder, while our following pipeline is different from previous feed-foward networks, where Gaussian Splatting also serves as an intermediate self-parameter refinement mechanism for a circuit paradigm, which is different from a single-pass regression.\n\nThanks for your suggestion. We will clarify our contribution on introducing the feed-forward model for Gaussian surface reconstruction from the perspective of Nyquisty Sampling Theorem.\n\n## 2. Efficiency\n### 2.1 Clarification on efficiency claims\n\nWe acknowledge that the efficiency of our method benefits from the feed-forward architecture. However, integrating surface reconstruction effectively into feed-forward networks presents significant challenges: the orientations of Gaussian primitives cannot be correctly recovered due to insufficient spatial sampling frequency.\nTo address this, we adopt surfel adaptation modules that enable each Gaussian primitive to acquire adequate geometric information, guided by the Nyquist sampling theorem, thereby achieving geometrically fine Gaussian radiance fields within the feed-forward framework.\n\nWe will clarify that our method achieves superior efficiency because we solve the geometric orientation problem that has prevented effective utilization of feed-forward networks' inherent speed advantages. By overcoming this core limitation, we unlock the computational efficiency of feed-forward architectures while maintaining high-quality surface reconstruction.\n\n### 2.2 Fairness of speed comparisons\n\nWe acknowledge that the costly training process requires consideration. For a fairer comparison, we list the training and inference time alongside reconstruction performance on DTU benchmarks in Table C. While some methods with pre-training [1,2,7] provide fast inference time, other methods [6,10] take longer inference time for per-scene optimization.\nOur method shows superiority on reconstruction quality over both two kinds of methods.\nIn practical applications, training can be done offline while users utilize the model online, making inference efficiency more critical than training time.\nFor more comprehensive comparison, we will replace Table 2 by Table C, which takes both training and inference time into consideration.\n\n**Table C Comparison on efficiency and reconstruction quality.**\n| | Training Time| Inference Time | Mean CD $\\downarrow$|\n|---|---|---|---|\n| FatesGS [6]| No need | 10 mins| 1.18 |\n| NeuSurf [10]|No need | 14 hours | 1.44|\n| UFORecon [7]| ~ 10 days | 60 s |1.91 |\n|pixelSplat [1]|~ 2 days | 0.104 s| 10.53|\n|MVSplat [2]|~ 2 days |0.044 s | 4.89|\n|Ours|~ 2 days | 0.997 s | 1.12|\n\n## 3. Results\n### 3.1 Quantitative results on BlendedMVS and Mip-NeRF 360 dataset:\nWe fully acknowledge the importance of cross-dataset evaluation. We have provided qualitative BlendedMVS results in Figure 1 of our supplementary material.\nFollowing your recommendation, we conducted additional quantitative experiments on BlendedMVS following the settings in [8], as shown in Table D. Since Mip-NeRF 360 is designed for novel view synthesis without ground truth 3D meshes, we report novel view synthesis metrics on this dataset in Table E.\n\n\n**Table D Quantitative experiments on BlendedMVS**\n| ScanID| bear | clock | dog | jade | man | sculpture | stone | Mean CD $\\downarrow$|\n|---|---|---|---|---|---|---|---|---|\n|FatesGS [6] |0.26 | 0.61| 0.83| 1.01|0.58 |0.47 | 0.40| 0.59| \n|2DGS [9] | 0.30| 1.06| 0.96| 1.16|0.61 | 0.52| 0.45| 0.73|\n|NeuSurf [10] |0.27 |0.93 | 0.83| 1.04| 0.57|0.50 |0.42 | 0.65  |\n|Ours |0.26 |0.53 | 0.80| 1.01|0.57 |0.46 |0.35 |  0.57 |\n\n**Table E Rendering quality on Mip-NeRF 360 dataset**\n| | PSNR $\\uparrow$ |\n|---|---|\n|FatesGS [6] |  24.89|\n|2DGS [9] | 20.03|\n|NeuSurf [10] | 23.78|\n|Ours | 25.69|\n\n### 3.2 Additional comparisons with feed-forward networks\nThank you for this valuable suggestion! We agree that more feed-forward network comparisons would strengthen our evaluation. Note that FatesGS [6] is not a feed-forward method. Table A above presents comprehensive comparisons with other feed-forward networks.\n\n## 4. Text & Figures\n\n### 4.1 References should not be grouped.\nWe will place references immediately after relevant statements. For example, in line 43, we will add citations directly after \"current feed-forward networks\" for improved clarity. \n\n### 4.2 Some wording and examples are unusual.\nThank you for the corrections! We will refine the vocabulary issues you identified. Regarding the inverted y-axis in Figure 1, this was an intentional design choice to enhance presentation clarity.\n\n## 5. Paper Formatting Concerns\n\n### 5.1 Supplementary material referenced but not present in the document.\nAll referenced supplementary explanations are included in the supplementary materials package. If you encounter any specific formatting concerns, please let us know.\n\n## References:\n> [1] Charatan D, Li S L, Tagliasacchi A, et al. pixelsplat: 3d gaussian splats from image pairs for scalable generalizable 3d reconstruction[C]\\\n> [2] Chen Y, Xu H, Zheng C, et al. Mvsplat: Efficient 3d gaussian splatting from sparse multi-view images[C]\\\n> [3] Tang S, Ye W, Ye P, et al. Hisplat: Hierarchical 3d gaussian splatting for generalizable sparse-view reconstruction[J]\\\n> [4] Ye B, Liu S, Xu H, et al. No pose, no problem: Surprisingly simple 3d gaussian splats from sparse unposed images[J]\\\n> [5] Yu Z, Chen A, Huang B, et al. Mip-splatting: Alias-free 3d gaussian splatting[C]\\\n> [6] Huang H, Wu Y, Deng C, et al. FatesGS: Fast and accurate sparse-view surface reconstruction using gaussian splatting with depth-feature consistency[C]\\\n> [7] Na Y, Kim W J, Han K B, et al. UfoRecon: Generalizable sparse-view surface reconstruction from arbitrary and unfavorable sets[C]\\\n> [8] Zhang Y, Hu Z, Wu H, et al. Towards unbiased volume rendering of neural implicit surfaces with geometry priors[C]\\\n> [9] Huang B, Yu Z, Chen A, et al. 2d gaussian splatting for geometrically accurate radiance fields[C]\\\n> [10] Huang H, Wu Y, Zhou J, et al. NeuSurf: On-surface priors for neural surface reconstruction from sparse input views[C]"}, {"review_id": "s6sr4AwDyV", "reviewer": "Reviewer_pJpP", "summary": "The paper investigates the problem of 3D scene surface reconstruction using Gaussian Splatting techniques. Specifically, the SurfaceSplat method is proposed as a feed-forward framework to generate efficient and generalizable surfel representations from sparse-view images. The main observation of the paper is that the spatial frequency of pixel-aligned Gaussian surfels exceeds the Nyquist sampling rate in existing works, which inspires the authors to modulate the geometric forms of diverse Gaussian surfels in the frequency domain and correlate pixel regions across multiple input views towards better Gaussian geometric feature learning. Experiments on the DTU dataset demonstrate the method's advantage in sparse-view surface reconstruction.", "questions": "Please respond to the points made in the Weaknesses section above.", "limitations": "Yes", "rating": 2, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths\n\nThe paper observes an interesting phenomenon in applying 2D Gaussian Splatting to learned surface reconstruction and provides a theoretical explanation.\n\nThe solution is simple and intuitive.\n\n## Weaknesses\n\nThe presentation of the paper is confusing. Too much important information is deferred to supplementary material, rendering the main text hard to follow. I suggest Section 1.1 from supp. be merged with the main text; otherwise, the paper lacks explanations for many basic concepts and terms.\n\nRegarding the main contribution, i.e., the adaptation based on the Nyquist sampling theorem, I find it flawed in the following two aspects;\ni) The authors are using the overall sampling frequency as the maximum frequency across all views, which lacks theoretical justification. Sampling is inherently additive with more views, and occlusion is not taken into consideration in this approximation.\nii) I did not understand what the \"real signal\" to recover is. Based on Eq.1, I assumed the real signal should be the ground truth surface as a 2D signal in a given view. However, the authors are applying Nyquist sampling theorem with spatial frequency of 2D Gaussian primitives, what is the loginc of this? How is that the \"real signal\" that we are supposed to sample from?\n\nThe experiments are not convincing. For the compared methods, are they re-trained for fairness, i.e., on the same data for two-view reconstruction?", "was_revised": true, "final_justification": "After reading the rebuttals and other reviews, I still find the paper limited by both experimental validation and theoretical justification.\n \nExperiment-wise, the results in the original paper are not convincing, as the proposed method uses more data and a different training setting than previous methods. The new results in the rebuttal mitigated the issue, but it is still unclear if all methods are trainied with RealEstate + DTU datasets.\n\nMore importantly, the theoretical justification is very weak. The paper and the rebuttal did not convince me regarding how Nyquist sampling theorem is applied. The \"real signal\" is the true surface, while the authors use the 2D Gaussian primitives as its proxy, which makes little sense, as there is no guarantee that the Gaussians approximate the surface well. In fact, they usually do not. Furthermore, I did not understand how frequency of Gaussian surfel is related to the maximum frequency of the real signal that Nyquist sampling theorem requires. \n\nFor the above reasons, I keep my recommendation as rejection.", "rebuttal": "### 1. Too much important information is deferred to supplementary material\nWe apologize for placing substantial content in the supplementary materials due to the NeurIPS page limitations. In the final version, we will integrate key derivations from the supplementary materials into the main text.\nHere are the specific improvements we will merge Section 1.1 from the supplementary material into Section 3.1 in the main text, as you suggested. This section contains crucial explanations of:\n* Basic definitions of spatial frequency and sampling rates from line 43 to line 77;\n* The relationship between pixel-aligned primitives and Nyquist constraints from line 79 to line 83.\n\nIf you have any question and recommendation, we welcome discussion during the discussion period.\n\n### 2. The use of maximum sampling frequency:\n\nWe sincerely appreciate the reviewer's insightful critique regarding our Nyquist-based adaptation. \nOur choice of using the maximum sampling frequency $\\hat \\nu_k = max(({\\mathbf V_i(p_k) \\cdot |J_i|})^N_{i=1})$ (Equation 3) is motivated by the design of Mip-Splatting [1] (Equation 7). \n\nThe key insight of Mip-Splatting is that for accurate reconstruction, we need to ensure that each 3D Gaussian primitive satisfies the Nyquist sampling criterion for **at least one camera view** where it is visible. This is because if a primitive can be accurately reconstructed from at least one view, we have captured its essential geometric information. Using max ensures we respect the highest sampling rate available, preventing aliasing in the view with the finest sampling.\nBy selecting the maximum frequency as our sampling frequency, our surfel adaptation module guarantees that the network captures **sufficient** geometric information from at least one input view, which is **sufficient** for recovering Gaussian surfels with fine geometric details.\n\n**Alternative design choices and their limitations:**\nWe considered two alternative additive aggregation strategies: Sum of **sampling frequencies** and **Root mean square of sampling frequencies**.\nThey would overestimate the effective sampling frequency, making it unlikely to satisfy the Nyquist criterion from any single perspective.\nTo validate our design choice, we conducted experiments with different frequency aggregation strategies. As shown in Table A, we evaluate surface reconstruction results on DTU benchmarks, and the result shows that our method can present better reconstruction quality.\n\n**Table A  Experiments on different final frequency settings**\n| | Mean CD $\\downarrow$|\n|---|---|\n|$ \\sum_i^N \\nu_i $ | 1.28|\n|$ \\sqrt{\\sum_i^N \\nu_i^2}  $ | 1.25|\n|$max(\\nu_i)$ | 1.12 |\n\n\nWe will enhance our manuscript by:\n\n(1) Acknowledging Mip-Splatting [1] as the motivation for our maximum frequency selection;\n\n(2) Providing detailed theoretical justification in Section 3.1.2 explaining why the maximum frequency is both sufficient and theoretically sound for accurate surfel prediction.\n\n\n\n### 3. Occlusion is not taken into consideration in this approximation\nWe appreciate the reviewer's attention to occlusion handling. In our current implementation, the visibility function $V_i(p_k)$ in Equation 3 accounts for basic visibility by checking if the Gaussian center falls within the view frustum. Similar to Mip-Splatting [1], we found the current approach sufficient for our experiments.\n\n\n### 4. Clarification on the \"real signal\" to recover\n\n**What is the \"real signal\" we want to recover?**\n\nThe real signal we aim to recover is the 3D surface geometry $\\mathcal M$ of the scene. However, we only have access to discrete 2D image observations of this continuous 3D signal.\nAnd 2D Gaussian surfels are our chosen representation to approximate this surface.\n\nSpecifically, we model the real signal $\\mathcal M$ using a collection of 2D Gaussian primitives (following the foundation established by 2DGS [2] and Gaussian Surfels [3]). The problem of reconstructing the surface from discrete 2D sampling is thus reformulated as reconstructing the Gaussian primitives from the 2D image data.\n\n**Why apply Nyquist theorem to 2D Gaussian primitives?**\n\nTo reconstruct Gaussian primitives accurately, we need to analyze three key components:\n* Spatial frequency of representation elements: Each 2D Gaussian surfel has an inherent spatial frequency $ \\nu$(Equation 4).\n* Spatial sampling frequency from 2D image: Given the sampling density in the image plane, we can compute the sampling frequency $\\hat \\nu$ (Equation 2)\n* Nyquist Sampling theorem constraint: To accurately represent a signal component with frequency $\\nu$, we need sampling rate $\\hat \\nu \\geq 2\\nu$.\n\nBy applying the Nyquist theorem to 2D Gaussian primitives, we can identify which Gaussian elements violate the Nyquist sampling criterion. Our network design then specifically addresses these under-sampled primitives to ensure complete recovery of all Gaussian elements, thereby achieving a high-fidelity approximation of the 3D surface geometry.\n\n### 5. Experimental fairness concerns\nThank you for raising this important point about experimental fairness. Let us clarify our experimental setup and provide additional results to address your concern.\n\n**Experimental setup clarification:** For the methods compared in our experiments:\n\n* Methods that don't require task-specific training: Some approaches like 2DGS [2] and FatesGS [4] are optimization-based methods that directly optimize on the given input views without requiring pre-training. These methods were run directly on the 2-view inputs.\n* Methods with pre-trained models: For learning-based methods (VolRecon [5], UFORecon [6]), we acknowledge that we initially used their publicly available pre-trained models, which were trained on 3-view datasets. We recognize this could introduce bias in the comparison.\n\n**Additional experiments with re-trained models:**\nTo address this fairness concern, we have conducted additional experiments where we re-trained the top-performing learning-based methods specifically for 2-view reconstruction. As shown in Table B, even with task-specific training, our method maintains superior performance while offering higher efficiency. We will include these results and clarify the experimental setup in the revised manuscript to ensure transparency.\n\n**Table B Additional 2-view training on VolRecon and UFORecon.**\n|ID|24|37|40|55|63|65|69|83|97|105|106|110|114|118|122|Mean|\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n|VolRecon [5]|1.32|3.03|1.66|1.42|1.64|2.11|1.40|1.74|1.49|1.25|1.50|1.52|0.95|1.34|1.63| 1.60 |\n|UFORecon [6]|1.12|2.22|1.61|2.53|1.72|2.40|1.46|1.40|2.02|0.93|2.10|1.87|1.34|1.98|1.55| 1.75|\n|Ours|1.23|2.64|1.63|0.90|1.24|1.14|1.12|1.18|1.13|0.79|0.84|0.54|0.51|0.84|1.04|1.12|\n\n## References:\n> [1] Yu Z, Chen A, Huang B, et al. Mip-splatting: Alias-free 3d gaussian splatting[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024: 19447-19456.\\\n> [2] Huang B, Yu Z, Chen A, et al. 2d gaussian splatting for geometrically accurate radiance fields[C]//ACM SIGGRAPH 2024 conference papers. 2024: 1-11.\\\n> [3] Dai P, Xu J, **e W, et al. High-quality surface reconstruction using gaussian surfels[C]//ACM SIGGRAPH 2024 conference papers. 2024: 1-11.\\\n> [4] Huang H, Wu Y, Deng C, et al. FatesGS: Fast and accurate sparse-view surface reconstruction using gaussian splatting with depth-feature consistency[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2025, 39(4): 3644-3652.\\\n> [5] Ren Y, Wang F, Zhang T, et al. Volrecon: Volume rendering of signed ray distance functions for generalizable multi-view reconstruction[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 16685-16695.\\\n> [6] Na Y, Kim W J, Han K B, et al. Uforecon: Generalizable sparse-view surface reconstruction from arbitrary and unfavorable sets[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024: 5094-5104."}, {"review_id": "e8Pdw0HZCa", "reviewer": "Reviewer_D7r6", "summary": "This paper proposes a generalizable 3DGS method for sparse view surface reconstruction. It focuses on dealing with the low frequency issue when projecting Gaussian primitives to input view grids due to their relatively small scales. After the commonly used generalizable 3DGS prediction, they compute the maximum spatial frequency of each gaussian, and use a low-pass filter to adjust their scales. After this, they aggregate the per-view features by projecting gaussians to each view, and re-predict the gaussian parameters.", "questions": "Please see the questions in the weaknesses above.", "limitations": "See the weaknesses.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Significance: The proposed method focuses on a novel viewpoint of gaussian surface reconstruction based on Nyquist Conditions. \n2. Results: The experiment results evaluate the state-of-the-art performance of the proposed method.\n\nWeaknesses:\n1. Clarity: I find some parts of this paper to be unclear:\n\n (i) The gaussian adaptation to increase their scales are performed before the feature aggregation step, however the final gaussian parameters are re-predicted by the same output head as the initial head. Then how to make sure that the final gaussians $\\hat{f}_i$ can satisfy the Nyquist Conditions? Or the Nyquist Conditions is just to improve the feature aggregation step? \n\n (ii) Is there any constraints on the initial gaussian attributes $f_i$? Are the depth and normal losses also conducted on the initial gaussian attributes? If not then the Figure 5 comparison is unfair.", "was_revised": false, "final_justification": "", "rebuttal": "### 1. How to make sure that the final gaussians $\\hat f_i$ can satisfy the Nyquist Conditions?\nOur method involves three stages of Gaussian primitives: initial Gaussians $f_i$, adapted Gaussians $f_i^{adapted}$ and the final Gaussians $\\hat f_i$. Only the adapted Gaussians $f_i^{adapted}$ need to satisfy the Nyquist theorem. \nThe surfel adaptation module's primary purpose is to gather sufficient information for accurate geometric attribute prediction. Its key function is obtaining image regions $\\mathcal R_i$ associated with Gaussian surfel $f_i$ regression (descibed in line 176). Once the adapted Gaussian attributes satisfy Nyquist conditions, we can recover the real signal $\\hat f_i$ from features in image regions $\\mathcal R_i$.\n\nConsequently, final Gaussians $\\hat f_i$ need not satisfy Nyquist conditions. Our goal is achieving surfels with correct spatial geometric orientation, which the feature aggregation module guarantees. Forcing final Gaussians to satisfy Nyquist conditions would expand surfels approximately 10-fold, compromising fine geometric detail representation.\n\nTo demonstrate this, we evaluated reconstruction on DTU benchmarks with an additional surfel adaptation module after $\\hat f_i$. As shown in Table A, the performance of our method decreased significantly. \n\n**Table A Evaluation on additional surfel adaption module**\n| | Mean CD |\n|---|---|\n| Ours | 1.12 |\n| Ours plus another surfel adaption module | 4.32 | \n\n### 2. Is there any constraints on the initial gaussian attributes $f_i$? Are the depth and normal losses also conducted on the initial gaussian attributes?\n\nFor the initial Gaussian attributes $ f_i $, we applied identical geometric constraints (depth and normal losses) during training. Despite these constraints, normal maps were incorrectly recovered. This demonstrates that satisfying the sampling theorem is essential for learning correct geometric distributions, regardless of geometric constraints.\n\nFigure 5 presents initial Gaussian attributes without geometric constraints for more striking comparison. For fairness, we conducted additional DTU experiments with consistent settings:\n\n**Table B Reconstruction results with Geometric losses**\n| |Normal Loss | Normal Covariance| Mean CD |\n|---|---| ---|---|\n| MVSplat | 0.148 | 0.023|8.33|\n| MVSplat w/ $Loss_{geo}$ | 0.140 |0.025 | 4.89|\n| Ours | 0.060 |0.540 | 1.12|\n\nIn the revised manuscript, we will add this in Section 4.2 for fair comparisons. Thank you for your constructive feedback, which has significantly improved our paper!"}, {"review_id": "uWUZ1AxTrQ", "reviewer": "Reviewer_v9Gt", "summary": "This paper presents a feed-forward (generalizable) framework for sparse-view surface reconstruction using Gaussian Splatting. The primary objective is to address the limitations of conventional feed-forward networks, which often misalign the covariance of Gaussians by orienting them parallel to the image plane. The authors analyze this issue from a signal processing perspective and attribute it to a violation of the Nyquist sampling theorem: the high spatial frequencies of pixel-aligned primitives exceed the system’s sampling rate, resulting in aliasing artifacts. To address this, the paper introduces two key contributions: (1) a Surfel Adaptation Module (Sec. 3.2.1), and (2) a Feature Aggregation Module (Sec. 3.2.2), both designed with guidance from the Nyquist theorem. Experiments on the standard DTU benchmark demonstrate that the proposed method achieves state-of-the-art performance in terms of Chamfer distance and computational efficiency.", "questions": "Based on the weaknesses discussed above, I would like to see the following points addressed during the rebuttal period:\n\n1. Baseline Comparison: A more thorough discussion of the presented baselines is necessary, particularly regarding FateGS, which demonstrated state-of-the-art performance prior to this work. In addition, the paper appears to lack comparisons with other relevant baselines. For instance, recent feed-forward multi-view stereo methods such as Dust3R [1] or diffusion-based generalizable surface reconstruction MeshLRM [2], could provide meaningful points of reference and should be considered or at least discussed.\n\n2. Justification of curriculum learning on Re10K: While the ablation study clearly demonstrates the effectiveness of the proposed modules, the role of pretraining on the Re10K dataset remains unclear. How crucial is this pretraining for achieving strong performance? Since some baselines may simply rely on more conventional backbones without such pretraining, a discussion or additional experiment aligned with those settings would strengthen the work.\n\n3. Sparse View Sampling Strategy: More details are needed on how sparse views are sampled for both training and testing. In feed-forward approaches, generalization should be evaluated not only over scene distributions but also over diverse camera configurations. Clarifying this aspect would help readers understand the difficulty of the task ideally in the main paper, or at least in the appendix.\n\n---\n\nThe points raised above are my primary concerns. Depending on how they are addressed during the rebuttal and reviewer discussion period, I may keep (accept) or lower (borderline accept to borderline reject) my final rating accordingly.", "limitations": "yes.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "### Strengths \n\n1.  The primary strength of this work lies in its novel analysis of why feed-forward networks struggle with sparse-view surface reconstruction using explicit primitives like Gaussian surfels. The authors identify the core issue as a fundamental violation of the Nyquist sampling theorem which could be occurred in pixel-aligned feed-forward setting. Framing the geometric inaccuracy—specifically, the tendency for surfels to overfit to the image plane—as an aliasing problem caused by the spatial frequency of primitives exceeding the sampling rate is a clever and original contribution in this field.\n\n2. The paper's claims are backed by a solid theoretical framework; They provide a clear and valid mathematical formulation to quantify both the spatial sampling rate of a pixel in the multi-camera system and the spatial frequency of Gaussian surfels.\n\n3. The proposed method is well-constructed, with each component logically addressing the problems identified in the initial analysis. The two main modules, the Nyquist-guided surfel adaptation and the cross-view feature aggregation, work in tandem to form a very coherent solution. \n\n4. The paper demonstrates significant and meaningful improvements over a strong set of baselines. The experimental evaluation is conducted on the standard and challenging DTU benchmark. The proposed approach not only achieves state-of-the-art results in reconstruction accuracy, but it also achieves this with efficiency—offering inference in one second.\n\n### Weaknesses\nThis is a solid paper with well-presented technical details, though several weaknesses remain that, if addressed, could further improve the work:\n\n1. The paper could be strengthened with a more in-depth methodological comparison to key baselines. For instance, FatesGS is the top-performing baseline in Table 1, yet the paper lacks a discussion on the fundamental differences between it and the proposed method. \n\n2. The necessity of the two-stage training strategy (pre-training on RealEstate10K before fine-tuning on DTU) is not fully justified. It is unclear how much of the performance gain is attributable to this extensive pre-training versus the novel modules themselves. A simple ablation study training directly on DTU from a standard backbones (e.g., DINO) would help isolate and more clearly validate the impact of the proposed components.\n\n3. A more detailed explanation of how sparse views are sampled would be helpful. While the supplementary materials provide information on which input pairs are used during inference, this detail is not included in the main paper. Readers may be interested in how the input views are configured to better understand the difficulty of performing surface reconstruction from such limited observations in a feed-forward manner.", "was_revised": true, "final_justification": "The initial recommendation of \"accept\" stands. The authors' rebuttal was clear and addressed all my questions with followup experimental validation. The paper's main contributions are its investigation of a key issue in generalizable surface reconstruction using 3DGS, and its state-of-the-art performance on sparse-view surface reconstruction. I recommend accepting the paper.", "rebuttal": "## 1. Baseline Comparisons\n\n### 1.1 More thorough discussion of baselines, particularly FatesGS\nThank you for the suggestion! FatesGS [1] deserves additional discussion as the second-best performer in reconstruction evaluations. FatesGS utilizes monocular depth ranking information to supervise depth distribution consistency within image patches, achieving fast runtime performance (~10 minutes). However, as an optimization-based method, FatesGS requires per-scene training and demonstrates relatively poor generalizability compared to our approach (shown in Supplementary Figure 1).\nOur method achieves high-fidelity Gaussian radiance fields through a highly efficient and generalizable feed-forward network. Regarding mesh quality (Figure 4), FatesGS produces complete but noisy surfaces, while our method extracts smoother results.\n\n### 1.2 More comparisons with other relevant baselines\nWe have evaluated against additional feed-forward networks and the mentioned works. Table A presents DTU benchmark results under consistent evaluation protocols, confirming our state-of-the-art performance among feed-forward approaches:  \n\n**Table A Comparisons with feed-forward networks on DTU benchmarks**\n| | mean CD |\n|---|---|\n|pixelSplat [2] |10.53 |\n|MVSplat [3]|4.89 |\n|HiSplat [4]| 4.63|\n|MeshLRM [5]| 8.12|\n|Dust3R [6]| 3.55|\n|Ours |1.12 |\n> MeshLRM [5] remains closed-source, but we evaluated their HuggingFace demo.\n\n## 2. Justification of curriculum learning on Re10K\n\n### 2.1 Ablation study of pre-training stage on Re10k\nThank you for this insightful comment. We chose Re10K pre-training to align with standard practices among Gaussian feed-forward networks. Now we evaluate performance without this costly pre-training stage. Table B shows that training solely on DTU achieves comparable DTU benchmark performance. However, Table C demonstrates that larger-scale pre-training significantly improves generalizability on BlendedMVS, following experimental settings from [7].\n\n**Table B Ablation study on pre-training with Re10k in DTU benchmarks**\n| | Mean CD|\n|---|---|\n|Ours |1.12 |\n|Ours w/o Re10k training | 1.14|\n\n**Table C Ablation study on pre-training with Re10k in BlendedMVS dataset**\n| | Mean CD|\n|---|---|\n|Ours | 0.57 |\n|Ours w/o Re10k pre-training |0.64 |\n\n### 2.2 Some baselines may simply rely on more conventional backbones without such pretraining\nThank you for this innovative suggestion! We experimented with adding DINO features to our backbone by concatenating DINO features extracted from input image pairs with our initial features in Equation 8, keeping the remaining network architecture unchanged. Results are shown in Table D, which demonstrate that DINO feature enhance the generalizability of our framework.\n\n**Table D Evaluation of our network plus DINO feature on BlendedMVS dataset** \n| | Mean CD|\n|---|---|\n|Ours + DINO | 0.56|\n|Ours +DINO w/o Re10k pre-training |0.60 |\n\n## 3. Sparse View Sampling Strategy\n\n### 3.1 Details on how sparse views are sampled\nOur main paper adopts FatesGS's **\"large-overlap\" setting** – the **standard sparse-view configuration** in this field. This provides 3 input views per scene; we randomly select 2 neighbor views for evaluation.  \n\n> Configuration note:  \n> - \"Little-overlap\": Originates from PixelNeRF [8]  \n> - \"Large-overlap\": Defined in SparseNeuS [9]\n\n\n### 3.2 Evalation on diverse camera configurations\nWe conducted detailed experiments on both FatesGS camera configurations (large-overlap and little-overlap). Table E shows our method achieves superior reconstruction quality in both settings.\n\n**Table E Evaluation results on DTU benchmarks with 2 major camera configurations**\n| Mean CD $\\downarrow$| large-overlap | little-overlap |\n|---|---|---|\n|FatesGS [1]| 1.18|1.57 |\n|2DGS [10]| 3.02| 3.52|\n|NeuSurf [11]| 1.44| 1.90|\n|Ours | 1.12| 1.55|\n\n## References:\n> [1] Huang H, Wu Y, Deng C, et al. FatesGS: Fast and accurate sparse-view surface reconstruction using gaussian splatting with depth-feature consistency[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2025, 39(4): 3644-3652.\\\n> [2] Charatan D, Li S L, Tagliasacchi A, et al. pixelsplat: 3d gaussian splats from image pairs for scalable generalizable 3d reconstruction[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024: 19457-19467.\\\n> [3] Chen Y, Xu H, Zheng C, et al. Mvsplat: Efficient 3d gaussian splatting from sparse multi-view images[C]//European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2024: 370-386.\\\n> [4] Tang S, Ye W, Ye P, et al. Hisplat: Hierarchical 3d gaussian splatting for generalizable sparse-view reconstruction[J]. arxiv preprint arxiv:2410.06245, 2024.\\\n> [5] Wei X, Zhang K, Bi S, et al. Meshlrm: Large reconstruction model for high-quality meshes[J]. arxiv preprint arxiv:2404.12385, 2024.\\\n> [6] Wang S, Leroy V, Cabon Y, et al. Dust3r: Geometric 3d vision made easy[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024: 20697-20709.\\\n> [7] Zhang Y, Hu Z, Wu H, et al. Towards unbiased volume rendering of neural implicit surfaces with geometry priors[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 4359-4368.\\\n> [8] Yu A, Ye V, Tancik M, et al. pixelnerf: Neural radiance fields from one or few images[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021: 4578-4587.\\\n> [9] Long X, Lin C, Wang P, et al. Sparseneus: Fast generalizable neural surface reconstruction from sparse views[C]//European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022: 210-227.\\\n> [10] Huang B, Yu Z, Chen A, et al. 2d gaussian splatting for geometrically accurate radiance fields[C]//ACM SIGGRAPH 2024 conference papers. 2024: 1-11.\\\n> [11] Huang H, Wu Y, Zhou J, et al. NeuSurf: On-surface priors for neural surface reconstruction from sparse input views[C]//Proceedings of the AAAI conference on artificial intelligence. 2024, 38(3): 2312-2320."}]

Author rebuttal:

Meta-review: This paper introduces SurfaceSplat, a feed-forward approach for surface reconstruction from images using 2D Gaussian surfels. The key insight is that 2D surfels are often incorrectly oriented parallel to the image plane due to a violation of the Nyquist sampling theorem: the spatial frequencies of pixel-aligned surfels are too high for the given sampling rate. The paper proposes a practical solution that allows for both fast inference times and superior geometry compared to state-of-the-art feed-forward methods.
During the review process, reviewers were satisfied with the novel Nyquist theorem-guided Gaussian surfel adaptations and the method's fast and accurate results.
However, the reviewers also raised several significant concerns, including:
1. A missing discussion of related feed-forward methods.
2. An unclear efficiency-accuracy trade-off when compared to other optimization-based and feed-forward models.
3. A lack of experiments on datasets other than DTU.
4. An unclear presentation of the Nyquist sampling issue and its theoretical justification.
5. Missing implementation details.

During the rebuttal and discussion phase, the authors thoroughly addressed these concerns, convincing three out of four reviewers to be in favor of accepting the paper. Since the paper provides an insightful, Nyquist Theorem-inspired analysis of a key issue with feed-forward 2D Gaussian surfels and presents an effective solution that significantly improves upon previous work, I recommend this paper for acceptance. I expect the authors to address all concerns raised by the reviewers in the final version by incorporating the answers and results provided during the review process.
Decision: Accept (poster)