1. Baseline Comparisons

1.1 More thorough discussion of baselines, particularly FatesGS

Thank 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). Our 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.

1.2 More comparisons with other relevant baselines

We 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:

Table A Comparisons with feed-forward networks on DTU benchmarks

MeshLRM [5] remains closed-source, but we evaluated their HuggingFace demo.

2. Justification of curriculum learning on Re10K

2.1 Ablation study of pre-training stage on Re10k

Thank 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].

Table B Ablation study on pre-training with Re10k in DTU benchmarks

Table C Ablation study on pre-training with Re10k in BlendedMVS dataset

2.2 Some baselines may simply rely on more conventional backbones without such pretraining

Thank 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.

Table D Evaluation of our network plus DINO feature on BlendedMVS dataset

3. Sparse View Sampling Strategy

3.1 Details on how sparse views are sampled

Our 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.

Configuration note:

• "Little-overlap": Originates from PixelNeRF [8]
• "Large-overlap": Defined in SparseNeuS [9]

3.2 Evalation on diverse camera configurations

We 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.

Table E Evaluation results on DTU benchmarks with 2 major camera configurations

References:

[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.
[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.
[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.
[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.
[5] Wei X, Zhang K, Bi S, et al. Meshlrm: Large reconstruction model for high-quality meshes[J]. arxiv preprint arxiv:2404.12385, 2024.
[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.
[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.
[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.
[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.
[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.
[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.

1. How to make sure that the final gaussians $\hat f_i$ can satisfy the Nyquist Conditions?

Our 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. The 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 $\mathcal R_i$.

Consequently, 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.

To 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.

Table A Evaluation on additional surfel adaption module

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?

For 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.

Figure 5 presents initial Gaussian attributes without geometric constraints for more striking comparison. For fairness, we conducted additional DTU experiments with consistent settings:

Table B Reconstruction results with Geometric losses

In 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!

1. Too much important information is deferred to supplementary material

We 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. Here 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:

• Basic definitions of spatial frequency and sampling rates from line 43 to line 77;
• The relationship between pixel-aligned primitives and Nyquist constraints from line 79 to line 83.

If you have any question and recommendation, we welcome discussion during the discussion period.

2. The use of maximum sampling frequency:

We sincerely appreciate the reviewer's insightful critique regarding our Nyquist-based adaptation. Our 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).

The 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. By 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.

Alternative design choices and their limitations: We considered two alternative additive aggregation strategies: Sum of sampling frequencies and Root mean square of sampling frequencies. They would overestimate the effective sampling frequency, making it unlikely to satisfy the Nyquist criterion from any single perspective. To 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.

Table A Experiments on different final frequency settings

We will enhance our manuscript by:

(1) Acknowledging Mip-Splatting [1] as the motivation for our maximum frequency selection;

(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.

3. Occlusion is not taken into consideration in this approximation

We 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.

4. Clarification on the "real signal" to recover

What is the "real signal" we want to recover?

The 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. And 2D Gaussian surfels are our chosen representation to approximate this surface.

Specifically, 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.

Why apply Nyquist theorem to 2D Gaussian primitives?

To reconstruct Gaussian primitives accurately, we need to analyze three key components:

• Spatial frequency of representation elements: Each 2D Gaussian surfel has an inherent spatial frequency $\nu$(Equation 4).
• Spatial sampling frequency from 2D image: Given the sampling density in the image plane, we can compute the sampling frequency $\hat \nu$ (Equation 2)
• Nyquist Sampling theorem constraint: To accurately represent a signal component with frequency $\nu$, we need sampling rate $\hat \nu \geq 2\nu$.

By 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.

5. Experimental fairness concerns

Thank you for raising this important point about experimental fairness. Let us clarify our experimental setup and provide additional results to address your concern.

Experimental setup clarification: For the methods compared in our experiments:

• 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.
• 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.

Additional experiments with re-trained models: To 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.

Table B Additional 2-view training on VolRecon and UFORecon.

References:

[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.
[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.
[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.
[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.
[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.
[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.

1. Motivation

1.1 Inadequate introduction to Feed-Forward networks

While we listed several feed-forward networks in line 38 of the Introduction, we acknowledge that recent progress in this area deserves more comprehensive coverage. Feed-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.

1.2 Unclear presentation of the motivation

The 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:

Existing feed-forward Gaussian networks reconstruct 3D scenes by predicting pixel-aligned Gaussian primitives, focusing on high-quality novel view synthesis. While 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. For 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. As shown in Table A, the high normal loss and small covariance of normal directions further confirm our findings.

However, 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. As 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. According 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.

Table A Evaluation of feed-forward networks on the DTU dataset

Table B Rendering quality on Re10k and surface reconstruction on DTU

1.3 Is the solution just an add-on to previous models?

While 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. We 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.

Thanks 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.

2. Efficiency

2.1 Clarification on efficiency claims

We 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 to acquire adequate geometric information, guided by the Nyquist sampling theorem, thereby achieving geometrically fine Gaussian radiance fields within the feed-forward framework.

We 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.

2.2 Fairness of speed comparisons

We 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. Our method shows superiority on reconstruction quality over both two kinds of methods. In practical applications, training can be done offline while users utilize the model online, making inference efficiency more critical than training time. For more comprehensive comparison, we will replace Table 2 by Table C, which takes both training and inference time into consideration.

Table C Comparison on efficiency and reconstruction quality.

3. Results

3.1 Quantitative results on BlendedMVS and Mip-NeRF 360 dataset:

We fully acknowledge the importance of cross-dataset evaluation. We have provided qualitative BlendedMVS results in Figure 1 of our supplementary material. Following 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.

Table D Quantitative experiments on BlendedMVS

Table E Rendering quality on Mip-NeRF 360 dataset

3.2 Additional comparisons with feed-forward networks

Thank 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.

4. Text & Figures

4.1 References should not be grouped.

We 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.

4.2 Some wording and examples are unusual.

Thank 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.

5. Paper Formatting Concerns

5.1 Supplementary material referenced but not present in the document.

All referenced supplementary explanations are included in the supplementary materials package. If you encounter any specific formatting concerns, please let us know.

References:

[1] Charatan D, Li S L, Tagliasacchi A, et al. pixelsplat: 3d gaussian splats from image pairs for scalable generalizable 3d reconstruction[C]
[2] Chen Y, Xu H, Zheng C, et al. Mvsplat: Efficient 3d gaussian splatting from sparse multi-view images[C]
[3] Tang S, Ye W, Ye P, et al. Hisplat: Hierarchical 3d gaussian splatting for generalizable sparse-view reconstruction[J]
[4] Ye B, Liu S, Xu H, et al. No pose, no problem: Surprisingly simple 3d gaussian splats from sparse unposed images[J]
[5] Yu Z, Chen A, Huang B, et al. Mip-splatting: Alias-free 3d gaussian splatting[C]
[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]
[7] Na Y, Kim W J, Han K B, et al. UfoRecon: Generalizable sparse-view surface reconstruction from arbitrary and unfavorable sets[C]
[8] Zhang Y, Hu Z, Wu H, et al. Towards unbiased volume rendering of neural implicit surfaces with geometry priors[C]
[9] Huang B, Yu Z, Chen A, et al. 2d gaussian splatting for geometrically accurate radiance fields[C]
[10] Huang H, Wu Y, Zhou J, et al. NeuSurf: On-surface priors for neural surface reconstruction from sparse input views[C]