Signal Structure-Aware Gaussian Splatting for Large-Scale Scene Reconstruction
Authors: Weiyi Xue
Fan Lu
Chi Zhang
Tianhang Wang
Sanqing Qu
Zehan Zheng
Boyuan Zheng
Junqiao Zhao
Guang Chen
Venue: ICLR 2026 Poster (2026)
Keywords: 3D Gaussian Splatting
large-scale scene reconstruction
signal structure recovery
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: 3D Gaussian Splatting has demonstrated remarkable potential in novel view synthesis. In contrast to small-scale scenes, large-scale scenes inevitably contain sparsely observed regions with excessively sparse initial points. In this case, supervising Gaussians initialized from low-frequency sparse points with high-frequency images often induces uncontrolled densification and redundant primitives, degrading both efficiency and quality. Intuitively, this issue can be mitigated with scheduling strategies, which can be categorized into two paradigms: modulating target signal frequency via densification and modulating sampling frequency via image resolution. However, previous scheduling strategies are primarily hardcoded, failing to perceive the convergence behavior of the scene frequency. To address this, we reframe scene reconstruction problem from the perspective of signal structure recovery, and propose SIG, a novel scheduler that Synchronizes Image supervision with Gaussian frequencies. Specifically, we derive the average sampling frequency and bandwidth of 3D representations, and then regulate the training image resolution and the Gaussian densification process based on scene frequency convergence. Furthermore, we introduce Sphere-Constrained Gaussians, which leverage the spatial prior of initialized point clouds to control Gaussian optimization. Our framework enables frequency-consistent, geometry-aware, and floater-free training, achieving state-of-the-art performance with a substantial margin in both efficiency and rendering quality in large-scale scenes.

Published as a conference paper ICLR 2026
SIGNAL STRUCTURE-AWARE GAUSSIAN SPLATTING FOR LARGE-SCALE SCENE RECONSTRUCTION
Weiyi Xue Fan Lu Chi Zhang". Tianhang Wang'.
Sanqing Qu' Zehan Zheng". Boyuan Zheng', Junniia Zhao', Guang Chen 1,2,3
1 Tongji University, 2 Shanghai Innovation Institute, 3 Shanghai Westwell Technology Co., Ltd
4 Beijing University of Technology, 5 Johns Hopkins University
Corresponding author
ABSTRACT
3D Gaussian Splatting has demonstrated remarkable potential in novel view synthesis. In contrast to small-scale scenes, large-scale scenes inevitably contain sparsely observed re- gions with excessively sparse initial points. In this case, supervising Gaussians initialized from low-frequency sparse points with high-frequency images often induces uncontrolled densification and redundant primitives, degrading both efficiency and quality. Intuitively, this issue can be mitigated with scheduling strategies, which can be categorized into two paradigms: modulating target signal frequency via densification and modulating sampling frequency via image resolution. However, previous scheduling strategies are primarily hardcoded, failing to perceive the convergence behavior of the scene frequency. To address this, we reframe scene reconstruction problem from the perspective of signal structure re- covery, and propose SIG, novel scheduler that Synchronizes Image supervision with Gaussian frequencies. Specifically, we derive the average sampling frequency and band- width of 3D representations, and then regulate the training image resolution and the Gaus- sian densification process based scene frequency convergence. Furthermore, we intro- duce Ophere-Constraane
Gaussians, which leverage the spatial prior of initialized point clouds to control Gaussian optimization. Our framework enables coometry-awart and floater-free training, achieving state-of the-art performance with a substantial margin in both efficiency and rendering quality in large-scale scenes.
1 INTRODUCTION
High-fidelity and real-time Novel View Synthesis (NVS) in large scale scenes is a fundamental require- ment for wide range of applications, including UAV navigation, autonomous driving. Recently, Neural Radiance Fields (NeRFs) (Mildenhall et al., 2021) have made significant progress in NVS, yet suffer from prohibitive optimization and rendering costs. In contrast, 3DGS (Kerbl et al., 2023) achieves comparable fidelity with fast rendering capability by modeling scenes with Gaussian primitives. Nonetheless, even with block-wise parallelism (Liu et al., 2024), training remains inefficient in city-scale scenes. The massive in- puts and numerous Gaussians, alongside the regions lacking initial point clouds and sparsely observed, lead redundancy and floaters, thereby compromising both efficiency and reconstruction quality.
Delving deeper into the issue, given that large-scale scenes inevitably require more image supervision and Gaussians, the degradation can be further attributed to the imbalance between the rendering resolution and the densification strategy. This can be further elaborated from two complementary perspectives: (1) The
Project leader, supervised the work and defined the conceptualization

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Published as a conference paper ICLR 2026
Well Initalleed
11/0ambr of Poayur 110))
Opt ekmin
High fescerency Imsiges
Direct High Frequency Superviion
Pontt-Inihilizes
V. Scurre Bandrottth
Loae weweerrruunneeee sbint moint clouds
dynami resolation
con-frequency images
Frequencc
2000
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Figure 1: Floaters and redundancy. Prior methods that directly supervise with high-frequency images lead to redundancy and cannot exploit more primitives to capture high-frequency details.
common practice of rendering high resolution images throughout training imposes substantial computation and memory overhead. (2) Supervising
frrequency-inittalle Gaussians with high-frequency images leads to uncontrolled densification and redundant Gaussians, excessive gradients induce premature growth focused on fine textures, while overlooking the underlying geometric structure. As shown in Fig. 1, redun- dancy and floaters emerge when supervision is insufficient.
We recognize that the rendering resolution and the densification strategy are not orthogonal concepts, and seek to address the challenges through unified framework. By reframing scene reconstruction from the per- spective of signal structure recovery, common schedulers for densification and resolution can be regarded as controlling the target signal's frequency content and the sampling frequency. However, such strategies raise a fundamental question: when should the resolution be increased and densification be performed? Some pre- liminary attempts have been made in prior works. DashGS (Chen al., 2025) progressively increases image resolution in non-linear fashion over training iterations, whereas methods such as TamingGS (Mallick et al., 2024), rely on predefined densification schedules. Since these schedulers are predetermined before training rather than being adapted during the optimization, we refer to such approaches hard-coded scheduling strategies. However, the sampling frequency and the fidelity signal reconstruction are inherently coupled. Hard-coded scheduling may impede effective learning by imposing premature high-resolution supervision or delaying essential refinements. Idcally, resolution should be increased only when further training at the current level ceases to yield significant improvements. This occurs when the spectral content encoded by the Gaussians reaches the maximum recoverable frequency (i.e., the Nyquist frequency). ), thereby allowing higher-resolution images guide the densification process in recovering high-frequency details.
Building on the above discussion, to ensure frequency-consiisent optimization, it is essential to characterize the frequency of the sampling and target signals. Thus, first mathematically derive the representation frequency of 3D Gaussians. This guides the supervision resolution according to the evolving scene fre- quency. By leveraging low resolution for structure recovery and high resolution for texture refinement, we enable adaptive resolution adjustment during training. Beyond the frequency inconsistency, unconstrained Gaussian movement and scaling in prior methods may lead the neglect of structural priors. While Neural Gaussians (Lu et al., 2024) introduce neural anchors, they remain limited by block-partitioned training with shared MLP decoders, hindering scalability and stability in large scale scenes. To leverage the spatial priors exhibited by point clouds, we further introduce Sphere- ConsteeConstraiied Gaussians to reduce redundancy and preserve scene structure, where all Gaussians are confined within a sphere based on density priors.
In summary, our contributions as follows: (1) We mathematically define the average frequency of 3D Gaussians representation and propose a novel scheduler that synchronizes image supervision with gaussian frequency, mitigates redundancy and accelerates training. (2) We propose Sphere-Constrant
Gaussians, which leverage structural priors to restrict the optimization space. (3) Our framework achieves substantial improvements in quality (+0.9 dB PSNR) and training speed (1.5x per block) across multiple benchmarks.
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2 RELATED WORK
Novel View Synthesis and 3D Representation. NeRF (Mildenhall al., 2021) and its related works (Gao et al., 2022; Chen et al., 2021; Barron al., 2021) have achieved remarkable progress in NVS. To achieve faster training and rendering, NeRFs have gradually incorporated explicit structures (Chen et al., 2022; Müller et al., 2022), while remain computationally expensive due to the dense sampling along each ray. In contrast, 3DGS (Kerbl et al., 2023) adopts a purely explicit representation, achieving photorealistic render- ing quality while significantly improving rendering speed. Subsequent works have further enhanced 3DGS by incorporating techniques such as anti-aliasing (Yu et al., 2024), training acceleration, and block-wise optimization (Liu et al., 2024; Lin et al., 2024). More recent GS-based approaches introduce neural Gaus- sians (Lu et al., 2024), combining implicit representations to improve adaptability. However, the implicit components compromises rendering efficiency and hinders block-wise optimization in large-scals scenes.
Scheduling Strategy for 3DGS Optimization. Multiscale representations (Müller et al., 2022) are com- monly employed in NeRF to enable coarse-to-fine optimization (Xue al., 2024; Lin al., 2021). which allows progressive exposure of high-resolution features during training. In 3DGS, the training scheduler can regulate the optimization via Gaussian densification and image resolution. For the former, prior works such as TamingGS (Mallick et al., 2024; Rota Buld et al., 2024) and DashGS (Chen et al., 2025) primarily focus on controlling Gaussian densification to limit the number of primitives early training. For the latter, DashGS reduces computational cost by dynamically adjusting the rendering resolution throughout training. However, prior scheduling of either resolution or primitive growth is predefined and static throughout the op- timization. This lack of adaptivity means that the training process cannot respond to the actual reconstruction progress. Premature introduction of high-resolution supervision may destabilize early optimization stages, while delayed scheduling may delay convergence and underutilize computational resources.
Large-scale Scene Reconstruction. Recent advances in large-scale scene reconstruction predominantly follow divide-and-conquer paradigm. NeRF-based approaches such as Block-NeRF (Tancik al., 2022; Zhenxing & Xu, 2022) and Mega-NeRF (Xu et al., 2024; Turki et al., 2022) partition the scene into spatial blocks, yet rendering latency remains critical limitation. In contrast, 3DGS has emerged more efficient alternative, with many studies focusing on block wise representations that incorporate level-of-detall render- ing. VastGS (Lin et al., 2024) performs progressive partitioning based on camera distribution. DOGS (Chen & Lee, 2025) and BlockGS (Wu et al., 2025) adopt recursive strategies to ensure balanced computation across blocks. CityGS (Liu et al., 2024) leverages coarse Gaussians to guide scene partitioning and performs direct merging of Gaussians within blocks. Octree-GS (Ren et al., 2024) initializes the scene with structured neural anchors and decodes gaussian using MLP-decoder, while lacks native support for block-wise training due to the shared MLP. MomentumGS (Fan et al., 2024) attempts to address this issue but incurs frequent inter-block synchronization. Recently, several methods have been proposed to accelcrate Gaussian rendering in large-scale scenes, such FlashGS (Feng et al., 2025) and FastGS (Ren et al., 2025). These methods be combined with existing approaches to further improve rendering speed, demonstrating significant prac- tical utility. Despite these advances, challenges such as Gaussian redundancy and floater artifacts persist in large-scale scenes, hindering both reconstruction quality and rendering efficiency.
3 METHOD
We first briefly revisit 3DGS in Section 3.1. Then, formalize average sampling frequency and scene frequency bandwidth in Section 3.2, and propose our frequency-aligned resolution and densification scheuler in Section 3.3. Section 3.4 introduces spatial-aware Gaussian optimization process.
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Frequency Matching
Cohere-Constrained Gaussian
frequency sampling
Goussons
Scheduler
Matching
Scheduler
Gussspping Fanegling (f d)
Frequency
Gavosaars
stose
speit
offres
Opacity Field
Sphere conatraint
3D Gaussio
tnttal point doud Optientationn
Figure 2: Overview. We define Gaussian frequency based on the opacity field, represented as a weighted sum of Gaussians. Using frequency metenhng module, we synchronize image supervision with Gaussian frequencies (SIG), and optimize with Sphere-Constraiig Gaussians incorporate geometric priors.
3.1 PRELIMINARIES
- to represent a 3D scene, where Σ; E 3x33 denotes the covariance matrix, and p; E RR represents the position. Each primitive also possesses opacity o, and color attributes c, Per-pixel colors obtained via a-blending: C Ei a [] (1 a;), a denotes the transparency weight, which is derived from o, and Σ, We adopt the partitioning strategy of CityGS, using coarse training to build scaffold and fine training for each block.
3DGS utilizes Gaussian primitives (9((x) exp (- E.)
3.2 RETHINKING THE SCHEDULER FROM SIGNAL STRUCTURE RECOVERY
Theoretical Foundations. Reconstruction can be viewed as the task of recovering continuous 3D signals from discretely sampled images. Existing methods typically schedule the training process along two axes: (1) adjusting the frequency of the 3D Gaussians via controlled densification; (2) modulating the frequeney of the supervision signal. For instance, DashGS computes the frequency of images sampled at different resolu- tions and linearly maps the frequency at different image scales to the training iterations. Taming focus on controlling densification. However, they all rely on hard-coded schedulers fixed prior to optimization. Con- sequently, premature introduction high-resolution supervision can destabilize early optimization, while delayed scheduling may slow convergence and lead to inefficient use of computational resources.
According to the Nyquist Sampling Theorem, sampling at frequency f limits recoverable components to f/]] known as the signal bandwidth. Given sampling frequency fimg- the effective bandwidth of the scene will converge to a fixed value Bscene (under certain assumptions in Appendix). Consequently, the sampling frequency should be increased once the current bandwidth converges, which indicates sufficient recovery. Once the relationship between the two is established, the key challenge is thus to determine the sampling frequency and the effective bandwidth of the 3D Gaussians.
Sample Frequency. For focal length f and sampling depth d, a unit screen-space interval corresponds to a 3D space with radius of d/f. Assuming constant depth, the sampling frequency of the entire image proportional to f/d. Downsampling an image by factor scales the focal length to f' = f/t, yielding a sampling frequency v' = v/t. Therefore, changing the image resolution modifies the sampling frequency of the signal. In practice, each image samples only subset of the scene, and varying depth d causes non-uniform sampling frequencies. From differential viewpoint, each local patch can be approximated as uniformly sampled. We thus define the average sampling frequency over the scene as:
== - I. w:(s) a/0) J. w;(s)ds 1.
(1)
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where denotes local patch, w;(s) the weight, representing the contribution of patch s to whole scene, and (s) 0 if is not observed. (s(s) denotes the depth of patch in the i-th view. Clearly, this average frequency increases with image number n and exhibits strict linear dependence on the focal length f.
Scene Signal Bandwidth. Based on the above discussion, local patch frequencies are inherently non- uniform. Fortunately, our goal is to recover dominant structures of the scene signal. In this context, the average signal bandwidth- bandwidth-cooputeed over all local patches- serves as global measure of the scene's s frequency content, and naturally corresponds to the average sampling frequency in Eq. (1). Geometrically, variations in the scene's 's density function capture the spatial frequency of its structure. We explicitly write the scene opacity field as a weighted sum of 3D Gaussians:
(xx) Σi= G2(x) = Ei= (2m) det (2) E,);
(2)
where G. denotes the unnormalized Gaussian centered 14, with covariance Σ, and opacity o;. x R represents point in 3D space. In signal analysis, average frequency or bandwidth is typically weighted by the power spectral density:
D(w) = Ei E. |D(w) Ei a.G.(w))
1 w (D(W) de
(3)
[Dw))
where D(w) and Cr(w) denote the frequency-domain counterparts of (()) and G.(t). Prior to compute W. first compute the Fourier transform F(w) of the Gaussian function e- and it's half-power (3dB) bandwidth waa as: F(w) V exp
and w3aB V2a ln Detailed derivation is given in the Appendix. waan commonly used to characterize the effective frequency range that contains the majority of the signal's 's energy, we use it to simplify the computation of the power spectrum (Dww) since performing continuous integration over tens of millions of Gaussian primitives is computationally challenging.
Given that the frequency of each Gaussian primitive (((w) x F(w)) follows bell-shaped distribution, with its energy predominantly concentrated within W3dB, we approximate the mean frequency of each primitive using Wsas and assume negligible intensity at other frequencies, the cotinuous-to-diiseee approximation shown Fig. 3(b). Consequently, the [[w)] can be approximated as:
[DW)) = Σ Jo, Σ
Σ (2 dct (E,)) 6(w W3aB, )
where Re(-) denotes the real part extraction, 8(-) is the unit impulse function, and det(-) denotes the deter- minant. As a result, we can estimate the average frequency of the entire scene as:
1 w D2w)) du Σr of det Eg JasaB, E. of det(E;)
(5)
- 1(w)) de
Y: T.Average Score Frequergy. X: Iteettion
Frequency Domain Counterparts of Opocity Figld
1o,022
Different
Approsi
x max 01
(b)
Figure 3: Effectiveness Validation: (a) Average Scene Bandwidth during Training under Different Image Resolutions and WsaB Estimation Methods, (b) Our approximation the power spectrum.
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Since for ID Gaussian function, w3dB 22a In 1. we refer to the scale of primitive as scale [01, 22, Ss. and adopt the average over the three axes as W3dB, W3dB, O Σ 2k=1 3
Effectiveness Validation. To identify the effectiveness of our definition of the average sample frequency and scene signal bandwidth, we conduct the following experiments using vanilla 3DGS (Kerbl al., 2023):
(1) To validate the relation between sampling frequency (i.e. image resolution in our perspective) and signal bandwidth, we reconstruct scenes at different image resolutions. For the relationship between W3dB, and scale, we adopt three metrics: max _, min L and Σ I In Fig. 3(a), our definition of recovered 3ar scene bandwidth, with waami x Σ =k=1 3rz shows clear positive correlation with the sampling frequency, whereas the remaining two lack such behavior. This arises as our focus is on the scene's average band- width, rather than isolated high or low frequencies. This strict positive correlation confirms our proposed definition's 's validity.
ov.
(2) We monitor the average scene bandwidth during training to validate the effectiveness of its definition. As shown in Fig. M(),, under our definition, scene bandwidth increases steadily with training iterations, indicating progressive recovery of Sigher-frequency signals.
3.3 COARSE-TO-FINE SIGNAL STRUCTURE RECOVERY
Based on the defined average sampling frequency and the effective scene bandwidth of the 3D Gaussian representation, we introduce a novel scheduler (SIG) that Synchronizes Image supervision with Gaussian frequencies to adaptively switch resolutions and regulate densification accordingly. SIG consists of two key components: frequency-aligned resolution scheduler and densification scheduler.
Frequency-Aligned Resolution Scheduler. As shown in Eq. (I), computing the average sampling fre- quency requires integrating over differential elements of each scene patch. While the Nyquist sampling theorem is valid locally for each infinitesimal element, the global average value does not strictly satisfy it. Hence, we assess convergence
given resolution by examining whether the average scene bandwidth stabilizes. Once convergence is achieved, we increase the resolution of training images for the next stage. Specifically, we compute the scene frequency Water at each iteration using Eq. (5), and obtain its gradient da
diler The resolution is updated once the condition as Eq. (6) is satisfied, where k is universal across scenes, NN) denotes bearest-neighbe search, which we use to normalize the scale, since the input point cloud may not correspond to real- world units.
df wi Wi-1; d d= N clouddy
d1 < k. ()ean())))
(6)
diter
This strategy enables rrequency-consiste signal recovery. As shown in Fig. 3(a), the resolution increased the scene approaches the maximum recoverable frequency.
Densification Scheduler. As noted earlier, increasing the sampling frequency requires more Gaussians to fit higher-frequencc signals. Therefore, after each resolution update, we perform m rounds of densification. This strategy avoids unconstrained over-densification in the early stage and prevents incfficient training caused by excessive number of Gaussians.
3.4 STRUCTURE- AWARE OPTIMIZATION
Sphere-Constraine Gaussians. Due to sparse initialization, the Gaussian primitives exhibit an exces- sively large optimization space. Spatial-agnostic optimization of Gaussian positions often results in floaters. Scaffold-GS (Lu et al., 2024) employ neural anchors to decode Gaussians, which helps mitigate this issuc. However, it prevents block-wise independent training due the shared Gaussian decoder. In contrast, we constrain our explict Gaussians within a similar explicit structural framework. Specifically, during opti- mization, assign each Gaussian ellipsoid two attributes: anchor and maximum offset. These attributes
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determine whether the current Gaussian deviates from the original geometric structure. Initially, all anchors are set to the initial points obtained from COLMAP (Schonberger & Frahm, 2016), and the offset is com- puted as Xcurrent Xanchor- The max_ see is determined based on the initialization by searching for the K nearest neighbors of each point and calculating their average distance, which serves as the maximum off- set. In practice, considering potential inaccuracies COLMAP results but overall structural reliability, we and setting K 15. When the offset exceeds x max_ feet, the Gaussian point exceeding this spherical constraint is pruned.
relax the pruning criteria by introducing a scale factor 1 >>>
Anchor-based adaptive control. Due the introduction of anchors, newly generated Gaussians during densification are also assigned both anchor and max ofaxxoofeee of attributes. The assignment rules as follows: (1) Replication. Replication signals under-reconstruccion -ie. the region exhibits low-freuueney textures and is initially under- ender-popplated with Gaussians. Therefore, to allow large-scale spatial displacement, the newly created Gaussian does not inherit the original anchor. Instead, its current position is set as the new anchor, while the max_o fset attribute is inherited from the original Gaussian.
(2) Splitring. Splitting targets higher-frequency details. In this case, the anchor is inherited from the orig- inal Gaussian to preserve structural alignment. The max_o fsse is scaled down to 0.7x x of the original, encouraging more conservative updates and ensuring stability in sehhfrrquency regions. (3) Densification Regularization. Constraining Gaussians densification solely via 2D image supervision (i.e., reconstruction loss) inherently limited. We introduce regularization mechanisms specifically tailored for densification, based on reprojection-based photometric loss, which is commonly used in sparse-view recon- struction. Specifically, we extract dense point clouds from rendered depth maps 2 and project them onto adjacent frame images compute photometric errors. It is effective for large textureless regions, enforcing geometric-color consistency, and is calculated as Eq. (7):
Leoms C35 (2.
(15)
where represents the camera pose. The C(-) denotes the color obtained by sampling from the image. F(z) denotes the projection function that maps 3D point onto 2D image. F=, denotes the back-projection, mapping a pixel p to a 3D point using depth z. We found that using it throughout the entire optimization does not improve accuracy. This indicates that GS-based depth estimation is not per- fectly precise, which makes the projections inexact. However, it can still provide useful constraints during densification, serving as densification regularization.
4 EXPERIMENTS
4.1 EXPERIMENTS SET UP
Datasets and Metrics. Following large-scale reconstruction methods (Liu et al., 2024; Wu et al., 2025), we evaluate our approach on three datasets: real-world Mill19 (Turki et al., 2022), UrbanScene3D (Lin et al., 2022), and synthetic MatrixCity (Li et al., 2023). We report results using metrics: SSIM, PSNR, and LPIPS (Zhang et al., 2018). A color correction is applied for metric computation, following (Lin et al., 2024).
Implementation Details. All images downsampled by factor of (from 5 1) to enable dynamic resolution. All methods are trained and evaluated on NVIDIA RTX 4090 GPUs. The resolution scheduler threshold for of is set to k- mean(3 2) with h Sphere-Cood Conetr-Contt Gaussians, we adopt scale factor of I = 15. We use 30,000 training iterations for both the coarse and fine stages. More details can be found in Appendix.
10-5 5 and df is evaluated every 100 iterations. For diter
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CityGS
DoGS
BlockGS
DashGS
Ours
Ground Truth
Figure 4: Qualitative Results. The top two rows illustrate sparse observations, whereas the bottom two rep- resent regular regions. For regions corresponding to sparse viewpoints, our approach effectively minimizes the generation of redundant and erroncous Gaussian components. For general regions, our method recovers figh-freyeeccy details while maintaining intact geometric structures.
4.2 COMPARISON WITH OTHER METHODS.
Baselines. Our method is benchmarked against both NeRF-based and GS-based approaches. The NeRF- based baselines include Mega-NeRF (Turki et al., 2022) and SwitchNeRR (Zhenxing Xu, 2022), whereas the 3DGS-based methods comprise VastGS (Lin et al., 2024), CityGS (Liu et al., 2024), DOGS (Chen & Lee, 2025), and BlockGS (Wu et al., 2025). Additionally, we compare our method with DashGS (Chen al., 2025) hard-coded scheduling strategy. More details can be found in Appendix.
Reconstruction Quality. Our method implements structure-aware optimization, enabling the fitting of high- frequency details with more Gaussian primitives while avoiding floaters. Consequently, number of Gaussians by adjusting the gradient threshold during densification, leading to two model variants with different Gaussian counts-where the model with more Gaussians (Ours-L) demonstrates the higher performance ceiling of our algorithm. Besides, for BlocKGS, We follow its official implementation and use a batch size of 4 for better reconstruction quality (processing images per iteration to enhance results, albeit with proportional time overhead). Please refer to Appendix for details of BlockGS, As shown in Table and Table 3, our method achieves comprehensive improvements over baseline approaches, such as a +0.9 dB gain in PSNR for the scene 'rubble'. Fig. 4 illustrates that compared to baselines, our method captures finer high- frequency details without producing floaters (NeRF-based results can be found in Appendix. Higher SSIM and LPIPS scores further validate its superior visual quality. Furthermore, while DashGS yields modest gains over baselines via its specialized training strategy. its ability to represent high-frequee frequency information in large-scale scenes remains limited, its design prioritizes training efficiency.
control the
Efficiency Analysis. Considering that different block partitioning strategies, as well as the size and number of blocks, affect computational time, select two baselines corresponding two partitioning strategies and report the average optimization time per block on scene 'rubble' in Table 3. Our method substantially improves training efficiency, achieving 1.5x and 1.4x speedups BlockGS and CityGS, respectively.
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OurstCitGG-LL CityGS-L++
GARSS
BlackGS+FARS
GiyGS-L
CiyGS-L
CityS
Block
Figure 5: Ablation. CityGS-L: lower densification threshold of CityGS for higher-frequeed fitting.
Table Quantitative comparison of NVS results. The best, the second best, and the third best results are
highlighted in red
orange and yellow
Scenes
building
PSNR
rubble
SSIM
LPIPS
residence
sci-art
SSIM
LPIPS
Matrix -itiia
SSIM
Mega-NeRF
20.92
0.547
0.454
24.06
0.553
0.508
22.05
0.628
0.401
25.60
0.770
0.312
Switch-NeRF
21.54
0.579
0.397
24.31
0,562
0.488
22.57
0.654
0.352
26.51
0.795
0.271
DashGS
26.37
0,802
0.237
0.833
0.239
VastSS
21.80
0.728
0.225
25.20
0.742
0.264
21.01
0.699
0.261
22.64
0.761
0.261
28.33
0.835
0.220
CitGS
22.70
0.774
0.246
26.45
0.809
0.232
23.35
0.822
0.211
24.49
0.843
0.232
28.61
0.868
0.205
DOGS
0.219
BlocKGS
21.11
0.750
0.234
25.52
0,801
0.233
22.15
0,830
0.211
24.18
0,831
0.219
28.17
0.863
0.199
Ours-L
22.86
0.778
0.225
27.35
0.843
0.189
23.46
0.840
0.194
25.94
0.890
0.170
29.04
0.888
0.184
Ours-S
0.830
0.208
0.196
0.863
0.200
0.181
4.3 ABLATION STUDY
As shown in Fig. 3, we have validated the effectiveness our definitions for the average sampling frequency and Gaussian representation frequency. In this section, conduct ablation studies the 'rubble' to verify the efficacy of each individual module, with results presented in Table 2.
Frequency-Aligneed Resolution Scheduler (w/o FARS). We directly train the highest-resolution images and, following CityGS, perform densification every 200 iterations between 500 and 15,000 iterations. Re- sults show that omitting FARS leads significant drop in reconstruction quality and increased training time. Due to the lower splitting threshold, over-densification even yields results inferior to CityGS. Fur- thermore, as illustrated in Fig. 5 and Table (1.5M points vs. 2.2M points), without dynamic resolution scheduling, redundant Gaussians and floaters tend to emerge in the early stages of optimization, particularly when the gradient threshold for densification is low.
Densification Scheduler (w/o DS). Building on the "w/o FARS" setup, we adopt dynamic resolution scheduling while retaining the original splitting strategy. This leads to a potential issue: the moment of reaching the highest resolution lags behind the termination of densification, no further Gaussian densification occurs afterward. Such mismatch impairs the model's capacity to represent high-frequency information.
Constrieon Gaussians (w/o SCG) and Densification Regularization (w/o DR). Sphere- Constrained Gaussians (SCG) explicitly leverages geometric structure initialized sparse point clouds, thereby reducing the probability of Gaussians being optimized into erroncous regions. As for the Densifi- cation Regularization, in the absence ground-truth depth, this method establishes geometric consistency constraints across multiple frames. Once floaters emerge, they disrupt depth prediction and thereby induce errors in adjacent views. As shown in Table 2, both methods effectively reduce the number of Gaussians that suffer from redundancy erroneous optimization (1.9M points 1.5M points).
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Table 2: Ablation. Frequency-consisten training
Table 3: Integration with other baselines. We
yields substantial performance gains.
improve quality and efficiency by augmenting baselines with our method (*). Opt.time: min/block.
Method
PNSR
SSIM
LPIPS
Points
Method
PNSR
SSIM
LPIPS
Opt.time
Wo--FRRS
26.18
0.807
0.231
2.2M
woo-DS
26.89
0.827
0.212
1.4M
BlockGS
25.52
0.801
0.233
201
w/--CG
27.05
0.818
0.210
1.8M
BlockGS+*
25.89
0.820
0.228
130
w/o-DR
27.01
0.820
0.209
1.9M
CityGS
26.45
0.809
0.232
98
w/ all(*)
27.35
0.843
0.189
1.5M
CityGS+*
27.35
0.843
0.189
71
Integration with Other Baselines. Notably, strategy compatible with most baseline methods and can be used as plug-and-plas component. As shown in Table 3, our approach significantly improves both rendering quality and efficiency when applied to BlockGS and CityGS.
5 LIMITATION
In large-scale scenes, Level-of-Detail (LoD) rendering strategy is usually required. While approach leverage existing LoD strategies such as those proposed CityGS, our coarse-to- fine training naturally pro- duces both coarse and fine Gaussians, providing more intrinsic way of constructing hierarchical structures. This also points to promising direction for future optimization.
6 CONCLUSION
We attribute low-quality reconstruction under sparse point cloud initialization, floaters, and redundant Gaus- sian primitives frequency misalignment between supervision and target signal. Based this, derive the average scene and supervision frequencies and present a novel training framework. We introduce a unified cesuutioondeeiiiiaaatinn scheduling strategy driven by scene frequency convergence, and propose Sphere Conttr-Cons Gaussians to leverage initial geometry while regularizing densification. This enables frequency-consisten and geometry-aware optimization.
ACKNOWLEDGEMENT
This work was supported by the National Key Research and Development Program of China (No. 3024YFE0211000 in part by the National Natural Science Foundation of China (No. 62372329, 62506263, 62506264), in part by the Shanghai Scientific Innovation Foundation (No. 23DZ1103400),, part by the China Postdoctoral Science Foundation (No. BX20250383, G7B20250385, 2025M771530, 2025M771539), in part by Tongli-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and part by Xiaomi Young Talents Program.
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Published as a conference paper ICLR 2026
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Reviews:
[{"review_id": "YtPSa5kDuM", "reviewer": "Reviewer_9Q3V", "summary": "The paper proposes Signal Structure-Aware Gaussian Splatting (SIG), a framework designed to improve large-scale 3D scene reconstruction using 3D Gaussian Splatting. The authors observe that prior methods supervise Gaussians initialized from sparse low-frequency points using high-frequency image signals, which leads to uncontrolled densification and redundant primitives. To address this, they reformulate scene reconstruction as a signal structure recovery problem and introduce a frequency-based synchronization between image supervision and the Gaussian representation.\n\nConcretely, the paper defines the \"average sampling frequency\" of images and the \"effective scene bandwidth\" of Gaussians, derived from a frequency-domain analysis of the opacity field. These metrics guide the adaptive adjustment of training image resolution and Gaussian densification as the scene frequency converges. Additionally, the authors introduce Sphere-Constrained Gaussians (SCG) that restrict each Gaussian’s optimization region to a local sphere determined by its initial point cloud neighborhood, mitigating floaters and structural drift. Experiments on large-scale benchmarks show performance gains in reconstruction quality and training efficiency compared to baselines.", "questions": "See the weakness. The LPIPS and SSIM columns appear to be swapped in Tables 2 and 3.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The idea of aligning the Gaussian frequency with the supervision signal frequency is intuitive and well-executed, beginning with a clear definition of Gaussian frequency and followed by thorough verification. Experiments show consistent gains in quality and speed, and the method works as a plug-in for existing frameworks like CityGS and BlockGS.", "weaknesses": "1. It remains unclear how sensitive the method is to the introduced hyperparameters.\n2. While the concept of progressive training from low to high resolution is not novel, the paper’s analytical framework for optimally aligning Gaussian frequency with signal frequency is interesting. However, a comparison with the more heuristic use of progressive training is missing.\n3. Evaluating the proposed method on conventional NVS benchmarks such as MipNeRF360 would further demonstrate its generalization capability.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "gFMhVGgvP5", "reviewer": "Reviewer_bS7H", "summary": "This paper aims at solving the frequency inconsistent issue during 3DGS training. It leverages the frequency information to check whether it is necessary to increases the image resolution during training. Moreover, it introduces the Sphere-Constrained Gaussians to constrain its moving offset. Experiments under large-scale dataset validates its effectiveness since it beats SOTA large-scale 3DGS approaches.", "questions": "(1) Eq. (5) and Eq.(6) are computed at each training iteration. Will that be time consuming?\n\n(2) At line327, the author mentioned \"we use 30,000 training iterations for both the coarse and fine stages\". How to define the coarse stage and fine stage? Since the method enlarges the resolution of training images in a coarse-to-fine manner, it is confused to me the 3DGS are trained with a coarse stage and a fine stage?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "(1) The idea is novel, which leverage the frequency information to schedule the resolution of training images.\n\n(2) The writing is good and the paper is easy to understand.\n\n(3) The proposed method is effective, and beats SOTA methods in large-scale datasets.", "weaknesses": "(1) The method is compared to many SOTA methods, but it lacks comparison with a naive baseline: scheduling the image resolutions during training at some hard-coded iterations (e.g. 10,000, 15,000, 20,000), I think some methods did this but it needs to be done in the experiment of this paper to provide a direct comparison.\n\n(2) The experiments part lacks comparison on some standard benchmarks, e.g. the mipnerf360 dataset and the tanks-and-temples dataset.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "K43e1WBIel", "reviewer": "Reviewer_P2B2", "summary": "This paper proposes a frequency-consistent framework for large-scale 3D scene reconstruction. It mathematically defines the average sampling frequency and signal bandwidth of 3D Gaussian representations, and introduces a scheduler that adaptively adjusts image resolution and Gaussian densification based on scene frequency convergence. Additionally, it proposes Sphere-Constrained Gaussians to enforce geometry-aware optimization and reduce redundancy. The paper achieves state-of-the-art rendering quality and faster training compared to the baselines.", "questions": "As noted in the weaknesses, I recommend that the authors include ablations on key hyperparameters, or at least provide a discussion on how these values are selected and whether they are kept consistent across all experiments. I also suggest to provide additional qualitative/quantitative comparisons with CityGaussianV2 and FlashGS.\n\nApart from above, I have an additional question:\n- Does the proposed method also improve geometry? Although it's hard to directly evaluate geometries in such large scenes, I would be interested to see a similar geometry evaluation as in CityGaussianV2.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper formalizes when to raise resolution and when to densify using a bandwidth convergence signal, which improves the performances of baselines that rely on predefined schedules\n- The proposed method is a plug-and-play component that could be applied to multiple baselines (e.g., 3DGS, CityGS, BlockGS) and leads to consistent performance gains and better efficiency\n- The ablations studies clearly show the benefits brought by each of the proposed components", "weaknesses": "- The convergence threshold k, neighbor count K, and scaling factor l (e.g., K=15, l=15, and max_offset is scaled down to 0.7×) are stated but not sufficiently justified. Are these values chosen empirically, or derived from any principled analysis? Moreover, do they require dataset-specific tuning, especially under varying levels of SfM sparsity or reconstruction noise?\n- Missing baselines: some relavant works in this domain are not compared to, especially: CityGaussianV2 (ICLR 2025), FlashGS (CVPR 2025)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "oJQEd6LlOO", "reviewer": "Reviewer_aMuM", "summary": "This paper identifies a key problem in scaling 3D Gaussian Splatting to large-scale scenes: the mismatch between sparse initial 3D points and high-frequency image supervision. This mismatch causes uncontrolled growth of redundant Gaussians, hurting both efficiency and quality. The authors reframe the problem as one of signal frequency synchronization and propose a scheduler to align the 2D image supervision with the 3D Gaussian representation's evolving complexity.", "questions": "See weakness.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 2, "contribution": 3, "strengths": "1. The sufficient experiments adequately illustrate the superiority of the method and the effectiveness of each model design. The settings of experiments and baseline implementations are also well explained, making it easier to follow the paper and reproduce results.\n2. The efficiency and quality of large-scale scene reconstruction are of significance. This paper introduces a sound and innovative method to push the performance bound over existing methods.", "weaknesses": "1. The order of LPIPS and SSIM in Tab.2 and Tab.3 seems to be wrong.\n2. Fig.2 itself is not well self-contained. The formulas and pipelines are, to some extent, confusing, such as the meaning of the blue dashed line. And it should provide a reference to the related sections.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)