AtlasGS: Atlanta-world Guided Surface Reconstruction with Implicit Structured Gaussians
Authors: Xiyu Zhang
Chong Bao
YiPeng Chen
Hongjia Zhai
Yitong Dong
Hujun Bao
Zhaopeng Cui
Guofeng Zhang
Venue: NeurIPS 2025 poster ()
Keywords: indoor surface reconstruction
gaussian splatting
Primary area: applications

Abstract: 3D reconstruction of indoor and urban environments is a prominent research topic with various downstream applications. 
However, existing geometric priors for addressing low-texture regions in indoor and urban settings often lack global consistency.
Moreover, Gaussian Splatting and implicit SDF fields often suffer from discontinuities or exhibit computational inefficiencies, resulting in a loss of detail. To address these issues, we propose an Atlanta-world guided implicit-structured Gaussian Splatting that achieves smooth indoor and urban scene reconstruction while preserving high-frequency details and rendering efficiency. By leveraging the Atlanta-world model, we ensure the accurate surface reconstruction for low-texture regions, while the proposed novel implicit-structured GS representations provide smoothness without sacrificing efficiency and high-frequency details. Specifically, we propose a semantic GS representation to predict the probability of all semantic regions and deploy a structure plane regularization with learnable plane indicators for global accurate surface reconstruction. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in both indoor and urban scenes, delivering superior surface reconstruction quality.

AtlasGS: Atlanta-world Guided Surface Reconstruction with Implicit Structured Gaussians
Xiyu Zhang
Chong Bao!*
Yipeng Chen' Zhaopeng Cui'
Hongjia Zhai'
Yitong Dong'
Hujun Bao'
Guofeng Zhang"
State Key Lab of CAD & CG, Zhejiang University
ScanNet
MatrisCity
2DGS
Ours
2DGS
Ours
Net+Net++
Replica
MonoSDF
Ours
ManhattanSDF
Ours
Qualitative comparison of indoor and outdoor reconstruction. For each scene, we visualize both the reconstructed geometry and the surface normals. As highlighted by the orange boxes, our method generates significantly smoother surfaces while capturing finer geometric details, clearly outperforming the compared methods.
Figure 1:
Abstract
3D reconstruction of indoor and urban environments is a prominent research topic with various downstream applications. However, existing geometric priors for addressing low-texture regions in indoor and urban settings often lack global consistency. Moreover, Gaussian Splatting and implicit SDF fields often suffer from discontinuities or exhibit computational inefficiencies, resulting in a loss of detail. To address these issues, we propose Atlanta-works guided implicit-structured Gaussian Splatting that achieves smooth indoor and urban scene reconstruction while preserving high-frequency details and rendering efficiency. By leveraging the Atlanta-world model, we ensure the accurate surface reconstruction for low-texture regions, while the proposed novel implicit-structured GS representations provide smoothness without sacrificing efficiency and high-frequency details. Specifically, we propose a semantic GS representation to predict the probability all semantic regions and deploy structure plane regularization with learnable plane indicators for global accurate surface reconstruction. Extensive experiments demonstrate that our method outperforms state-of of-the-art approaches in both indoor and urban scenes, delivering superior surface reconstruction quality.
"Equal contribution 'Correpponing author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
Recently, indoor and urban 3D reconstruction from multi-view images has emerged as a popular research area, fueled by its applications in digital twins [[3]], robotic navigation [ and aug- mented reality 77] These technologies demand accurate and efficient reconstruction of real-world environments. However, man-made scenes often contain large low-texture planar regions, such as floors, ceilings, and unadorndd walls, which pose significant challenges for image-based 3D reconstruction. Traditional multi-view stereo methods struggle on these textureless surfaces due to the lack of distinctive visual features, leading to incomplete or distorted geometry. Geometric priors play a crucial role in addressing this challenge. Monocular geometric priors provide locally smooth geometry signals for low-texture regions g but they often lack global consistency across different viewpoints, often resulting in inconsistent geometry like bumpy surfaces. Alternatively, the Manhattan-world assumption [9] leverages planar priors to address low-texture regions in man-man mane scenes but cannot be applied in urban scenes where buildings are not mutually orthogonal structures, such as the building marked by the yellow rectangle in Fig.
Concurrently, 3D representation methods for indoor and urban reconstruction have evolved rapidly and achieved remarkable success. For example, 2DGS [10] employs Gaussian splitting (GS) with surfel primitives to efficiently and effectively reconstruct complex geometry. However, its discrete primitives induce discontinuities in surface reconstruction, resulting in broken surfaces in low-texture or under-observed regions, as depicted in Fig. [ Previous implicit SDF representations MH4 leverage the inductive continuity of coordinate-basee multi-layer perceptrons (MLPs) to recover complete surfaces in these challenging regions. However, they are computationally expensive and struggle to represent complex geometries. Some methods [15H77] have explored the simultaneous learning of both representations, using implicit methods to guide GS optimization for smoother outcomes. Unfortunately, this mutual interaction often compromises reconstruction quality.
Based on these observations, we identify two critical challenges: 1) A globally consistent geometric prior is essential to regularize low-texture regions in both indoor and urban reconstructions: 2) A 3D representation is needed that retains the efficiency and detail- peteil-preserving capabilities of GS while incorporating the smoothness of implicit methods.
In this paper, we propose an Atlanta-wond guided implicit-struee -tructurt Gaussian Splatting for indoor and urban scene reconstruction.
First, the man-made indoor and urban environments can be described as an Atlanta world model [8 where there is one vertical direction aligned with gravity and multiple horizontal directions oriented from walls or urban buildings. To establish globally consistent and accurate geometry in low-texture regions, such as floor, ceiling, and walls, we incorporate this global geometric assumption into GS optimization, thereby regularizing the geometric relationships among these regions. Specifically, we propose a semantic GS representation to predict the semantic probability of floor, ceiling, and wall in the 3D scene. Besides, we design a structure plane regularization with learnable explicit plane indicators for globally accurate surface reconstruction.
Secondly, we propose a novel implicit-structured Gaussian representation, which integrates the continuity of implicit functions with the efficiency and detail preservation of 2DGS. Unlike prior works that simply overlay implicit priors on Gaussian optimization, we embed implicit voxel grids within the Gaussian Splatting framework, allowing implicit geometry to act as a smooth regularizer while maintaining high-frequency representation. Besides, we adopt a view-independent decoding on GS spatial distribution to enhance the geometric consistency across multiple viewpoints. Our representation not only improves the smoothness of surface reconstruction but also facilitates the efficient modeling of intricate geometry, striking better balance between accuracy and efficiency.
The contribution of our paper can be summarized as: 1) We propose a novel Atlanta-world guided implicit-structured Gaussian Splatting to achieve smooth indoor and urban scene reconstruction while preserving high-frequncyy details and rendering efficiency. 2) To integrate the Ailantawworle assumption, we design semantic GS representation to predict the semantic probability of low-texture regions such as floor, ceiling, and walls, and propose a structure plane regularization with learnable explicit plane indicators to regularize the global geometry of these low-texture regions. 3) Extensive experiments in indoor and urban scenes demonstrate the effectiveness of our method. We show the best surface reconstruction quality quantitatively and qualitatively compared to other state-of-the-an methods.
2

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2
Related Works
Neural Implicit Surface Reconstruction. Neural Radiance Fields [99 (NeRF) designs neural implicit representation to reconstruct the scene from multi-view 2D images. To obtain the scene surface, some NeRF variants [1]
12 20 combine SDF-based neural representation with volume rendering for better geometry reconstruction. In addition, to obtain better reconstruction results in some challenging scenarios, some research works introduced more prior information during the optimization process, such as geometric regularization [13], monocular depth [21-23), normal [14 23
24 20). and semanties [3 26) However, due to the limited representation capacity of MLPs (27]
relying solely on MLPs may result in slow optimization and poor reconstruction performance of large scenes. Therefore, additional feature encoding is used enhance the scene representation ability and speed up the reconstruction, such as dense feature grid [28] 22], hash table [29] 30) sparse voxel [3T] and tetrahedron [4 However, despite the use of feature encoding, all of these implicit methods still require hours of training and exhibit low inference times and insufficient detail during the reconstruction. contrast, our method enables efficient surface reconstruction (< 30 minutes) with high-quality details.
Surface Reconstruction with Gaussian Splatting. 3D Gaussian Splatting [39] (3DGS) has emerged as a promising technique for efficient and high-quality novel view synthesis. Starting from SIM points, 3DGS represents the scene with 3D Gaussians and employs fast splatting-based rasterization to accelerate both training and inference. SuGaR [40] extends 3DGS to surface reconstruction by associating 3D Gaussians with the mesh surface and jointly optimizing both the Gaussians and the mesh. PGSR [1] utilizes planar-based Gaussian splatting combined with unbiased depth rendering to maintain global geometric accuracy. To reconstruct complete surfaces in unbounded scenes, GOF [42] leverages a ray-tracing- basedd volume rendering, which enables a mesh to be extracted directly from the Gaussian representation. Furthermore, 2DGS IIO and Gaussian Surfels (45 argue that the multi-view inconsistency inherent in 3DGS compromises reconstruction quality. To address this, they replace 3D Gaussians with 2D surfels, enabling more precise capture of intricate geometric details. However, the discrete nature of Gaussian Splatting undermines the smoothness of reconstructed surfaces, particularly in regions with low texture or limited observational coverage. DN-Splatter 44 employs depth and normal priors to improve the smoothness of surface reconstruction based on 3DGS. Certain methods [1 45) simultaneously learn an implicit Signed Distance Function (SDF) field alongside 3D Gaussian Splatting, utilizing the smooth SDF field to regularize the noisy geometry inherent in 3DGS. However, the mutual interaction between these components often compromises reconstruction quality, resulting in suboptimal outcomes. In contrast, our approach integrates the implicit field with Gaussian Splatting under the Atlanta-world assumption, enabling smooth surface reconstruction while preserving high-frequency geometric details.
Methods
Our goal is to reconstruct scenes with strong structural priors from posed images. To achieve this, we first introduce the preliminaries of 2DGS [10] in Sec. [3.1, followed by our implicit-structured representation in Sec. 3.2 To leverage structural priors under the Atlanta world assumption, we propose 3D global planar regularization and 2D local surface regularization, as detailed in Sec. [3.
Finally, we describe the training process in our framework. An overview of our approach is illustrated in Fig.
3.1 Preliminary
models scenes surfels distributed around the surfaces. Each surfel is defined in local tangent plane in world space. To render images, 2DGS rasterizes surfels to the image plane with tile-based rasterization and Ray-Splat intersection to reduce depth bias. Then, 2DGS performs alpha blending (46) get the rendered attribute A by composing these primitives sorted by depth:
Instead of representing scenes with blobs as 3D Gaussian Splatting [39 2DGS 10
A =
Σ aj ai
(1 a3),
(I)
3

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Implicit
Splutting
Are buttul Depoder
Bi Ponts
Sparos Fassiu
Semrrtt Dococer
Radwerndion
Atlanta-worid Guidanoe
Reguibricatio
Rardering
Overview of AtlasGS. Given posed images and SIM points, we construct sparse feature grid and represent scenes as implicit-structun Gaussians. Attributes are decoded using attribute decoder and semantic decoder, followed by rasterization and supervision with RGB images, monocular geometry priors, and semantic maps. To address multiview inconsistency in textureless regions, introduce learnable explicit plane indicators based on the Atlanta world assumption [18]. The indicators refine the global scene structure by regularizing Gaussian positions and orientations using 3D global planar and 2D local surface losses, ensuring alignment with structural elements such as walls, floors, and ceilings.
Figure 2:
where A are the rendered 2D scene information (c.g., color depth d, normal semantics z), a, and og denote the 3D property and opacity contribution of i-th Gaussian primitive, and [] - aj) is the accumulated transmittance. Then, 2DGS optimizes these Gaussians with photometric loss and distortion loss to reduce floaters. The Ray-Splat intersection and well-defined normal introduce multiview consistency depth, providing better reconstruction quality. Though 2DGS produces plausible surfaces and models high-frequency details with explicit Gaussian representation, the discrete nature introduces discontinuities, which leads to broken or protruding texture-less walls.
3.2 Implicit-Structtree Gaussian Splatting
In this section, we present our implicit-structure Gaussian representation, which leverages a sparse feature grid and implicit functions to organize discrete Gaussian primitives, ensuring locally coherent geometry while preserving high-frequency details.
Specifically, given the sparse point clouds generated from SIM 47), we first construct sparse feature grid V = (V/ Vi, { 1 (') y with predefined voxel size, including geometry V and semantic features Vi, offsets K. local Gaussians (= scaling factor (r) shared with local Gaussians. Given voxel located in v, we deocde all Gaussian geometry attributes of K. local Gaussians via corresponding geometry MLP My(.) and semantic MLP (-(()
(akk 8k:; Jx. {= = M2 (V), (cx = (Y,
Here, is view direction which assists in capturing view-dependent appearance, a E IR s E R² E R24, c E RR3 and z E IR refer to the opacity, scale, rotation, color, and semantic attributes of each Gaussian, respectively, whose positions p defined as P v, + A Then we render images with all these Gaussian attributes decoded from the sparse feature grid by surfel rasterization from [10]. In contrast 2DGS [10,, which optimizes Gaussians independently, our decoder predicts local Gaussian attributes, allowing each Gaussian's 's optimization to influence its neighbors and capture fine object details through the predicted Gaussian primitives. Consequently, the implicit-structured Gaussian framework combines the strengths of MLPs and Gaussians, achieving smooth local geometry while preserving high-frequency details.
Gaussian Semantic Lifting. To recognize structural regions in scenes, we lift 2D semantics to each Gaussian. We use the 2D pseudo-labels 2 obtained by the pre-trained semantic segmentation model 48 as supervision and optimize the semantic Gaussians with the rendered semantic probability Z. To obtain the rendered semantics probability Z, render the 3D semantic attribute defined

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in Eq. (2) into image space with Eq. ( and optimize the semantic feature grid V, and semantic
MLP M, by minimizing the cross-entropy loss:
Z z=
Σ 2
I aj)l,
(1-aj)
(3)
==1
sem
Σ wEN
(())
log (
U
where [ denotes the stop-graud noopgradieet operator, used to prevent inconsistent supervision from distorting the geometry, and U denotes the set of training pixels in each iteration. Here, we define E R indicating wall, floor, ceiling, and others.
3.3 Atlanta World Guided Planar Regularization
Man-made indoor and urban environments typically exhibit rich structural information and conform to the Atlanta world assumption [18]. To leverage the globally consistent structural priors inherent to such scenes, first propose learnable explicit plane indicators to effectively represent scene structural information, such as the ceiling and floor. We then introduce two types of regularization: 3D global planar regularization, which refines Gaussian positions and orientations align with the plane indicators, and 2D local surface regularization, which provides positional supervision in poorly defined wall regions by aligning them with the plane indicators.
Explicit Plane Indicators The Atlanta world assumption [8] hypothesizes that such scene can be approximated by a combination of a dominant horizontal plane, like the floor for indoor scenes and ground for outdoor scenes, and multiple vertical planes, such as walls and buildings. Based on this assumption, we define explicit plane indicators with a gravity direction and two distance offsets to represent the floor and ceiling of an indoor scene. Specifically, the floor plane and ceiling plane can be represented with π (ng: ( Tee = (-ng. de), and their plane parametric equations are as follows:
d, d n p O, d. - n2 p 0 0,
(5)
where E 3 is the location of 3D points, d, and de are the distances from the origin to their respective planes, and ng is the gravity direction. For the urban scenes, we omit the ceiling plane.
To achieve this, we extract ceiling points and floor points, either from semantic Gaussians or semantic lifted sparse points. We then apply RANSAC [49] to regress the plane coefficients and determine gravity direction to initialize plane indicators. Finally, we optimize the plane indicators alongside the Gaussians. Please refer to our supplementary for further details.
3D Global Planar Regularization. According to the associated probability distribution E R. we can obtain the semantic label of each Gaussian. We enforce two critical geometric regularizations: normal alignment and planar constraint. The normal alignment enforces normals to be perpendicular to the gravity direction in wall regions while ensuring they remain parallel in ceiling and floor regions. Besides, the planar constraint ensures that the Gaussian positions p. lie in their corresponding ceiling or ground plane. Thus, the 3D global planar regularization formulated as:
Cap
Σ pn |n nnl) n:l)
sEM
(6)
+
Σ REML
Pı Piin In n:l + Σ Pold, - p:I+ Σ
Pyldy + ny Pil.
sE::
iE
where Mr, Mc, Mj and M1 are the floor, ceiling, parallel, perpendicular sets, P PL. Pe: Py are the corresponding probabilities, n, and p: are the normal and position of i-th Gaussian.
2D Local Surface Regularization. Previous methods 14 derive normals from the gradient of the given points, while optimizing normals can also optimize the
13 with implicit representation
5

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ScanNNt
ScanNet++
Replica
MDD
MonoSDF
Scaffold-GS
2DGS
GSRec
Ours
GT
Figure 3: Qualitative comparison of indoor scene reconstruction. We show the reconstruction performance of the baselines and our approach ScanNet (50), ScanNet++ [51], and Replica [52] datasets. As highlighted in the boxes, our approach maintains local smoothness and preserves high frequency. The red dashed boxes mark regions that zoomed in below for closer inspection.
local surface. However, the Gaussian representation explicitly decouples the positions and normals of Gaussians. It poses challenge that only optimizing Gaussian orientations in 3D space does not directly affect their spatial distribution. Without explicit positional regularization, wall Gaussians may not lie on the same plane, resulting in misalignment between the surface and the plane indicators.
To address this issue, we introduce 2D local surface regularization by regularizing the normal N from the rendered depth D. With the semantic Gaussians, we obtain coherently rendered semantics and depth, from which we derive local surface normals in wall regions. Then, we align the surface normal with our plane indicators, optimizing Gaussian positions more directly. Besides, to mitigate misclassification introduced by the semantic segmentation model [48), we weigh the loss according to the probabilities. Thus, 2D local surface regularization loss is formulated
L2D Σ Pw ([Na n2l) + Pe, (1 Naa ngl).
(7)
NEML
P V.PXV
N
(8)
where Pe,f is the sum of the probabilities of the floor and ceiling, Pw the probability of the wall, P are the points backprojected from depth, V is the gradient operator. So, our structural regularization loss is:
Creg LaD + L2D
3.4 Training
We optimize Gaussians and structure with the following:
-= Ligh + X Ldepth + An + AgGreg + Ca + Ap + Ag
(10)
where Ligh photometric loss proposed in original 3DGS, the distortion loss Ldist and normal consistency loss Lnc from 2DGS [10]. X {1... 6} are the loss weight, Lvom is the semantic

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Table I: Quantitative comparison Replica and ScanNet++ [51 and completeness (Comp) em, others percentage with a 5cm threshold. The first three results highlighted in red, orange, and yellow, respectively.
We report accuracy (Ace)
Replica
S
ScanNet++
[1]
Category
Methods
Acc|
Compl
Prect
Recall
R-scoref
Acc|
Compl
Prect
Recalft
F-scoref
MF
13
4.76
5.59
68.80
66.40
67.57
3,96
4,98
77.30
76.16
76.67
Implicit
MoneSDF
[4]
5.38
75.50
70.89
73.08
4.05
5.57
76.25
75.16
75.65
Scaffold
63.53
54.91
23.11
15.36
28.18
31.75
29.78
2DGS
74.54
65.37
16.53
17.91
22.84
20.79
Explicit
DN-Splatter
16.97
15.52
32.67
30.90
31.75
16.77
15.05
22.42
21.97
22.16
GSRec
4,90
6.89
73.32
67.69
70.37
9.37
9.13
47.12
53.81
50.14
Ours
2.25
4.08
93.18
82.22
87.35
3.22
4.09
87.59
87.47
87.48
Table 2: Quantitative comparison on ScanNet [50]. We report accuracy (Acc) and completeness (Comp) cm, others in percentage with a 5cm threshold. The first three results are highlighted in red, orange, and htwplooiwrspecivv.l.
Category
Methods
Acc|
Compl
Prect
Recall
F-scoret
Time
FPS
ManhattanSDF
13
4.25
5.23
72.39
63.18
67.25
>
10
Implicit
MonoSDF
14
4.25
4.76
73.53
69.18
71.21
> 7 h
< 10
Scaffold-GS
54
9.47
7.99
51.41
49.08
50.17
12 mins
279
2DGS 10
11,46
13.89
43.15
36.17
39.27
11 mins
118
Explicit
DN-Splatter
13.54
14.77
21.71
18.94
20.22
12 mins
145
GSRec
6.71
5.40
60.36
66.63
63,30
35 mins
Ours
3.62
3.93
80.31
75.85
77.98
27 mins
loss mentioned in Sec. 3.2 To provide the smoothness of local surfaces, incorporate monocular geometry priors from pre-trained models [
53 for indoor reconstruction during training.
Ldepth
=
Σ (ww + -
(11)
Lnormal (II-N- + (1-Na. N).
(12)
where N, Ñ, Đ are the rendered normal, the normal prior and depth prior from 53), respectively. w, q are the scale and shift computed from sast-squares to align rendered depth D to monocular depth D.
4 Experiments
incorporating custom sur- fel rasterization module for semantic learning, and optimize the parameters with Adam optimizer (56). The hyperparameter K. is set to 10, and the voxel size is fixed at 0.01. During training, the loss weights Å1, 22, A3, Aq, Aso Ag are set to 0.25, 0.1, 0.1, 1.0, 100, and 0.05, respectively. The explicit plane indicator is initially derived from the semantic lifted SIM points and is reinitialized using the semantic Gaussians if the discrepancy exceeds a predefined threshold. Surfaces are extracted using TSDF Fusion [57]. All experiments performed on single NVIDIA 4090D GPU. Additional implementation details are provided in the supplementary material.
Implementation Details. We implement our approach in PyTorch 55
Datasets. Our method leverages the Atlanta world assumption, making it well-suited for both indoor and urban scenes. We evaluate our method using well-known datasets for both indoor and outdoor scene reconstruction. For indoor environments, we use ScanNet [50], ScanNet++ [51], and Replica [52]. For outdoor settings, we employ the MatrixCity [58] dataset for surface reconstruction. ScanNet and ScanNet++ feature large-scale RGB-D images and 3D surfaces akin real-world see- narios, while Replica offers synthetic dataset with high-quality images from 3D meshes. MatrixCity provides a synthetic, city-scale dataset for neural rendering. In line with previous studies [13] 14, we select four scenes from ScanNet, seven from Replica, and four from ScanNet++, sampling images
7

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GoussianPo
GSRec
2DGS
Ours
Figure 4: Qualitative comparison of outdoor scene reconstruction. As highlighted the boxes, approach produce detailed and noise-free surfaces in textureless regions.
uniformly from the sequences. For outdoor evaluation, four city blocks from MatrixCity are used. Additional details are provided in the supplementary material.
Baselines. For indoor scenes, we compare our approach against two types of methods: Neural
implicit representations: ManhattanSDF [3 and MonoSDF [14]; 2) Gaussian-based representations:
Scaffold-GS [54], 2DGS [00, DN-Splatter [44), and GSRec [17]. Additional supervision with monocular depth and normals, as noted in Eq [T] and Eq (12), is integrated into Scaffold-GS
and 2DGS for indoor scenes. The quantitative evaluation for indoor scenes includes accuracy, completeness, precision, recall, and F-score. For outdoor scenes, comparisons are made with 2DGS, GSRec, Scaffold-GS, and GaussianPro [59]. In this context, the geometric evaluation relies on accuracy, completeness, and chamfer distance.
4.1 Comparison
Indoor Surface Reconstruction. We evaluate surface reconstruction on ScanNet [50]. Scan-
Table 3: Quantitative comparison on Matrix- City [58).
Net++ (51) and Replica [52]. shown Tab. [
and 2 our method outperforms both implicit and explicit basclines, achieving statc-of-the-art re- sults. SDF-based implicit methods like Manhat- tanSDF [3] and MonoSDF [4] ensure smooth surfaces but struggle with fine details, e.g., "lamp" in orange box of Fig. 3) and suffer from multiview inconsistency in textureless regions, e.g., there is discontinuity on the floor in MonoSDF.
Methods
Acc|
Comp.
CDJ
GaussianPro
0.102
0.081
0.091
Scaffold-GS
54
0.328
0.303
0.316
GSRec 17
0.048
0.175
0.112
2DGS 10
0.115
0.098
0.106
Ours
0.022
0.034
0.028
Additionally, the time-consuming ray sampling in NeRF-based frameworks is to blame for the training time exceeding hours and the inability to achieve real-time rendering- Gaussian-based explicit methods, such as Scaffold-GS and 2DGS, are fast but produce discontinuous surfaces due to

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Sea
Replica
Scaffold-GS
2DGS
DN-Spaltter
GSRec
Figure Qualitative comparison novel view synthesis. We show the novel view synthesis results of different Gaussian splatting-basee approaches ScanNet++ (51] and Replica [52] datasets. Our method can obtain higher-fidelity rendering results with less noisy information than the baselines.
Table 4:
Quantitative comparison of novel view synthesis. We perform experiments Replica 52 and ScanNet++ [51] datasets.
Replica
52
ScanNel++
51
Methods
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS_
ScaffolGGS
38.08
0.9660
0.0961
18.25
0.7749
0.2764
2DGS 10
41.59
0.9823
0.0464
21.87
0.8114
0.3060
DN-Splatter 44
29.02
0.8967
0.2312
22.76
0.8226
0.2971
GSRec 17
36.00
0,9574
0.1205
22.96
0.8314
0.2708
Ours
39.58
0.9756
0.0766
22.51
0.8321
0.2517
independent primitive optimization or view-dependent geometry. GSRec [17 improves geometry via IMLS but still yields noisy results. contrast, our implicit-structuree Gaussians combine locally coherent geometry with high-frequency detail preservation, enabling smoother and more accurate reconstructions. While slower than prior Gaussian methods due decoding all Gaussians when rendering, approach remains much faster than implicit ones and delivers superior quality.
Urban Surface Reconstruction. Structural priors are common in man-made environments, in- cluding both indoor scenes and urban buildings. evaluate our method under such priors, we use the MatrixCity dataset [58]. We compare against GaussianPro [59], Scaffold-GS [54]. GSRec (17), and 2DGS [10]. As shown in Tab. 3] our method yields more accurate and complete surfaces by leveraging the Atlanta world assumption. In Fig. [4] GaussianPro suffers from noisy surfaces and inconsistent depth despite normal propagation. GSRec reduces noise via IMLS regularization but produces sparse reconstructions in textureless regions, and its Poisson surface reconstruction trims low-density areas, resulting in missing geometry. 2DGS also struggles in textureless regions like the and building facades, leading to artifacts such protrusions holes. In contrast, approach delivers smoother and more accurate surfaces in these challenging regions.
Novel View Synthesis. We evaluate novel view synthesis on the Replica [52) and ScanNet++ [51] datasets. As demonstrated in Tab. and Fig. 5 our method achieves superior quantitative results, rendering photorealistic views with accurate geometry while avoiding the artifacts common in other approaches. While Scaffold-GS and 2DGS perform well on synthetic datasets without significant lighting variations, they struggle to render photorealistic novel views in real scenes. Scaffold-GS models significant lighting variations using view-dependent geometry, which can lead to overfitting in scenes with substantial lighting changes, such as those in [51]. This overfitting results in inaccurate lighting environment and geometry, as shown Fig. 2DGS I0] achieves a higher quantitative result on Replica with discrete representation, however, the discrete representation exhibits protrud-

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ing surfaces and results in noisy images on real scenes. GSRec [77] improves geometric accuracy but produces blurry background and objects, lacking detailed modeling. In contrast, with its precise geometry, our method effectively models lighting variations across views while accurately capturing the appearance of the background and objects.
4.2 Ablation Study
Table 5: Quantitative ablation on ScanNet [50]
Merthod
Leopph fevormal
CoD L2D
CDJ,
F-scoref
a) 2DGS
x
x
12.68
39.27
b) Ours
/
/
V
3.77
77.98
w/o LaD
x
3.97
75.52
(a) w/o Lreg
(b) w/ Lreg
(c) GT
d) w/o Ler
x
x
4.10
74.23
Figure 6: Qualitative ablation on ScanNet [50]. (a) Ours w/o Ligg (Row b in Tab. 5): (b) Ours w/
e) w/o Lnamal
x
3.89
76.30
X
freg (Row f in Tab. 5 (c) GT.
f) w/o Ldepth
4.23
74.22
We conduct an ablation study on the ScanNet [5 dataset to evaluate the contribution of each component in our method, including the implicit-straaturred Gaussian, depth and normal priors, as well as the proposed 3D global planar and 2D local surface regularization terms. We report geometric evaluation metrics including Chamfer Distance (CD) and F-score (5 cm threshold), as summarized in Tab. 5
As shown in Tab. 5 each component contributes positively to surface reconstruction quality. Com- pared to 2DGS (Row a) which uses normal and depth priors, our method with implicit-structurred Gaussians (Row d) significantly improves geometry, as it provides locally coherent structures and better leverages the guidance from geometry priors. By comparing Rows b, c, and we observe that our 3D global planar regularization and 2D local surface regularization enhance geometry quality and yield superior geometric metries. These regularization terms ensure globally consistent geometric supervision under the Atlanta world assumption, mitigating the inconsistencies and inaccuracies inherent in depth and normal priors. Furthermore, Fig. illustrates the geometric comparison of our structural regularization, demonstrating straighter wall regions. Additionally, on the geometry priors themselves. As seen in rows e and f, removing either the normal prior or the depth prior leads to noticeable degradation, confirming that both types of geometric supervision are critical for high-quality reconstruction. Our full model (Row b) integrates all components and achieves the best performance with the lowest CD and highest F-score.
perform ablations
5 Conclusion & Limitations
This work presents a novel framework, AtlasGS, which reconstructs structured scenes using implicit- structured Gaussians under the Atlanta world assumption. We introduce our inplicit-structuree Gaussian representation as hybrid approach that provides locally coherent geometry via MLPs and preserves seeeffreuency details through explicit Gaussian representation. To resolve the global inconsistency of geometric priors, we propose 3D and 2D regularization strategies based on the Atlanta world assumption, effectively correcting textureless regions. As result, our method achieves fast and accurate surface reconstruction, and extensive experiments demonstrate that it achieves state-of-the of-the-art performance. However, there are also some limitations in our work. First, the training and rendering speed are slower than the previous Gaussian-based methods [54] 10 339. Second, our method is primarily based on the Atlanta world assumptions, which depend on a pretrained semantic segmentation model for limited set of elements. The future extension of our work is speed up the training and rendering speed and facilitate SAM [60] and geometry priors to provide planar information, which can provide better performance and broader applicability.
10

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Acknowledgement
This work was partially supported by NSF of China (No. 62425209).
References
[1] Xiaoliang Ju, Zhaoyang Huang, Yijin Li, Guofeng Zhang, Yu Qiao, and Hongsheng Li. Diflind- scene: diffusion-based high-quality 3d indoor scene generation. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4526-4535, 2024.
[2] Shougao Zhang, Mengqi Zhou, Yuxi Wang, Chuanchen Luo, Rongyu Wang, Yiwei Li, Zhaoxi- ang Zhang, and Junran Peng. Cityx: Controllable procedural content generation for unbounded 3d cities. arXiv preprint arXiv:240711777, 2024.
[3] Chong Bao, Yinda Zhang, Yuan Li, Xiyu Zhang, Bangbang Yang, Hujun Bao, Mare Pollefeys, Guofeng Zhang, and Zhaopeng Cui. Geneavatar: Generic expression-ave aware volumetric head avatar editing from single image. In /EEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8952-8963, 2024.
[4] Michal Adamkiewicz, Timothy Chen, Adam Caccavale, Rachel Gardner, Preston Culbertson, Jeannette Bohg, and Mac Schwager. Vision-only robot navigation neural radiance world. IEEE Robotics and Automation Letters, 7(2):4606-4613 2022.
[5] Obin Kwon, Jeongho Park, and Songhwai Oh. Renderable neural radiance map for visual navigation. In IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 9099-9108, 2023.
[6] Timothy Chen, Ola Shorinwa, Joseph Bruno, Aiden Swann, Javier Yu, Weijia Zeng, Keiko Nagami, Philip Dames, and Mac Schwager. Splat-nav: Safe real-time robot navigation in gaussian splatting maps. IEEE Transactions Roboties, 2025.
[7] Hongjia Zhai, Xiyu Zhang, Boming Zhao, Hai Li, Yijia Hc, Zhaopeng Cui, Hujun Bao, and Guofeng Zhang. Splatloe: 3d gaussian splatting- based visual localization for augmented reality. IEEE Transactions on Visualization and Computer Graphics, 2025.
[8] Lihe Yang. Bingyi Kang, Zilong Huang, Zhen Zhao, Xiaogang Xu, Jiashi Feng, and Hengshuang Zhao. Depth anything v2. Advances in Neural Information Processing Systems, 37:21875- 21911, 2025.
[9] James Coughlan and Alan Yuille. The manhattan world assumption: Regularities in scene statistics which enable bayesian inference. Advances in Neural Information Processing Systems, 13, 2000.
[10] 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.
[11] 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. Advances in Neural Information Processing Systems, 11-27171-27188 2021.
[12] 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.
[13] Haoyu Guo, Sida Peng, Haotong Lin, Qianqian Wang, Guofeng Zhang, Hujun Bao, and Xiaowei Zhou. Neural 3d scene reconstruction with the manhattan- world assumption. In IEEF/CVF Conference on Computer Vision and Pattern Recognition, pages 5511-5520, 2022.
[14] 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 1580018-253222 2022.

---

[15] 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. 2024.
[16] Xiaoyang Lyu, Yang-Tian Sun, Yi-Hua Huang, Xiuzhe Wu, Ziyi Yang, Yilun Chen, Jiangmiao Pang, and Xiaojuan Qi. 3dgsr: Implicit surface reconstruction with 3d gaussian splatting. ACM Trunsuctions on Graphics, (3(6))1-12, 2024.
[17] Qianyi Wu, Jianmin Zheng, and Jianfei Cai. Surface reconstruction from 3d gaussian splatting via local structural hints. In European Conference on Computer Vision, pages 441-458, 2024.
[18) Grant Schindler and Frank Dellaert. Atlanta world: An expectation maximization framework for simultaneous low-level edge grouping and camera calibration in complex man-made envi- ronments. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition., volume I, pages I-1, 2004.
[19] Ben Mildenhall, Pratul Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In European Conference on Computer Vision, pages 405-421, 2020.
[20] Jiepeng Wang, Peng Wang, Xiaoxiao Long, Christian Theobalt, Taku Komura, Lingjie Liu, and Wenping Wang. Neuris: Neural reconstruction of indoor scenes using normal priors. In European Conference on Computer Vision, volume 13692, pages 139-155, 2022.
[21] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6290-6301 2022.
[22] Jingwen Wang. Tymoteusz Bleja, and Lourdes Agapito. Go-surf: Neural feature grid optimiza- tion for fast, high-fidelity RGB-D surface reconstruction. In International Conference on 3D Vision, pages 433 442, 2022.
[23] Zihan Zhu, Songyou Peng, Viktor Larsson, Zhaopeng Cui, Martin R. Oswald, Andreas Geiger, and Mare Pollefeys. Nicer-slam: Neural implicit scene encoding for rgb slam. In International Conference on 31) Vision, pages 42-52, 2024.
[24] Xu Cao and Takafumi Taketomi. Supernomaa: Neural surface reconstruction via multi-view normal integration. In /EEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20591- 2024.
[25] Ruibo Wang, Song Zhang, Ping Huang, Donghai Zhang, and Wei Yan. Semantic is enough: Only semantic information for nerf reconstruction. In IEEE International Conference on Unmanned Systems, pages 906-912, 2023.
[26] Abhijit Kundu, Kyle Genova, Xiaoqi Yin, Alireza Fathi, Caroline Pantofaru, Leonidas J. Guibas, Andrea Tagliasacchi, Frank Dellaert, and Thomas A. Funkhouser. Panoptic neural fields: A semantic object- aware neural scene representation. In JEEE/CVF on Computer Vision and Pattern Recognition, pages 12861-12871 2022.
[27] Edgar Sucar, Shikun Liu, Joseph Ortiz, and Andrew J. Davison. imap: positioning in real-time. In JEEE/CVF International Conference on Computer Vision, pages 6209 6218, 2021.
Implicit mapping and
[28] Zihan Zhu, Songyou Peng. Viktor Larsson, Weiwei Xu, Hujun Bao, Zhaopeng Cui, Martin R. Oswald, and Mare Pollefeys. Nice-slam: Neural implicit scalable encoding for slam. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12786-12796. 2022.
[29] Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution hash encoding. ACM Transactions on Graphics, 414:::002:1 102:15, 2022.
[30] Hengyi Wang, Jingwen Wang, and Lourdes Agapito. Co-slam: Joint coordinate and sparse parametric encodings for neural real-time SLAM. In IEEF/CVE Conference on Computer Vision and Pattern Recognition, pages 13293-13302, 2023.
12

---

[31] Hai Li, Xingrui Yang, Hongjia Zhai, Yuqian Liu, Hujun Bao, and Guofeng Zhang. Vox-surf: Voxel-based implicit surface representation. IEEE Transactions on Visualization and Computer Graphics, 30(3):1733-1555 2024.
[32] Tong Wu, Jiaqi Wang, Xingang Pan, Xudong Xu, Christian Theobalt, Ziwei Liu, and Dahua Lin. Voxurf: Voxel-based efficient and accurate neural surface reconstruction. In International Conference Learning Representations, 2023.
[33] Lingjie Liu, Jiatao Gu, Kyaw Zaw Lin, Tat-Seng Chua, and Christian Theobalt. Neural sparse voxel fields. In Advances in Neural Information Processing Systems, 2020.
[34] Jonás Kulhánek and Torsten Sattler. Tetra-nerf: Representing neural radiance fields using tetrahedra. In IEEE/CVF International Conference on Computer Vision, pages 18412-18423, 2023.
[35] Jacob Munkberg, Jon Hasselgren, Tianchang Shen, Jun Gao, Wenzheng Chen, Alex Evans, Thomas Müller, and Sanja Fidler. Extracting triangular 3d models, materials, and lighting from images. In IEEE/CVF Conference on Computer Vision and Puttern Recognition, pages 8280-8290, 2022.
[36] Tianchang Shen, Jun Gao, Kangxue Yin, Ming-Yu Liu, and Sanja Fidler. Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. In Advances in Neural Information Processing Systems, pages 6087-6101, 2021.
[37] Radu Alexandru Rosu and Sven Behnke. Permutosdf: Fast multi-view reconstruction with implicit surfaces using permutohedral lattices. In IEEE/CVF Conference on Computer Vision and Puttern Recognition, 2023.
[38] Hongjaa Zhai, Gan Huang, Qirui Hu, Guanglin Li, Hujun Bao, and Guofeng Zhang, NIS- SLAM: Neural implicit semantic RGB-D SLAM for 3D consistent scene understanding. IEEE Transactions on Visualization and Computer Graphics,
2024.
[39] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkuehler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics, 12(4) 2023.
[40] Antoine Guédon and Vincent Lepetit. Sugar: Surface-aligned gaussian splatting for efficient 3d mesh reconstruction and high-quality mesh rendering. In /EEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5354 5363, 2024.
[41] Danpeng Chen, Hai Li, Weicai Ye, Yifan Wang, Weijian Xie, Shangjin Zhai Nan Wang. Haomin Liu, Hujun Bao, and Guofeng Zhang. Pgsr: Planar-based gaussian splatting for efficient and high-fidelity surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 2024.
[42] Zehao Yu, Torsten Sattler, and Andreas Geiger. Gaussian opacity fields: Efficient adaptive surface reconstruction in unbounded scenes. ACM Transactions on Graphics, 43(6):271:1- 271:13, 2024.
[43] Pinxuan Dai, Jiamin Xu, Wenxiang Xie, Xinguo Liu, Huamin Wang, and Weiwei Xu. High- quality surface reconstruction using gaussian surfels. In ACM SIGGRAPH Conference Papers, page 22, 2024.
[44] Matias Turkulainen, Xuqian Ren, laroslav Melekhov, Otto Seiskari, Esa Rahtu, and Juho Kan- nala. Dn-splatter: Depth and normal priors for gaussian splatting and meshing. Proceedings of the IEEE/CVF Winter Conference Applications of Computer Vision (WACV), 2025.
[45] Haodong Xiang, Xinghui Li, Xiansong Lai, Wanting Zhang, Zhichao Liao, Kai Cheng, and Xueping Liu. Gaussianroom: Improving 3d gaussian splatting with sdf guidance and monocular cues for indoor scene reconstruction. arXiv preprint axXiv:2455.1967. 2024.
[46] Nelson Max. Optical models for direct volume rendering. IEEE Transactions on Visualization and Computer Graphics, (12)99--08,, 1995.
13

---

[47] Johannes Lutz Schönberger and Jan-Michael Frahm. Structure- fromture-from--ee motion revisited. In IEEE Conference on Computer Vision and Pattern Recognition, 2016.
[48] Bowen Cheng, Ishan Misra, Alexander G. Schwing, Alexander Kirillov, and Rohit Girdhar. Masked-attention mask transformer for universal image segmentation. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1280-1289.
[49] Martin Fischler and Robert C Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-399 1981.
[50] Angela Dai, Angel X. Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. ScanNet: Richly-annotated 3D reconstructions of indoor scenes, In IEEE Conference on Computer Vision and Pattern Recognition, pages 2432 2443, 2017.
[51] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes. In IEEE/CVE International Conference on Computer Vision, pages 12-22, 2023.
[52]
Julian Straub, Thomas Whelan, Lingni Ma. Yufan Chen, Erik Wijmans, Simon Green, Jakob J. Engel, Raul Mur-Artal, Carl Ren, Shobhit Verma, Anton Clarkson, Mingfei Yan, Brian Budge, Yajie Yan, Xiaqing Pan, June Yon, Yuyang Zou, Kimberly Leon, Nigel Carter, Jesus Briales, Tyler Gillingham, Elias Mueggler, Luis Pesqueira, Manolis Savva, Dhruv Batra, Hauke M. Strasdat, Renzo De Nardi, Michael Goesele, Steven Lovegrove, and Richard Newcombe. The 2019.
Replica dataset: A digital replica of indoor spaces, arXiv preprint
[53] Chongjie Ye, Lingteng Qiu, Xiaodong Gu, Qi Zuo, Yushuang Wu, Zilong Dong, Liefeng Bo, Yuliang Xiu, and Xiaoguang Han. Stablenormal: Reducing diffusion variance for stable and sharp normal. ACM Transactions on Graphics, 43(6):1-18, 2024
[54] Tao Lu, Mulin Yu, Linning Xu, Yuanbo Xiangli, Limin Wang. Dahua Lin, and Bo Dai. Scaffold- gs: Structured gaussians for view-adaptive rendering. IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20654-20664, 2024.
[55] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killcen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems, 32, 2019.
[56] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.668 69800, 2014.
[57] Angela Dai, Matthias Nießner, Michael Zollhöfer, Shahram Izadi, and Christian Theobalt. BundleFusion: Real-time globally consistent 3D reconstruction using on-the-fly surface reinte- gration. ACM Transactions on Graphics, 36(3):24:1-24:15 2017.
[58] Yixuan Li, Lihan Jiang, Linning Xu, Yuanbo Xiangli, Zhenzhi Wang, Dahua Lin, and Bo Dai. Matrixcity: A large-scale city dataset for city-scale neural rendering and beyond. In /EEE/CVF 2023.
International Conference on Computer Vision, pages
[59] Kai Cheng, Xiaoxiao Long, Kaizhi Yang, Yao Yao, Wei Yin, Yuexin Ma, Wenping Wang, and Xuejin Chen. Gaussianpro: 3d gaussian splatting with progressive propagation. In International Conference on Machine Learning, 2024.
[60] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander Berg, Wan- Wan-Yen Lo, et al. Segment anything. In IEEE/CVF international conference on computer vision, pages 4015 4026, 2023.
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Please refer to our L.M policy http:ses//eerrpppoccc///o/rerees for what should or should not be described.
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A Appendix
A.1 Planar Indicator Initialization
As described in Sec. 3.3, we initialize the plane indicator using ceiling and floor points derived from semantically lifted SIM points or semantic Gaussian primitives. The SfM points gener- ated by triangulating posed images through 2D feature matching, establishing 2D-3D correspon- dences. Utilizing these correspondences, we ag- gregate semantic labels for each 3D point from 2D semantic maps across multiviews and apply voting procedure identify the most preva- lent semantic label, including those for ceiling and floor. The Gaussian semantic lifting mod- ule, mentioned in Sec. 3.2, lifts 2D semantic maps to each Gaussian primitive, and each prim- itive contains a semantic probability of the wall, floor, ceiling, or other categories. Consequently, SfM points and Gaussian primitives are assigned structural semantic labels such as wall, floor, or ceiling, allowing us to extract ceiling and floor points.
SIM Peints
Gazsian Primiive
Penpactive View
Side View
Figure 7: Plane Indicator Visualization. We vi- sualize the plane indicators derived from both the semantic lifted StM points and the semantic Gaus- sian primitives from both the perspective and side views. In the visualization, the ceiling plane is colored in blue, while the floor plane colored in orange.
Subsequently, we conduct plane fitting identify the floor plane (ny, dy) using RANSAC [49]
applied to the extracted floor points. The normal vector n is chosen as the gravity direction ng The offset of the ceiling plane, de, is calculated based on the ceiling points and the gravity direction as follows:
de
mean (n),
(13)
pE Peiing cailng
where P ceilling represents the set of ceiling points. The plane indicator is initially determined using the semantic lifted points. the angle deviation or the offset discrepancy surpasses a threshold, the plane indicator is reinitialized using semantic Gaussian primitives to minimize inaccuracies in textureless regions. Fig. 7 further illustrates plane indicators derived from both semantic lifted sparse points and semantic Gaussian primitives, demonstrating that both approaches can provide reliable structural priors.
A.2 Additional Implementation Details
Our implementation is based on PyTorch, utilizing cus- tomized surfel rasterization techniques for semantic learning. Parameters are optimized using the Adam op- timizer. Most of the training learning rates are similar to those used in [54]. We set the hyperparameter IC to 10 for indoor scenes and 5 for urban scenes, with voxel size 0.01, and the feature dim is 32 in our sparse fea- Gaus-
Table 6: Defination of metrics. P and P* are the 3D points from the predicted and the GT mesh.
Metrie
Definition
ture grid. For all scenes, the implicit-structure sian is trained for 40,000 steps. Voxels grow between steps 1,500 and 20,000, provided the gradients of the Gaussians exceed 2e-4 and are pruned if the opacities of all local Gaussians fall below 0.005. During training, we start our 3D global planar regularization from step 7000 and 2D local surface regularization from 20000. After completing training, surfaces are extracted using
Acc
meange? (mitgee gP= lp p"
Comp
ge (milger lpp p²))
CD
Prec
meallpe (mingrer= llp p'1 0.05)
Recull
meaagre p- (minger ||p p'l < 0.05)
Fl-score
2x Recal
TSDF-Fusion 577 following the approach described in
A.3 Additional Exprimental Details
Similar to previous works for indoor scene reconstruction 14,, we select four scenes in Sean- Net [50), including scene0050 00, scene0084 00, scene0580 00, scene0616 00 and seven scenes
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in Replica [52]. office0-office,, room0-room2, and as for ScanNet++ [1] we select four scenes, 8b5caf3398, 120a261fdj, f34d532901, f6659331776
As described in Sec. 4, we uniformly sample images on the indoor scenes due to redundant images in the original dataset. For each scene in ScanNet [50] and Replica (52), select out of every 10 images in the original image sequence. For ScanNet++ [5]], we use the image sequence from the iPhone and select one out of every 60 images. All the images are cropped and resized, and center-cropped to x80. For MatrixCity [58], we use all the provided images and make the image resolution x 540. The SfM points are triangulated by COLMAP 47 with given images and corresponding poses.
A.4 Evaluation Metrics
Following previous methods T 14
evaluate aceuracy (Acc), completeness (Comp), Chamfer Distance (CD), precision (Prec), recall (Recall), and Fl-score on ScanNet [50], ScanNet++ [51]. and
Replica 52 Tab. shows the definition of these metrics.
A.5 Additional Indoor Experiments
Semantic Segmentation. We evalu- ate the semanties from the rendered and the pre-trained segmentation model Mask2Former [48] Replica [52] and ScanNet++ [51] As shown Tab. 7 ours achieves better results across all three classes on both datasets. By lever- aging Gaussian semantic lifting, model effectively aggregates multi-view information into 3D space and renders view-consistent semantic maps. In con- trast, the 2D semantic segmentation model is more susceptible to image noise, leading to misclassifications, as illus- trated in Fig. 8 The joint optimization scheme also helps correct semantic mis- classifications, particularly around the boundaries between floors and walls.
Table 7: Quantitative comparison of structural lay- out segmentation on Replica S2 and ScanNet++ dataset.
Methods
Replica
58
ScanNote4 5
ToU
ToUr
JoU,
1oC, 1
ToUr
1o0. f
Mask2Pormen
48
0.628
0.823
0.900
0.684
0.780
0,707
Ours
Mask2Former
Ours
Figure 8: Qualitative comparison of structural layout segmentation.
A.6 Additional Qualitative Results
We present qualitative top-view results for ScanNet, ScanNett+, and Replica in Figs. to 11 respectively. For additional comparisons, please refer our accompanying video.
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ManhuttanSDF
MonoSDF
Scaffold-GS
2DGS
GSRec
Ours
Figure 9: Qualitative comparison of surface reconstruction on ScanNet (50]
ManhattanSDF
MonoSDF
Scaffold-GS
2DGS
GSRec
Ours
GT
Figure 10: Qualitative comparison of surface reconstruction on ScanNet++ 51]
24

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Figure 11: Qualitative comparison of surface reconstruction Replica
52
25


Reviews:
[{"review_id": "wY09T2IjfP", "reviewer": "Reviewer_3sjd", "summary": "This paper proposes to address the gaussiona-splat-based surface reconstruction problem with the assumption of the Atlanta world, for achieving better continuity for texture-less area as well as richer high frequency details. This is achieved by incorporating a sparse-volume-grid-based surface representation built on top of the 2DGS representation while maintaining neighbourhood modeling and semantic guidance. Furthermore, to better leverage the Atlanta world assumption, two additional regularization terms are further imposed for failure imposition of the assumption. The experimental results demonstrate overall good results both quantitatively and qualitatively. The paper is well written and executed and clear for reading.", "questions": "Please address my questions presented in the \"weakness\" section above.", "limitations": "Yes (mostly). \n\nOne minor (that might be pressumed to be - so no need for explictly listed) - the proposed approach primarily works for scenes with the Atlanta world assumption.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength\n\nThe paper points out the insufficiency of existing GS-based surface model, in particular like 2DGS with the collapsed ellipsoid onto the surface that leads to discontinuity and lack of details of the surface. These are valuable observations that the authors are motivated to propose their new representation, in particular, a sparse-volume-grid for rich representation power while maintaining budgeted memory footprint, and the MLP “head” for smooth local neighbourhood modeling. While such hybrid feature form is observed also in the NeRF-related literatures, they are nonetheless new in this context. \n\nThe authors proposed to impose semantic / attribute predictions that would potentially aid the imposition of the Atlanta world assumption. The proposed regularization terms for maintaining consistent geometry among textureless area are neat, and the overall learning pipeline can lead to promising and high quality reconstruction results.\n\nThe authors have conducted with efforts a set of experiments, showcasing that the proposed optimization algorithm can indeed demonstrate faithful local geometric results, especially in those areas where otherwise holes (discontinuity) or irregular / overly smoothed geometric textures presented. Quantitative results on geometric evaluation shows promising outcomes. The pixel reconstruction quality, as expected, occasionally not the best, as the main focus and model design are toward the faithful reconstruction of the geometry. The overall results are convincing.\n\nWeakness\n\nAs what the primary goal of this study presented, the proposed approach would be mostly suitable for scenes with the Atlanta world assumptions, meaning the performance might get some level of degradation on datasets otherwise. I am actually pretty curious regarding whether the proposed model could maintain geometric accuracy over scenes without such assumptions, and which of the new components shown in this paper could correspond to the potential improvement on non-Atlanta scenes? (the volume grid?) \n\nWhile the authors have presented with sufficient arguments regarding their improvement over 2DGS (models that collapse ellipsoid onto the surfaces), the authors nonetheless seemed to provide very brief discussions about to-what-extent that the addressed issues in the context of papers where the Gaussians are regularized to the mesh (e.g. [36]) or an SDF is attached [10]. Are those branches of works can also cope with surface continuity over textureless areas or providing rich geometric textures? Is the volume grid presented in the model that contributes most to the geometric details while the MLP contributed to the continuity (plus semantic guidance)? The relations between what the model has improved and what is proposed would be better elaborated.", "was_revised": true, "final_justification": "I appreciate the authors for taking great efforts addressing my concerns. Overall, I believe the good execution of this work in nature, the adequate evaluation, the idea of particularly addressing scenes with special properties (with no one works on before under the GS context) outweigh the limitation that the methodology proposed mostly for a particular set of scenes. I do believe there are components in this work (e.g. the hybrid representation) could also benefit scenes beyond the Atlanta-world assumption. I believe when the authors mention the monocular priors, they primarily treat it as one viable way to address the issue for textureless regions (not something caused by a baseline method), but it nonetheless brings new problems (not consistent among views). I do not believe it is a critical problem that warrants rejection. I would maintain my score for acceptance.", "rebuttal": "We thank Reviewer 3sjd for the encouraging feedback and insightful review comments. We are glad that you found our work to be promising and that it has high-quality reconstruction results. We address your concerns in detail below.\n\n-----\n\n### **Reconstruction quality without such Atlanta assumption.**\n\n> W1: I am actually pretty curious regarding whether the proposed model could maintain geometric accuracy over scenes without such assumptions, and which of the new components shown in this paper could correspond to the potential improvement on non-Atlanta scenes? (the volume grid?)\n\nFor scenes without such an assumption, monocular geometry priors cannot provide globally consistent supervision on textureless regions, which may lead to performance degradation as shown in the following table. However, our implicit structured Gaussian will provide local coherent geometry within a voxel and provide better geometry reconstruction quality, which potentially improves the surface reconstruction on non-Atlanta scenes.\n\n|             | CD | F-score |\n|-------------|--------------|------------|\n| 2DGS |  12.68 | 39.27 |\n|  Ours (w/o Atlanta Assumption)       |  4.10| 74.23|\n|  Ours(w/ Atlanta Assumption)        | 3.77 | 77.98 |\n\nFor more general scenes without such assumption, we perform the experiments on Tanks and Temples, and Waymo, and compare our implicit structured Gaussian with 2DGS. Our method is still comparable with the previous method as following table. We report the F-score on the Tanks and Temple datasets and the Chamfer Distance on Waymo.\n\n|             | TnT(F-score) | Waymo (CD) |\n|-------------|--------------|------------|\n|  2DGS        | 0.32 | 1.29 |\n|  Ours        | 0.33 | 0.96 |\n\n### **The relations between what the model has improved and what is proposed.**\n\n> W2: Are those branches of works can also cope with surface continuity over textureless areas or providing rich geometric textures? Is the volume grid presented in the model that contributes most to the geometric details while the MLP contributed to the continuity (plus semantic guidance)? The relations between what the model has improved and what is proposed would be better elaborated.\n\nGSRec and GSDF, two related methods, suffer from issues in textureless regions. GSRec's expensive sampling process, based on sparse Gaussian distributions in these areas, produces noisy surfaces and increases training time and memory. GSDF also has high computational demands, taking about 2 hours and 40 GiB of GPU memory to train its dual Gaussian and NeRF models. Furthermore, its reliance on monocular geometry priors for regularization in textureless regions can lead to globally inconsistent and error-prone results.\n\nIn contrast, our implicit-structured Gaussian framework tackles these challenges at the representation level. By using a sparse feature grid and implicit functions to organize Gaussian primitives, we avoid the need for costly external regularizers like SDFs. Our approach is further enhanced by Atlanta world assumption guided planar regularization, ensuring geometric consistency across large, textureless surfaces without the high computational overhead and quality trade-offs of previous methods.\n\n### **Geometry details and continuity.**\n\n> W2: Is the volume grid presented in the model that contributes most to the geometric details while the MLP contributed to the continuity (plus semantic guidance)?\n\nOur framework utilizes a hybrid approach to accurately model scene geometry.  A sparse feature grid captures the coarse geometric structure, while explicit Gaussians model the fine details. During training, gradients guide the densification and movement of these Gaussians, allowing them to accurately represent the scene's geometry. The MLP decoder provides local continuity. It acts as a continuous function that predicts the attributes of all local Gaussians from the features stored in the grid. \nBecause a single, shared MLP generates these attributes for a neighborhood, optimizing one Gaussian inherently influences its neighbors through the shared features and the MLP itself. This ensures the resulting Gaussians are locally coherent and smooth, overcoming the discrete nature of Gaussian splatting."}, {"review_id": "12TIcSVNEv", "reviewer": "Reviewer_pVvf", "summary": "This paper introduces a Gaussian Splatting method for reconstructing a man-made environment with high surface quality, utilizing the Atlanta-world assumption to constrain and guide the scene reconstruction process. \n\nThis paper first constructs a sparse feature grid on top of the SfM points, allowing the attributes (also the semantic features) of the Gaussians to be decoded from it. The semantic feature for representing planar structures is learned with supervision from a 2D semantic segmentation model.\n\nThen comes the Atlanta World Guided Planar Regularization, in which the planar region is explicitly indicated with RANSAC, then used for regulating the plane constraint with the proposed loss functions.", "questions": "1. I failed to find details about how the predicted 3D mesh is generated from a trained 3D Gaussian Field, whether all Gaussian Splatting-based methods mentioned in the experiments are processed with the same meshing method, or not?\n\n2. The experiments are conducted by evaluating the global geometric reconstruction accuracy. I would like to see the geometric accuracy of non-planar surfaces using AtlantaGS, like running the same evaluation but removing walls, ceiling, and ground floor. From the qualitative result, I see some cases, the constrained planar region also brings better reconstruction quality of other objects nearby the plane. But quantitative results will be even better.", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe methodology of this paper is simple, straightforward, and presented in a clear way. The following experiments on indoor and outdoor datasets showcase the effectiveness of the proposed method. Discussions about the training time and rendering FPS without concealing are also considered a plus mark.\n\nWeaknesses:\nAtlanta World assumption is, from my point of view, would break in many cases, e.g., indoor space at the roof floor where the ceiling is not parallel with the ground, a cinema or theater where the ground steps down, a modern design art museum with complex non-plane structured ceiling and even walls which is not plane at all. In that case, the 3D Global Planar Regularization may not stand. A mechanism for dealing with such a situation is not explored in this paper.", "was_revised": true, "final_justification": "The rebuttal addressed my questions well and helped me to further understand the performance of the proposed method. So I decided to change my rating to accept.", "rebuttal": "We thank Reviewer pVvf for the encouraging feedback and insightful review comments. We are glad that you found our work to be simple, straightforward, and of high surface quality. We address your concerns in detail below.\n\n-----\n\n### **Scenes without Atlanta assumption.** \n>  W1: Atlanta World assumption is, from my point of view, would break in many cases, e.g., indoor space at the roof floor where the ceiling is not parallel with the ground, a cinema or theater where the ground steps down, a modern design art museum with complex non-plane structured ceiling and even walls which is not plane at all. In that case, the 3D Global Planar Regularization may not stand. A mechanism for dealing with such a situation is not explored in this paper.\n\nWe agree that the Atlanta-world assumption does not hold in all scenarios, and we acknowledge this as a limitation of our current work. However, our framework includes a mechanism that provides a degree of robustness for scenes that only partially adhere to this assumption.\n\nOur semantic lifting process explicitly includes an \"others\" category alongside \"wall\", \"floor\", and \"ceiling\". Any surface that is not confidently identified as one of the primary structural elements falls into this \"others\" category. These Gaussians are subsequently excluded from the planar regularization constraints. This effectively acts as a gating mechanism, ensuring that the strong geometric prior is primarily applied where strong semantic evidence exists.\n\nAs for more general scenes without such an assumption, our method still shows comparable results. The following table shows the reconstruction quality on the Tanks and Temples compared with 2DGS.\n\n|  F-score       | 2DGS | Ours |\n|-------------|------|------|\n| Barn        | 0.41 | 0.40 |\n| Caterpillar | 0.23 | 0.20 |\n| Truck       | 0.45 | 0.55 |\n| Couterhouse | 0.16 | 0.14 |\n| Meetingroom | 0.17 | 0.22 |\n| Ignatius    | 0.51 | 0.47 |\n| mean        | 0.32 | 0.33 |\n\n\n### **Surface extraction methods.** \n> Q1: I failed to find details about how the predicted 3D mesh is generated from a trained 3D Gaussian Field, whether all Gaussian Splatting-based methods mentioned in the experiments are processed with the same meshing method, or not?\n\nAll GS-based methods, except for GSRec, use the same meshing method. For GSRec, we follow the meshing method from its original paper. Specifically, GSRec performs Poisson surface reconstruction, and others (including our method) do TSDF-fusion on rendered depth maps using the Open3D package.\n\n### **Geometric accuracy of non-planar surfaces.**\n> Q2: The experiments are conducted by evaluating the global geometric reconstruction accuracy. I would like to see the geometric accuracy of non-planar surfaces using AtlantaGS, like running the same evaluation but removing walls, ceiling, and ground floor. \n\nWe evaluate the accuracy of non-planar surfaces on the ScanNet dataset and use ground-truth semantic masks to exclude planar elements like floors and walls.\n\nThe table below provides a quantitative comparison against 2DGS and MonoSDF on ScanNet. Each cell shows the mean/median performance, with arrows indicating the desired direction for each metric ($\\downarrow$ lower is better, $\\uparrow$ higher is better).\n\n\n|         | Acc $ \\downarrow $     | Comp$ \\downarrow $      | Prec$ \\uparrow $        | Recal$ \\uparrow $       | F-score $ \\uparrow $     |\n|---------|-----------|-----------|-------------|-------------|-------------|\n| MonoSDF | 7.23/5.23 | 3.76/3.38 | 72.46/75.54 | 78.98/81.56 | 75.22/78.51 |\n| 2DGS    | 9.14/8.00 | 6.41/6.63 | 60.89/64.78 | 62.11/60.78 | 61.37/62.70 |\n| Ours    | **6.95/4.88** | **3.03/2.68** | **74.04/78.26** | **83.88/87.92** | **78.49/82.87** |\n\nAs shown above, our method consistently and significantly outperforms both baselines across all five metrics, for both mean and median scores. This underscores our method not only benefits the planar surface in the Atlanta world assumption, but also the non-planar surface."}, {"review_id": "2o085CVqhF", "reviewer": "Reviewer_QZGu", "summary": "The task of this paper is to reconstruct 3D scenes from multi-view images for indoor and urban scenes. This paper points out two problems in current task: 1) The geometry priors is not global consistent while handling low-texture regions, like planes(floors/ceilings/walls) in the scenes. 2) Gaussian Splatting and implicit SDF filed methods either suffer from discontinuities and inefficient issues. To handle these issue, this paper proposed an Atlanta-world guided implicit-structured Gaussian Splatting which can achieve smoother reconstruction results while preserving high-frequency details and rendering efficiency. Experiment shows that the proposed method well alleviates the problems both qualitatively and quantitatively.\n\nIn conclusion, the problem presented in this paper is important for 3D reconstruction, and the proposed scheme is effective. I think it can bring inspiration for the reconstruction community. But due to the weakness and questions comments. I decide to give an border reject for this paper. But I feel open to adjust the score from 3 to higher if the author gives a more clearer response.", "questions": "1. I have seen an another work for urban scenes reconstruction[2], they also achieve a great results. What is difference or strength between your work and [2]?\n2. Can the latest work VGGT[3] handle the problem of “Traditional multi-view stereo methods struggle on these textureless surfaces due to the lack of distinctive” in Line 22?\n3. Was the “plane indicators” mentioned many times the same as  “plane normal”?\n4. In Line 253, you mentioned that the scheme need to decode gaussians online? Why need online operation? Isn't gaussians fixed after it has been trained? Further, how about the total GPU memory usage during inference in indoor/urban scenes and how about the additional GPU memory increased by the online decoding operation?\n5. Can the proposed scheme used to reconstruct the static scenes in autonomous driving scenario like nuscenes and waymo?\n6. In which case the proposed scheme will fail?", "limitations": "Same with weakness", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths*\n1. The studied problem is important, the technical details are complete and clearly written which I think can bring insights for the reconstruction community.\n2. The proposed method is simple but effective, resulting good in both qualitative visualization results and quantitatively geometry metrics.\n\nWeaknesses*\n1. The problem is not clearly presented. According to Line 25 and 27, this paper have mentioned two problems, global inconsistency for monocular geometric priors and failure in not mutually orthogonal structures for Manhattan-world assumption. But according to Figure 1, this paper use 2DGS as baseline to present this problem, but did 2DGS use geometric priors or Manhattan-world assumption? I have searched the 2DGS paper[1], but there are not ‘prior’ or ‘Manhattan’ word in the paper. So Did the problem present by Figure 1 stem at these prior? Actually, I only realize the discontinue issue in ScanNet part in Figure 1.\n2. In the experiment, this paper only present the geometry metrics, but how about the semantics metrics after reconstruction like PSNR/SSIM/LPIPS and how about the qualitative results of the semantics reconstruction? Further, can you provide the training time and FPS in Table 3 in urban scenes like Table 2? \n3. The rendering efficiency of the scheme seems affected a lot by the newly proposed component.", "was_revised": true, "final_justification": "All of the questions and weaknesses 2&3, have been adequately addressed and clarified in the rebuttal. \nHowever, weakness 1 and its corresponding rebuttal still leave me confused. \n1.I am still confused about the issue of “global inconsistency for monocular geometric priors”. Since Figure 1 does not clarify this issue, it seems that the paper does not formally address it either, neither in a visual nor a mathematical way. \n2. In the rebuttal, you mentioned that the problem in Figure 1 “doesn't result from priors but from the discrete nature of Gaussian splatting in low texture regions.” To validate this, you conducted an experiment removing priors from 2DGS, but this experiment does not seem to be related to the issue you are trying to validate. It seems that what you are validating is just whether the performance of 2DGS without priors worsens. \n3. Base on the second point, in the rebuttal experiment, you removed priors from 2DGS. Which priors were removed? I also asked in my weakness whether 2DGS uses priors, but it seems that this was not clarified in the rebuttal.\n\nOverall, the rebuttal has addressed most of my concerns, but there are still some issues mentioned above that leave me confused. Therefore, I would like to keep my original rating.\n\nFinal justification again.\nActually, after reading the authors' rebuttal, I am still somewhat confused about the geometry prior and related issues. However, considering that I am not a specialist in this particular field (2DGS), other reviewers who are more familiar with this area may have a better understanding of these issues. At the same time, given the paper's strong performance both qualitatively and quantitatively, I believe the methods presented will contribute positively to the field of 2DGS. As a result, I have decided to raise the paper's score from \"borderline reject\" to \"borderline accept.\"", "rebuttal": "We thank Reviewer QZGu for the valuable review comments. We are encouraged that you found our work both simple and effective, good in both qualitative and quantitative results. We address your concerns in detail below.\n\n---\n\n###  **Geometry priors are not the cause of the problem presented by Figure 1.**\n> W1: So Did the problem present by Figure 1 stem at these prior? Actually, I only realize the discontinue issue in ScanNet part in Figure 1.\n\nThe broken and distorted surface of 2DGS in Figure 1 doesn't result from priors but from the discrete nature of Gaussian Splatting in low-texture regions. To validate this, we perform an ablation study by removing geometric priors from the 2DGS framework. The results are shown below.\n\n|   | Acc$\\downarrow$| Comp$\\downarrow$  | Prec$\\uparrow$ | Recal$\\uparrow$| F-score$\\uparrow$|\n|-----------------|-----------|-----------|-------------|-------------|-------------|\n| 2DGS w/ priors  |     11.46 |     13.89 |       43.15 |       36.17 |       39.27 |\n| 2DGS w/o priors |     15.64 |     14.93 |       39.82 |       38.06 |       38.81 |\n\nAs shown in the table above, Acc and Comp are lower compared to the case without geometry priors.\n\n\n\n### **Rendering efficiency and online decoding** \n> Q4: In Line 253, you mentioned that the scheme need to decode gaussians online? Why need online operation? Isn't gaussians fixed after it has been trained? Further, how about the total GPU memory usage during inference in indoor/urban scenes and how about the additional GPU memory increased by the online decoding operation?\n\n> W3: The rendering efficiency of the scheme seems affected a lot by the newly proposed component.\n\nDecoding online means that at each training step, we need to decode all Gaussians from the voxel grid with an MLP. After training, the Gaussians are fixed, and we can preextract the view-independent attributes, which will reduce the memory footprint and improve the rendering performance. \n\nThe total memory required for inferencing is approximately 1.06 GB for scene0050_00 and 2.24 GB for the matrixcity block6 with the online decoding operation. By pre-extracting the Gaussians, memory usage is reduced by approximately 300 MiB for the indoor scene and 700 MiB for the urban scene.\n\nWhile preparing this rebuttal, we re-validated our experiments and discovered a CUDA-synchronization error with considering I/O in our original rendering speed evaluation. We sincerely apologize for this oversight and provide the corrected results below.\n\nThe following table compares the rendering performance (in FPS) of our method against other approaches on both indoor and urban scenes. We report speeds using pre-extracted features and speeds in brackets that include online feature decoding.\n\n|    FPS     | Scene0050_00 | Block6 |\n|-------------|---------------------------|-------------------|\n| GSRec       | 264                       | 260               |\n| Scaffold-GS | 282                       | 200               |\n| Ours (Online decoding)       | 180                | 90         |\n| Ours (Per-extracted)       | 280                | 191         |\n\nOn both indoor and urban scenes, the online decoding operation leads to a significant performance drop; however, with pre-extraction, the rendering performance is comparable to our methods.\n\n\n### **Rendering, semantic segmentation quality, and training time, rendering speed for urban scenes.**\n> W2: In the experiment, this paper only present the geometry metrics, but how about the semantics metrics after reconstruction like PSNR/SSIM/LPIPS and how about the qualitative results of the semantics reconstruction? Further, can you provide the training time and FPS in Table 3 in urban scenes like Table 2?\n\nWe report the rendering quality and semantic reconstruction quality in Section A.5 of the supplementary material. And here're the results excerpted from the supplementary material.\n\nThe following table shows the rendering quality and semantic quality, respectively. And IoUw, IoUf, IoUc represent the intersection of the union of the wall, floor, and ceiling, respectively. \n\n| Replica         | PSNR  | SSIM   | LPIPS  | ScanNet++       | PSNR  | SSIM   | LPIPS  |\n|-----------------|-------|--------|--------|-----------------|-------|--------|--------|\n| ScaffoldGS   | 38.08 | 0.9660 | 0.0961 | ScaffoldGS   | 18.25 | 0.7749 | 0.2764 |\n| 2DGS         | 41.59 | 0.9823 | 0.0464 | 2DGS         | 21.87 | 0.8114 | 0.3060 |\n| DN-Splatter | 29.02 | 0.8967 | 0.2312 | DN-Splatter | 22.76 | 0.8226 | 0.2971 |\n| GSRec       | 36.00 | 0.9574 | 0.1205 | GSRec       | 22.96 | 0.8314 | 0.2708 |\n| Ours            | 39.58 | 0.9756 | 0.0766 | Ours            | 22.51 | 0.8321 | 0.2517 |\n\n| Replica     | IoUw  | IoUf  | IoUc  | ScanNet++   | IoUw         | IoUf         | IoUc         |\n|-------------|-------|-------|-------|-------------|--------------|--------------|--------------|\n| Mask2former | 0.628 | 0.823 | 0.900 | Mask2former | 0.6945714286 | 0.7802857143 | 0.7674285714 |\n| Ours        | 0.701 | 0.846 | 0.927 | Ours        | 0.7317142857 | 0.8581428571 | 0.7771428571 |\n\nWe use block6 in MatrixCity to test the performance and training time. The training time is 37 minutes, and the rendering speed could reach 191 FPS with per-extraction.\n\n### **Differences or strengths between our work and [2].**\n> Q1: What isthe  difference or strength between your work and [2]?\n\nSorry, there's no reference about [2]. We suppose that you may refer to CityGaussian, which is an urban scene reconstruction method. These urban scene reconstruction methods mainly focus on the problem that is how to reduce memory footprint and maintain the rendering efficiency, and some partitioning or compression methods have been developed. And in our method, we mainly focus on the surface reconstruction and don't take these problems into consideration. \n\n### **The reconstruction quality of VGGT.**\n> Q2: Can the latest work VGGT[3] handle the problem of “Traditional multi-view stereo methods struggle on these textureless surfaces due to the lack of distinctive” in Line 22?\n\nWhile VGGT shows powerful reconstruction ability and short inference time, it can provide the desired reconstruction quality on these textureless regions, in which the geometry is simple and easy to estimate. We perform the experiments on ScanNet and Replica with 50 images at a resolution of 518 due to limited GPU memory. Before we evaluate the geometry reconstruction quality, we first use the input pose and ground truth pose to align the point cloud from VGGT, and then use ICP to refine the transformation matrix. The reconstruction quality is shown as follows. As a result, VGGT shows comparable results and higher speed with feed feed-forward model.\n| Replica/ScanNet  | Acc$ \\downarrow $| Comp$ \\downarrow $  | Prec$ \\uparrow $ | Recal$ \\uparrow $| F-score$ \\uparrow $|\n|-----------------|-----------|-----------|-------------|-------------|-------------|\n| VGGT  | 3.14/3.76 | 8.59/6.14 | 84.99/84.99 | 73.06/73.29 | 78.39/76.40 |\n| Ours  | 2.25/3.62 | 4.08/3.93 | 93.18/80.31 | 82.22/75.85 | 87.35/77.98 |\n\n### **The “plane indicators” mentioned many times are not the same as “plane normal”.**\n> Q3: Was the “plane indicators” mentioned many times the same as “plane normal”?\n\nPlane indicators are not plane normal but the plane equation. As mentioned in L165, we define explicit plane indicators with a gravity direction and two distance offsets to represent the floor and ceiling.\n\n### **More results on the autonomous driving scenario.** \n> Q5: Can the proposed scheme used to reconstruct the static scenes in autonomous driving scenario like nuscenes and waymo?\n\nWe perform our experiments on 3 static sequences in the Waymo Open Dataset and compare our method with 2DGS, and evaluate the reconstruction results with the GT lidars. We report the Chamfer Distance in meters and F-score with a 0.5m threshold. As shown in the table below, our method shows better accuracy of surface reconstruction than 2DGS.\n\n| Waymo | CD(m)           | F-score     |\n|-------|--------------|--------------|\n| 2DGS  | 1.29 | 44.55 |\n| Ours  | 0.96 | 63.43 |\n\n### **The proposed scheme will fail when the segmentation model predicts the wrong label.**\n> Q6: In which case the proposed scheme will fail?\n\nOur method uses a segmentation model to distinguish structural elements, such as walls, ceilings. If the segmentation model predicts the wrong label, such as walls being recognized as ceilings, the plane indicators will be biased by wrong-labeled structures, and the surface reconstruction quality of these structural elements may be degraded."}, {"review_id": "x9RjNyzNW9", "reviewer": "Reviewer_p8vj", "summary": "* For the reconstruction of indoor and urban scenes, a geometric prior that can properly restore low-texture regions is necessary, and a new representation is required that overcomes the limitations of GS and SDF.\n* First, a good geometric prior can be created by introducing the concept of the Atlanta world model. The Atlanta world model assumes that the vertical direction appears only in the direction perpendicular to the surface, and is applied to most indoor or urban scenes. Using this assumption, proper surface reconstruction is possible even in low-texture regions through regularization.\n* The authors proposed an implicit-structured Gaussian representation that can perform efficient rendering while preserving details effectively. By embedding an implicit voxel grid, both the accuracy and efficiency of surface reconstruction are improved.", "questions": "In Equation 10, many hyperparameters are used to calculate the loss. I wonder if there is an analysis on how the performance changes depending on the value of each hyperparameter. Also, $\\lambda_{sem}$ in L202 should be changed to $\\mathcal{L}_{sem}$.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths\n* The authors demonstrated higher reconstruction quality than existing 3D reconstruction models by utilizing the Atlanta world model, which well represents the characteristics of cuboid-shaped indoor rooms or urban cities consisting of buildings.\n* The authors stated the limitations of existing 3D representations and proposed a mixed version called implicit-structured Gaussian splitting.\n\n## Weaknesses\n* The prime concern of the work is the limited scope of the proposed model.  As stated in the paper, since this method is based on the Atlanta world model assumption, it cannot be applied to more complex scenes with complicated objects. When experimenting with a dataset where the Atlanta assumption is valid, it is trivial to observe that the proposed method outperforms existing methods. However, the scenarios to which this assumption is applied are quite limited, and the performance of AtlasGS may be inferior to existing models in real-world scenarios. The author should demonstrate that the model can achieve comparable performance to more general scenes with complex objects, thereby validating the contribution of the work.\n* In implicit structured GS, is a Gaussian predicted for every voxel in a predefined voxel grid? If so, what is the total number of voxels ($N_v$) and the number of GSs estimated for each voxel ($K$)? If a fixed number of GSs is created for every voxel instead of estimating valid anchors (Scaffold-GS), it will generate many redundant Gaussians and become memory-inefficient. This can be seen by comparing the memory cost difference between AtlasGS and other models.\n* How are the values of depth and normal calculated? Are they computed through alpha-blending, as in Equation 1? If so, the rendered depth and normal vector might be vulnerable to the attribute of Gaussian splats in the back, which should not be considered in real measurements.", "was_revised": true, "final_justification": "My major concern is the Atlanta world assumption would hinder the performance of other scenes where the ratio of such segments (floor, wall, and ceiling) is not high. During the rebuttal, the authors demonstrated that their model does not affect the performance even if the most of the scene consists of objects where Atlanta world assumption does not hold. Also, the authors acknowledged that the proposed module will cost a computational overhead but showed the overhead is marginal and it still can run in real time.", "rebuttal": "We thank Reviewer p8vj for the valuable review comments. We are encouraged that you found our work to have higher reconstruction quality. And we have to apologize for the typos in our paper, and we will fix them in the final version. We address your concerns in detail below.\n\n-----\n\n### **The limited scope of the proposed model.**\n> W1: The prime concern of the work is the limited scope of the proposed model. As stated in the paper, since this method is based on the Atlanta world model assumption, it cannot be applied to more complex scenes with complicated objects. When experimenting with a dataset where the Atlanta assumption is valid, it is trivial to observe that the proposed method outperforms existing methods. However, the scenarios to which this assumption is applied are quite limited, and the performance of AtlasGS may be inferior to existing models in real-world scenarios. The author should demonstrate that the model can achieve comparable performance to more general scenes with complex objects, thereby validating the contribution of the work.\n\nOur method specifically targets the challenging problem of surface reconstruction in indoor and urban scenes, environments prevalent in daily life and often poorly addressed by existing literature. General-purpose methods, such as 2D Gaussian Splatting (2DGS), frequently falter in these settings due to the common presence of low-texture regions. The integration of an Atlanta-world model provides a crucial global geometric constraint, ensuring consistent surface reconstruction in these difficult scenarios.\n\nHowever, it's important to clarify that this focus does not restrict our method's applicability. To demonstrate its performance in general scenes, we conducted a comparative analysis on the Tanks and Temples dataset, a standard benchmark for general-purpose reconstruction. Our reported F-score results indicate that our method achieves comparable performance to established techniques, thereby addressing concerns regarding its generalization capabilities.\n\n|    F-score   | 2DGS | Ours |\n|-------------|------|------|\n| Barn        | 0.41 | 0.40 |\n| Caterpillar | 0.23 | 0.20 |\n| Truck       | 0.45 | 0.55 |\n| Couterhouse | 0.16 | 0.14 |\n| Meetingroom | 0.17 | 0.22 |\n| Ignatius    | 0.51 | 0.47 |\n| mean        | 0.32 | 0.33 |\n\n### **Memory analysis.**\n\n> W2: In implicit structured GS, is a Gaussian predicted for every voxel in a predefined voxel grid? If so, what is the total number of voxels and the number of GSs estimated for each voxel? If a fixed number of GSs is created for every voxel instead of estimating valid anchors (Scaffold-GS), it will generate many redundant Gaussians and become memory-inefficient. This can be seen by comparing the memory cost difference between AtlasGS and other models.\n\nIn implicit structured Gaussian, a fixed number $K$ of Gaussians is predicted for each voxel in the voxel grid; however, the voxel grid is not predefined. We initialize the voxel grid with a sparse point cloud, then we generate new voxels with gradient-based densification following Scaffold-GS, and prune the voxel if the opacities of all the Gaussians are lower than a threshold. In our experiments, we set $K$ to 10. \n\nWhen compared to Scaffold-GS, our method consumes slightly more memory during training, which is a deliberate trade-off. Scaffold-GS reduces memory by estimating only a subset of valid anchors, but this strategy can inadvertently mask visible Gaussians, leading to depth inconsistencies across views and a slight degradation in performance.  But compared with 2DGS, our method is relatively memory-efficient, because 2DGS grows redundant Gaussians in a single voxel, while ours only allows limited Gaussians.\n\n|   Memory   | scene0050_00(Indoor) | matrixcity block6 (Urban) |\n|-------------|---------------------------|-------------------|\n| 2DGS | ~3.6GiB| ~12GiB |\n| GSRec       | ~2GiB / ~20GiB             | ~2.6G /  ~20GiB   |\n| Scaffold-GS | ~1.3GiB                     | ~3.5 GiB             |\n| ours        | ~2GiB                     | ~3.5 GiB            |\n\n\n### **Biased depth caused by alpha blending.**\n> W3: How are the values of depth and normal calculated?\n\nIn our framework, we use mean depth and mean normal, which are obtained from alpha blending as mentioned in 2DGS. \nA well-known artifact in volume rendering, used by both NeRF and Gaussian Splatting, is biased depth. Because the rendered depth for a pixel is a weighted average of all samples along a ray, it can be influenced by points in front of or behind the true surface.\nTo alleviate biased depth, our framework combines two techniques. First, we apply the distortion loss from 2DGS to promote a compact opacity distribution. Second, our 3D Global Planar Regularization aligns floor and ceiling Gaussians with a single surface by explicitly regularizing their positions.\n\n### **Hyperparameter analysis.**\n> Q1: How the performance changes depending on the value of each hyperparameter?\n\nTo analyze the impact of key hyperparameters, we conducted a series of ablation studies on the ScanNet (scene0050) dataset. We focused on the weights for the depth prior $\\lambda_{depth}$，normal prior  $\\lambda_{normal}$, distortion loss $\\lambda_{dist}$, and our regularization loss $\\lambda_{reg}$. When changing one value, the other one remains the same. The results, presented in the tables below, demonstrate that our chosen hyperparameters are well-justified and that each component contributes positively to the final reconstruction quality.\n\nThe distortion loss encourages compact ray sampling along the viewing direction. Increasing its weight from 1.0 to 10.0 results in a noticeable improvement in all metrics. This suggests that a stronger distortion penalty leads to a more coherent and less noisy surface representation. The performance saturates when increasing the weight further to 100.\n\n| scene           | Acc  | Comp | Prec  | Recal | F-score |\n|-----------------|------|------|-------|-------|---------|\n| $\\lambda_{dist}$ = 1.0   | 3.40 | 3.68 | 81.15 | 78.73 |   79.92 |\n| $\\lambda_{dist}$ = 10  | 3.35 | 3.58 | 82.33 | 79.72 |   81.01 |\n| $\\lambda_{dist}$ = 100 | 3.26 | 3.63 | 83.00 | 79.13 |   81.02 |\n\nOur proposed regularization term also plays a vital role. With a minimal weight of 0.001, the performance is suboptimal. As we increase the weight, performance improves, peaking at $\\lambda_{reg}$=0.1 with the best F-score of 81.02. However, if the weight becomes too large, the performance begins to decline. This is because an excessively large loss of weight can pull the structural Gaussians too strongly towards the initial planes, potentially causing the entire structure to converge to an incorrect plane.\n\n| scene               | Acc  | Comp | Prec  | Recal | F-score |\n|---------------------|------|------|-------|-------|---------|\n| $\\lambda_{reg}$ = 0.001 | 3.59 | 4.12 | 78.90 | 74.80 |   76.80 |\n| $\\lambda_{reg}$ = 0.05  | 3.32 | 3.60 | 82.34 | 78.22 |   80.23 |\n| $\\lambda_{reg}$ = 0.1   | 3.26 | 3.63 | 83.00 | 79.13 |   81.02 |\n| $\\lambda_{reg}$ = 0.2   | 3.41 | 3.83 | 80.72 | 77.39 |   79.02 |\n\nAs the following tables show, incorporating and appropriately weighting geometric priors is crucial for high-quality surface reconstruction. These priors improve the results by directly affecting the Gaussian positions and by helping to train the plane indicators, which provide better structural regularization for the scene.\n\n| scene             | Acc  | Comp | Prec  | Recal | F-score |\n|-------------------|------|------|-------|-------|---------|\n| $\\lambda_{depth}$ = 0.01 | 3.80 | 4.29 | 77.68 | 73.81 |   75.70 |\n| $\\lambda_{depth}$ = 0.1  | 3.40 | 3.96 | 80.01 | 75.69 |   77.79 |\n| $\\lambda_{depth}$ = 0.2  | 3.33 | 3.62 | 82.29 | 78.35 |   80.27 |\n\n\n| scene               | Acc  | Comp | Prec  | Recal | F-score |\n|---------------------|------|------|-------|-------|---------|\n| $\\lambda_{normal}$ = 0.01  | 3.45 | 3.73 | 79.85 | 76.90 |   78.34 |\n| $\\lambda_{normal}$ = 0.1   | 3.26 | 3.63 | 83.00 | 79.13 |   81.02 |\n| $\\lambda_{normal}$ = 0.2   | 3.30 | 3.68 | 83.12 | 79.63 |   81.34 |"}]

Author rebuttal:

Meta-review: The reviewers value that the "MLP head for regularization is new in this context and neat regularization term" (3sjd), the method is "simple, straightforward, and presented in a clear way" (3sjd), simple and effective (QZGu), important and clearly written (QZGu), that the experients are convincing (3sjd), and prove to be effictive in indoor and outdoor datasets (pVvf). 

A major critique from reviewers was the loss of generality due to the Atlanta World assumption (3sjd, pVvf, p8vj). However, in the rebuttal response to reviewer pVvf, the authors have shown that their method also works well on the general Tanks and Temples scenes. 

Overall the remainig concerns were resolved and all reviewers vote for accepting the paper. Therefore, the AC recommends the paper for acceptance.
Decision: Accept (poster)