DOGS: Distributed-Oriented Gaussian Splatting for Large-Scale 3D Reconstruction  Via Gaussian Consensus

Authors: yu  chen
hee  gim
  lee
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-06 06:47:10

Abstract: The recent advances in 3D Gaussian Splatting (3DGS) show promising results on the novel view synthesis (NVS) task. With its superior rendering performance and high-fidelity rendering quality, 3DGS is excelling at its previous NeRF counterparts. The most recent 3DGS method focuses either on improving the instability of rendering efficiency or reducing the model size. On the other hand, the training efficiency of 3DGS on large-scale scenes has not gained much attention. In this work, we propose DoGaussian, a method that trains 3DGS distributedly. Our method first decomposes a scene into $K$ blocks and then introduces the Alternating Direction Method of Multipliers (ADMM) into the training procedure of 3DGS. During training, our DoGaussian maintains one global 3DGS model on the master node and $K$ local 3DGS models on the slave nodes. The $K$ local 3DGS models are dropped after training and we only query the global 3DGS model during inference. The training time is reduced by scene decomposition, and the training convergence and stability are guaranteed through the consensus on the shared 3D Gaussians. Our method accelerates the training of 3DGS by $6+$ times when evaluated on large-scale scenes while concurrently achieving state-of-the-art rendering quality. Our code is publicly available at [https://github.com/AIBluefisher/DOGS](https://github.com/AIBluefisher/DOGS).

Main paper: 
 introduction: 
 Neural 3D scene reconstruction has taken a giant step beyond the limitations of traditional photogrammetry tools. Neural radiance fields (NeRFs) [36, 17, 47] , which encode scenes implicitly in MLP or explicitly in voxels, exhibit superior resilience to non-Lambertian effects, appearance changes, dynamic scenes, etc. However, most NeRF-based methods are inefficient in rendering scenes due to the need to query massive points for volume rendering to infer scene geometry and color. Recently, 3D Gaussian Splatting (3DGS) [21] has shown promising results on real-time applications and inspires many follow-up works. 3DGS encodes scenes into a set of 3D anisotropic Gaussians, where each 3D Gaussian is represented by a covariance matrix, a center position, opacity, and the latent features to encode color information. Pixel colors by projecting 3D Gaussians into 2D image space can be efficiently computed via rasterization, which is highly optimized on modern graphics processors. However, 3DGS often requires larger memory during training compared to NeRF methods. This is because 3DGS needs millions of 3D Gaussians to represent a scene to recover high-fidelity scene details. Consequently, the memory footprint increases drastically for training 3DGS on larger scenes, e.g. city-scale scenes. Moreover, the training of a huge number of 3D Gaussians on larger scenes leads to longer training time. Unfortunately, in comparison to NeRF where the rays can be conveniently distributed into different compute nodes, dispatching 3D Gaussians into different compute nodes is much more difficult due to the highly customized rasterization procedure of 3DGS. In summary, the two challenges for reconstructing large-scale scenes with 3DGS are: 1) High GPU memory to hold the large 3D model during training; 2) Long training time due to the large areas of scenes.Previous large-scale NeRF methods [49, 51, 35] solve the above-mentioned two issues by embracing a divide-and-conquer approach, where scenes are split into individual blocks with smaller models fitted into each block. However, these methods require querying multiple sub-models during inference, which slows down the rendering efficiency. This leads us to the following question: "Can we apply a similar methodology to 3DGS during training while querying only a global consistent model during inference?"In this work, we propose DOGS to answer the aforementioned question. Following previous largescale NeRF methods, our DOGS splits scene structures into blocks for distributed training. Inspired by previously distributed bundle adjustment methods [15, 62] , we apply the Alternating Direction Method of Multipliers (ADMM) [5] to ensure the consistency of the shared 3D Gaussians between different blocks. Specifically, we first estimate a tight bounding box for each scene. Subsequently, we split training views and point clouds into blocks. To guarantee each block has a similar size, we split scenes into two blocks each time along the longer axis of the bounding box. Scenes are split recursively in the same way until we obtain the desired number of blocks. Finally, we re-estimate a bounding box for each block and expand the bounding box to construct shared 3D Gaussians between blocks. During training, we maintain a global 3D Gaussian model on the master node and dispatch local 3D Gaussians into other slave nodes. We further guarantee the consistency of the shared 3D Gaussians and the convergence of the training through 3D Gaussian consensus. Specifically, the local 3D Gaussians are collected onto the master node and averaged to update the current global 3D Gaussian model at the end of each training iteration, and then the updated global 3D Gaussian model is shared to all slave nodes to regularize the training of local 3D Gaussians. In this way, our method guarantees that the local 3D Gaussians converge to the global 3D Gaussian model during training. By training 3DGS in a distributed way, our DOGS can reduce the training time by 6+ times compared to the original 3DGS. Furthermore, our DOGS guarantees training convergence and therefore achieves better rendering quality than its counterparts with the 3D Gaussians consensus in the distributed training. After training, we can drop all local 3D Gaussians and maintain only the global 3D Gaussians. During inference, we only need to query the global model while maintaining the rendering performance of 3DGS.Our contributions are summarized as follows:• We propose a recursive approach to split scenes into blocks with balanced sizes.• We introduce a distributed approach to train 3D Gaussians for large-scale scenes. The training time is reduced by 6+ times compared to the original 3DGS.• We conduct exhaustive experiments on standard large-scale datasets to validate the effectiveness of our method.Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: Refer to the abstract and the last paragraph of Sec. 1 for our contribution.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
related work: 
 Neural Radiance Fields. Neural radiance fields [36] enable rendering from novel viewpoints with encoded frequency features [50] . To improve training and rendering efficiency, follow-up works [27, 59, 17] either encodes scenes into sparse voxels, or a multi-resolution hash table [37] where the hash collision is implicitly handled during optimization. TensoRF [6] uses CP-decomposition or VM-decomposition to encode scenes into three orthogonal axes and planes. While the previously mentioned work focuses on per-scene reconstruction, other methods also focus on the generalizability of NeRF [54, 7, 19, 46, 28] , bundle-adjusting camera poses and NeRF [25, 34, 8] , and leveraging sparse or dense depth to supervise the training of NeRF [56, 14, 42] , etc. To address the aliasing issue in vanilla NeRF, Mip-NeRF [1] proposed to use Gaussian to approximate the cone sampling, the integrated positional encodings are therefore scale-aware and can be used to address the aliasing issue of NeRF. Mip-NeRF360 [2] further uses space contraction to model unbounded scenes. Zip-NeRF [3] adopted a hexagonal sampling strategy to handle the aliasing issue for Instant-NGP [37] .NeRF2NeRF [18] and DReg-NeRF [9] assumes images are only available during training in each block, and they propose methods to register NeRF blocks together.Gaussian Splatting. Gaussian Splatting [21] initializes 3D Gaussians from a sparse point cloud.The 3D Gaussians are used as explicit scene representation and dynamically merged and split during training. Real-time novel view synthesis is enabled by the fast splatting operation through rasterization. Scaffold-GS [31] initializes a sparse voxel grid from the initial point cloud and encodes the features of 3D Gaussians into corresponding feature vectors. The introduction of the sparse voxel reduced the Gaussian densities by avoiding unnecessary densification on the scene surface. Octree-GS [41] introduces the level-of-details to dynamically select the appropriate level from the set of multi-resolution anchor points, which ensures consistent rendering performance with adaptive LOD adjustment and maintains high-fidelity rendering results. To reduce the model size, methods [16, 38] also remove redundant 3D Gaussians through exhaustive quantization. Other methods also focus on alleviating the aliasing issue of 3D Gaussians [60, 58] , or leveraging the efficient rasterizer of point rendering for real-time indoor reconstruction [20, 33] .Large-Scale 3D Reconstruction. The classical photogrammetry methods utilized Structure-from-Motion (SfM) [43] and keypoint extraction with SIFT [30] to reconstruct sparse scene structures. One of such foundational software is Phototourism [45] . To handle city-scale scenes, the 'divideand-conquer' strategy is widely adopted for the extensibility and scalability of the 3D reconstruction system. SfM methods [4, 63, 10, 12, 11] splitting scenes based on the view graph, where images with strong connections are divided into the same block. By estimating similarity transformations and merging tracks, all local SfM points and camera poses are fused into a global reference system. Existing NeRF methods also follow a similar strategy for reconstructing city-scale scenes. When camera poses are known, the scene can be split into grid cells. Block-NeRF [49] focus on the day-night or even cross-season street views. It utilizes the appearance encoding in NeRF-W [32] to fix the appearance inconsistency issue between different blocks, while Mega-NeRF [51] aims at encouraging the sparsity of the network under aerial scenes. Urban-NeRF [40] leverages lidar points to supervise the depth of NeRF in outdoor scenes. SUDS [52] further extended Mega-NeRF into dynamic scenes. Different from previous large-scale NeRF methods, Switch-NeRF [35] uses a switch transformer that learns to assign rays to different blocks during training. Grid-NeRF [57] designed a two-branch network architecture, where the NeRF branch can encourage the feature plane [6] branch recover more scene details under large-scale scenes. However, the two-branch training scheme is trivial and needs a long time to train. Concurrent works to our method are VastGaussian [26] and Hierarchy-GS [22] , which also utilize 3D Gaussians for large-scale scene reconstruction. VastGaussian and Hierarchy-GS split scenes into independent chunks and train independent chunks simultaneously. However, VastGaussian relies on exhaustive searching of the training views and initial points to guarantee the convergence of training, and each block is trained without data sharing. Hierarchy-GS consolidates independent chunks into intermediate nodes for further rendering. However, the hierarchical approach needs to preserve redundant models and it is specially designed for street view scenes. Our method, on the other hand, focuses on the distributed training of 3DGS and built upon the consensus of shared 3D Gaussians between different blocks has a guaranteed convergence rate that achieves better performance.3 Our MethodThe first constraint is proposed to ensure that: 1) Each block can be fed into GPUs with the same capacity. This is important since a larger block can cause an out-of-memory of the GPU during training due to the imbalanced splitting results. 2) Each block has a similar training time at each iteration. After every t iteration, we collect all local 3D Gaussians from each block. Intuitively, larger blocks require a longer time to train. Consequently, the master node and all other slave nodes have to wait for the nodes with larger blocks to finish, which increases the training time unnecessarily.The second constraint is used to boost the convergence of ADMM. From Eq. (8b), the local 3D Gaussians would converge to the global 3D Gaussians by averaging the shared local 3D Gaussians during training. Sufficient shared 3D Gaussians encourage reconstruction consistency between different blocks. Too many shared local 3D Gaussians can bring more communication overhead, which inevitably slows down the training while a lack of shared 3D Gaussians leads to divergence of the algorithm. Although there is no theoretical analysis to show the optimal value of overlapping parts, we empirically use a constant value which we will introduce later in our experiments. We assume one of the axes of the scene is aligned to physical ground, which can usually be done under the Manhattan world assumption. VastGaussian [26] adopts a grid-splitting method that first splits the scene into m cells along the x-axis, and then splits each of the m cells into n sub-cells along the y-axis. As we show in Fig. 3a , this strategy can result in imbalanced blocks. Our splitting method is inherited from VastGaussian while adopting a recursive spitting method to resolve the imbalanced issue. Specifically, we first estimate a tight bounding box for the initial scene. We then split the scene into two parts along the longer axis of the scene. Splitting the scene along the longer axis can prevent the blocks from becoming too shallow on one axis. We re-estimate a tighter bounding box for each of the two cells and split them into smaller blocks. This step is repeated until the number of blocks reaches our requirement. We present the result of this recursive method in Fig. 3b . Compared to Fig. 3a , we produce more balanced blocks. To construct overlapping areas, we expand the bounding box of each block by a scale factor s, any points/views that are covered by the same bounding box are grouped into the same block. The training views and point clouds are split in the same way as is shown in Fig. 3c .Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes]Justification: Please refer to Sec. A.8 in the appendix for the limitations.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
preliminary: 
 Gaussian Splatting. 3D Gaussian Splatting represents a scene with a set of anisotropic 3D Gaussians G = {G i | i ∈ N }. Each 3D Gaussian primitive G i has a center u ∈ R 3 and a covariance Σ ∈ R 3×3 and can be described by:EQUATIONDuring training, the covariance is decomposed into a rotation matrix R ∈ R 3×3 and a diagonal scaling matrix S ∈ R 3×3 , i.e. Σ i = RSS ⊤ R ⊤ to ensure the covariance matrix is positive semi-definite. To render the color for a pixel p, the 3D Gaussians are projected into the image space for alpha blending:EQUATIONwhere α i is the rendering opacity and is computed byα = o • X proj (p).When training 3D Gaussian Splatting, we minimize the loss function below:EQUATIONwhere x i = {u i , q i , s i , f i , o i }, q are quaternions corresponds to the rotation matrix R, s are vectors corresponds to the three diagonal elements of S, and f are coefficients of the spherical harmonics.The 'divide-and-conquer' method is a common paradigm for large-scale 3D reconstruction, which we also adopt in our framework. Different from previous methods such as Block-NeRF [49] and VastGaussian [26] which are pipeline parallelized, our method is optimization parallelized with guaranteed convergence. The pipeline of our algorithm is shown in Fig. 2 . Firstly, we split a scene (training views and point clouds) into K intersected blocks. Secondly, we assign training views and points into different blocks. By introducing the ADMM into the training process, we also maintain a globally consistent 3DGS model on a master node. Thirdly, during training, we collect and average the local 3D Gaussians to update the global 3DGS model in each consensus step. The global 3D Gaussians are also shared with each block before we distributedly train the local 3D Gaussians in each block. Finally, we drop all local 3D Gaussians while only using the global 3D Gaussians to render novel views. In this section, we first introduce the ADMM algorithm. Subsequently, we derive the distributed 3DGS training algorithm. We also present a scene splitting algorithm, which recursively and evenly splits the scene into two blocks each time.ADMM. A general form for consensus ADMM is given by: minimizeEQUATIONBy definition, the constraints are applied such that all the local variables x i agree with the global variable z. By applying the augmented Lagrangian method, we have:EQUATIONwhere y i is the dual variable, ρ is the penalty parameter. During optimization, ADMM alternatively updates the local variables x i , global variable z and the dual variables y i at the t + 1 iteration by:EQUATIONEQUATIONEQUATION)Distributed Training. We apply the ADMM method to distributedly train a large-scale 3D Gaussian Splatting model. In our problem, f i (•) in Eq. ( 4) corresponds to the loss function L(•) in Eq. (3). To simplify the implementation for Eq. (6a), we adopt a scaled form of ADMM by defining u i = 1 ρ y i . We can then rewrite Eq. ( 5) into (see supplementary for the derivation):EQUATIONCompared to Eq. ( 5), Eq. ( 7) can be made easier to implement by expressing all terms in the squared difference errors. Suppose the variables are decomposed into K blocks, we then denote the ith 3D Gaussians in the kth block as x k i . Accordingly, we revise the ADMM updating rule by:EQUATIONEQUATIONEQUATIONEq. (8a) is the original loss function in Gaussian Splatting with an additional regularizer termρ 2 ∥(x k i ) t -z t + (u k i ) t ∥ 2 2. Note that Eq. (8b) should be z t+1 := 1 K k=1 (x k i ) t+1 + (u k i ) t . However, the dual variables have an average value of zero after the first iteration. Consequently, Eq. (8b) can be simplified as the global 3D Gaussians are formed by the average of the local 3D Gaussians from all blocks. Moreover, Eq. ( 8b) is called a 'consensus' step and it requires collecting the local 3D Gaussians from all blocks. After updating the global model z, we update the dual variables u i in Eq. (8c) and share the global 3D Gaussians z to each block for optimizing the local 3D Gaussians in Eq. (8a). Note that each 3D Gaussianx i has different properties {u i , q i , s i , f i , o i }.As a result, the penalty terms and dual variables should be represented separately according to these properties. The detailed form of Eq. ( 8) is given in the supplementary.Scene Splitting. We decompose the scene into K blocks before applying the updating rule in Eq. ( 8). Unlike VastGaussian [26] , which focuses mostly on splitting large-scale scenes and needs exhaustive search on the training views and point clouds to ensure the consistency of 3D Gaussians in different blocks, our method relies on the consensus step to ensure the consistency of the 3DGS. However, scene splitting is still important to the convergence of our method. We propose two constraints for the scene-splitting method to best balance the training efficiency and rendering quality:1. Individual blocks should have a similar size.ADMM is known to be sensitive to the initialization of penalty parameters. Since improper initial penalty parameters can slow down the training, we introduce the adaptive penalty parameters and over-relaxation to improve the convergence rate.Primal Residual and Dual Residual. We define the primal residual r t and the dual residual s t asEQUATIONIn ADMM, the primal residual and dual residual are used as the stopping criteria which terminate the optimization. In our method, we use a hard threshold of training iteration to terminate the algorithm. The primal residual and dual residual are used to adaptively adjust the penalty parameters.Adaptive Penalty Parameters. We adopt a similar scheme from [5] to adaptively adjust the penalty parameters:EQUATIONwhere µ > 1, τ inc , τ dec are hyper-parameters. The existing convergence proof of the ADMM algorithm is based on the fixed penalty parameters [5] . To guarantee the convergence of our algorithm, we stop adjusting the penalty parameters after 2000 iterations in all of our experiments.Over Relaxation. Similar to [5] , we replace x t+1 with α t x t+1 -(1 -α t )(-z t ) in Eq. (8b) and Eq. (8c), where α t ∈ (0, 2) is the relaxation parameter and experiments show that the over-relaxation with α t ∈ [1.5, 1.8] can improve convergence.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer: [Yes] Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer: [No] Justification: We will release related code and checkpoints upon the acceptance of the paper.Guidelines:• The answer NA means that paper does not include experiments requiring code. Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. • The full details can be provided either with the code, in appendix, or as supplemental material. 
experiments: 
 Datasets. We evaluate our method on the two large-scale urban datasets, the Mill19 [51]1 dataset, the UrbanScene3D [29]2 dataset, and the MatrixCity [24] dataset. Both datasets are captured by drones and each scene contains thousands of high-resolution images. During training and evaluation, we adopt the original image splitting in Mega-NeRF [51] , and downsample the images by 6+ times from the original resolution. Implementation Details. For Mill19 and UrbanScene3D, we use the camera poses provided by the official site of Mega-NeRF [51] . The y-axis of the scene is aligned to the horizontal plane by COLMAP [43] under the Manhattan world assumption. We use the CPU version of SIFT (SIFT-CPU) in COLMAP [43] to extract keypoints and match each image to its nearest 100 images using vocabulary trees. With known camera poses and keypoint matches, we further triangulate 3D points and bundle adjust them. The SIFT-CPU can extract more points than the SIFT-GPU, which can benefit the initialization of 3D Gaussians. For the original 3D Gaussian Splatting (denoted as '3DGS'), we train it in 500,000 iterations and densify it for every 200 iterations until it reaches 30,000 steps. We train both VastGaussian and our method in 80,000 iterations. The densification intervals and termination steps are the same as the 3DGS. We reimplement VastGaussian [26] since its code was not released during this work. Note that we did not implement the decoupled appearance embedding in VastGaussian, which can be used to remove floaters caused by inconsistent image appearance. We argue that we still provided a fair comparison since this module can be applied to all 3DGS-based methods. For our method, consensus and sharing are enabled every 100 iterations. We leverage the remote procedure call (RPC) framework of PyTorch [39] to implement our distributed algorithm and transmit data across different compute nodes.Results. We employ PSNR, SSIM [55] and LPIPS [61] as metrics for novel view synthesis. We compare our method against the state-of-the-art large-scale NeRF-based methods: Mega-NeRF [51] , Switch-NeRF [35] 3 , and 3DGS-based methods: 3DGS [21]4 , Fed3DGS [48] , VastGaussian [26] , Hierarchy-GS [22] . For Mega-NeRF and Switch-NeRF, we use the officially provided checkpoints on 8 blocks for evaluation. The results of Hierarchy-GS are cited from the original paper since its code has not been released during this work.We present the quantitative visual quality results in Table 1 . The training time and rendering efficiency are also provided in Table 2 . As shown in the tables, methods based on 3D Gaussians achieved better results than NeRF-based methods. Although NeRF-based methods are comparable to 3DGS methods in PSNR, the rendered images lack details in such large-scale scenes. This is also validated from Fig. 4 and Fig. 5 . Moreover, NeRF-based methods are much slower than 3DGS-based methods and take longer time to train -even if they are trained distributedly. Notably, our method achieves the best results in almost all the scenes. The original 3DGS has results comparable to ours. However, it takes 6 ∼ 8× more training time than our method. We also emphasize that we build a strong baseline of 3DGS for fair comparison: the densification interval is 200 iterations, which is 8 times more frequent than the 3DGS baseline in VastGaussian; the training iteration is 500K (in comparison, the training iteration of the 3DGS baseline is 450K in VastGaussian). VastGaussian trains 3DGS faster than our method. This is because our method requires additional time for data transmission. However, our method achieves better rendering quality than VastGaussian. Moreover, the data transmission time does not become the bottleneck of our method due to our balanced scene splitting method. Particularly, each block has a similar training time and the master node does not need to wait for a long time for the fat nodes to finish its job.To further show the applicability of our method to larger-scale scenes, we evaluated our method on the 2.7km 2 Small City scene in the MatrixCity [24] dataset, which contains 5, 620 training views and 741 validation views. We early terminated the training of the original 3DGS since it did not finish the training within two days. VastGaussian failed on this dataset since two blocks produce no 3D Gaussian primitives due to the imbalanced splitting. From Table 3 , our method achieved the best results in rendering quality. The visual qualitative results are shown in Fig. 6 .Table 1 : Quantitative results of novel view synthesis on Mill19 [51] dataset and Urban-Scene3D [29] dataset. ↑: higher is better, ↓: lower is better. The red , orange and yellow colors respectively denote the best, the second best, and the third best results. † denotes without applying the decoupled appearance encoding. Ablation Study. We ablate the effectiveness of our method and present the results in Table 4 . Our method without applying the 3D Gaussian consensus is denoted as w.o. CS, our method without adopting the self-adaptation of penalty parameters is denoted as w.o. SD, our method without adopting the over-relaxation is denoted as w.o. OR. As shown in the table, the performance drastically drops without the ADMM consensus step. Furthermore, the results without applying the self-adaptation of penalty parameters is about 1.5 dB lower than the full model in PSNR. The model without applying over-relaxation is comparable to the full model in SSIM and LPIPS but has lower PSNR. We thus employ over-relaxation in our method. We also present the qualitative differences in Fig. 7 , and it clearly shows the full model has better quality in the rendered images and geometries. We include more qualitative results in Fig. 8 to show the importance of the consensus step. We can observe that the distributed training presents noisy results without the consensus step. From the two bottom-right figures, we can observe obvious artifacts along the block boundary without the consensus step.Scenes Building Rubble Campus Residence Sci-Art PSNR ↑ SSIM ↑ LPIPS ↓ PSNR ↑ SSIM ↑ LPIPS ↓ PSNR ↑ SSIM ↑ LPIPS ↓ PSNR ↑ SSIM ↑ LPIPS ↓ PSNR ↑ SSIM ↑ LPIPS ↓ Mega-Moreover, we ablate the scale factor in constructing the overlapping areas in Table 5 . We can find that the performance of our method is improved with a larger scale factor. Our method has similar performance when the scale factor is 1.4 and 1.5. However, we select 1.4 in our experiments since a larger scale factor brings a longer time and more memory requirement. 
conclusion: 
 In this paper, we proposed DOGS, a scalable method for training 3DGS distributedly under large-scale scenes. Our method first splits scenes into multiple intersected blocks recursively and then trains each block distributedly on different workers.  
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [No] Justification: We follow related works for the setting of error bar.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. • The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).• The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors). • It should be clear whether the error bar is the standard deviation or the standard error of the mean. Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [Yes]Justification: Societal impacts is included in Sec. A.9 in the supplementary.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.• Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. • The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [NA] Justification: This paper has no such risks.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification: We included the urls and cited the papers for code and datasets used in this paper.Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.• If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. • If this information is not available online, the authors are encouraged to reach out to the asset's creators. • We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution. • For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. 
 
 Appendix: A.1 Derivation of Eq. (7)Given Eq. ( 5)EQUATION)Substitute Eq. ( 11) into Eq. ( 5), we have the scaled form ADMM:L ρ (x, z, u) = N i=1 f i (x i ) + ρ 2 ∥x i -z + u i ∥ 2 2 - ρ 2 ∥u i ∥ 2 2 A.2 Proof of Eq. (8b)The complete form of Eq. (8b) of is:EQUATIONWe denote the average of a vector with an overline. Then the consensus step for Eq. (8b) can be rewritten by:EQUATIONMoreover, averaging both sides of Eq. (8c) for the dual variables gives:EQUATION)Substituting Eq. ( 13) into Eq. ( 14) gives that ūt+1 = 0, which shows that the dual variables have average value zeros after the first iteration. Therefore, we provedz t+1 := 1 K i=1 x t+1 i .A.3 Detailed form of Eq. (8)We provide the detailed form of Eq. ( 8) in this section. Note that each 3D Gaussian can be represented by X i = {u i , q i , s i , f i , o i }, we need to apply different penalty terms to different properties of 3D GS. Specifically, the dual variables correspond to different properties of 3D GS are denoted as:EQUATIONwhere u p , u q , u s , u f , u o are respectively denote the dual variable corresponds to the mean p, the quaternion u q , the scaling matrix u s , the feature vectors to encode color information u f , and the opacity u o . Therefore, we can expand Eq. (8) as:EQUATIONEQUATIONEQUATIONWe present the algorithm for the recursive scene splitting in Alg. 1.Input: 3D points {X i }, number of blocks K.Output: Local 3D points in each block X = {X i,k } 1: Estimate a bounding box aabb which tightly covers all 3D points. Group points X k located in the same cell C k into a same block We present the algorithm for the distributed training of 3D Gaussian Splatting in Alg. 2.Note that we adopt Eq. ( 16) in our implementation.All experiments are conducted on the Nvidia RTX 6000 GPUs with 48 GB memory. For our method, we initialize the dual variables u p , u q , u s , u f , u o to zeros. For the penalty parameters, we set ρ p , ρ q , ρ s , ρ o to 1e4 and ρ f to 1e3 empirically. Though there are other choices of the initial values Algorithm 2 Distributed 3D Gaussian Training AlgorithmInput: Initial 3D Gaussians in each block {X k | k ∈ [1, K]}, consensus interval intv Output: Global 3D Gaussians z = {u i , q i , s i , f i , o i } 1: Initialize u i as 0 2: for t < T do 3:for block k < K distributedly do 4:{u t+1 i,k , q t+1 i,k , s t+1 i,k , f t+1 i,k , o t+1 i,k } := arg min f i (x i,k ) + ρ 2 ∥x t i,k -z t + u t i,k ∥ 2 2 5:if t mod intv == 0 then 6:for block k < K distributedly do 7:Send local 3D Gaussians X t+1 k to the master node 8:Apply the consensus stepz t+1 := 1 K K i=1 x t+1 i,k 9:Broadcast the global 3D Gaussians z t+1 to all slave nodes 10:for block k < K distributedly do 11:Update the dual variablesu t+1 i,k := u t i,k + x t+1 i,k -z t+1that could improve the results of our method, we found this set of values is good enough for all scenes in our experiments and we did not do more ablations on the initial values. Due to computational resources limitation, we test our method on only 5 GPU nodes, where one is the master node that maintains the global model and the others are slave nodes for training local 3D Gaussians. The performance of our method can be improved further with more GPU nodes.We present more qualitative results of our method in Fig. 9 and Fif. 10. We provide qualitative comparisons with VastGaussian in areas where blocks overlap in Fig. 10 . Both methods produce fairly consistent results. However, our method presents higher fidelity rendering results than VastGaussian near the splitting boundary, which also validated the effectiveness and importance of the consensus step.Our method can distributedly train 3D GS on large-scale scenes. However, it brings additional communication overheads to the system. Fortunately, we found the communication overhead did not slow down the training performance. This is due to our balanced splitting algorithm minimizing the synchronization time when there is a need to consensus the local 3D Gaussians from all blocks. Moreover, we pruned unnecessary small 3D Gaussians to further reduce the number of 3D GS, which also reduced the communication overhead.Though our method can train large-scale scenes efficiently, the GPU memory requirement can still be an issue. This is because when we zoom out to capture larger areas, more 3D Gaussians are included in the rasterization step, which consumes more GPU memory. Our future work will consider introducing the level-of-details (LOD) technique into our distributed training pipeline. Similar to existing LOD GS methods [41, 44] , LOD can be utilized to reduce the number of 3D Gaussians that are far away from the cameras.Training and Waiting Time of Each Block. We tested the time cost from transferring the data to the master node to receiving data from the master node for each slave node on the Campus dataset. The mean and variance of time are respectively 5.63 seconds and 0.75 seconds each time. The low variance indicates that our method can balance the training time well. We argue that the data transfer time of our method can be kept constant since we can always control the number of local Gaussians to a constant number (e.g. <= 6000, 000 3D Gaussian primitives) with enough GPUs, no matter how large the scene is, since the data transfer between different slave nodes and the master node is executed distributedly instead of sequentially. Implementation Flexibility. One another issue with our method is that the implementation of our method is not as flexible as VastGaussian. Our method relies on an RPC module for the data transmission and communication between the master node and the slave nodes. On the other hand, VastGaussian can be implemented decentralized without the master node. However, our method can render higher-quality images and the communication overheads can be neglected compared to the long training time of the original 3D GS. Therefore, this is not a limitation of our work.Shift to Other 3D GS Representations. Many follow-up works improved the original 3D GS. Some works focus on compressing the size of 3D GS [16, 38] and some of the other works focus on constraining the training without changing the optimization parameters [64, 23, 13] . These methods can also be applied to the training of each block in our method. Some other works also adopted intermediate representations to improve the original 3D GS, i.e., OctreeGS [41] decoded the properties of 3D GS from the feature embedding in each anchor node, and SAGS [53] adopts hash encodings for each 3D Gaussian, a GNN encoder, and a corresponding decoder to generate the properties of 3D Gaussians. In this case, we can change the optimization parameters and the corresponding penalty parameters and dual variables to these intermediate feature embeddings/encodings. In our future work, we will consider a more consolidated implementation that can easily shift to these 3D GS representations.Comparison to Concurrent Works. 1) VastGaussian [26] focuses mostly on the data splitting strategy and guaranteeing the consistency of different 3D Gaussians can also be a challenge in different scenes. However, our method ensured the consistency of the shared 3D Gaussians through the 3D Gaussian consensus with only a quite simple splitting approach. Nonetheless, the data splitting approach in VastGaussian can be introduced into our framework to enhance the robustness. Moreover, the decoupled appearance encoding can also be applied to our method to reduce floaters. Our work and VastGaussian are thus complementary to each other. 2) Hierarchy-GS [22] also trains 3DGS distributedly in different grid cells. However, Hierarchy-GS focuses more on the rendering speed by designing a hierarchical tree structure for 3D Gaussians. During training, the generated hierarchy is loaded and optimized by randomly selecting a training view and a target granularity. After training all individual chunks, Hierarchy-GS first runs a coarse initial optimization on the full dataset and adds an auxiliary skybox. This coarse model serves as a minimal basis for providing backdrop details for parts of the scene that are outside of a chunk. When consolidating different chunks, a 3D Gaussian primitive is deleted if it is associated to-but outside-chunk and is closer to another chunk to maintain the consistency of 3D Gaussians. The naive pruning approach neglects the gradient flow of the 3D Gaussians to other 3D Gaussians that are inside only in an associated chunk. Therefore, its rendering quality can be worse than VastGaussian and our method. Nonetheless, its hierarchical LOD approach can still serve as a good complement to our method and VastGaussian.Social Impact. DOGS, VastGaussian and Hierarchy-GS focus on different parts of training 3D GS on large-scale scenes and therefore are complementary to each other. These methods can be consolidated into a more robust and scalable system to open a new world in city-scale 3D reconstruction. Our method, however, requires an additional master node for controlling the training of the 3DGS, which consumes more GPU resources.NeurIPS Paper Checklisthttps://github.com/cmusatyalab/mega-nerfhttps://vcc.tech/UrbanScene3Dhttps://github.com/MiZhenxing/Switch-NeRFhttps://github.com/graphdeco-inria/gaussian-splatting 


Decision: The paper received good scores, and the authors-reviewers engaged in a productive discussion during the rebuttal phase. The consensus is to accept the paper. 

The paper presents an ADMM-based solution to split any large scene reconstruction into multiple small/local GS reconstruction tasks while maintaining consensus using a global GS solution using ADMM for synchronization. All the reviewers liked the approach and appreciated the 6x improvement in computation. Questions around the role of the global node and comparisons with alternatives (VastGS, etc.) were resolved in the rebuttal phase. Authors are encouraged to add additional clarifications while preparing the final version of the submission.

Reviews: review: paper_summary: paper_summary: The paper presents DoGaussian, a novel method for accelerating the training of 3D Gaussian Splatting models for large-scale 3D scene reconstruction. It introduces a distributed training approach using scene decomposition and the ADMM, resulting in a 6x faster training time while maintaining high-quality rendering. The method involves maintaining a global 3DGS model on a master node and local models on slave nodes, with a consensus mechanism ensuring consistency across models. Experiments on standard large-scale datasets confirm the effectiveness of DoGaussian.
strength_weakness: strength_weakness: 1. The qualitative comparisons are not that convincing, especially compared with the original 3DGS and vastGaussian. The authors are encouraged to provide more results in the rebuttal. I will raise the score accordingly.
2. The training and inference speed of DoGaussian is slightly slower than vastGaussian.
3. More baselines should be included, such as [Fed3DGS](https://arxiv.org/pdf/2403.11460).
questions: questions: Can you provide more qualitative results and comparisons?
limitations: limitations: Yes
paper_summary: paper_summary: This paper introduces traditional ADMM to Gaussian Spaltting and achieves distributed Gaussian Splatting training. The proposed distributed approach reduces training time and guarantes training convergence and stability. Experiments demonstrates both effectivenss and efficiency of this method.
strength_weakness: strength_weakness: 1. More experiments are needed to prove the superiority of the consensus step. I hope to see more qualitative and quantitative comparisons with VastGaussian in areas where blocks overlap.
2. The authors claim that proposed split method can balance the training time of each block. However, there is a lack of experiments showing the training and waiting time of each block.
3. The authors enable consensus and sharing when every block reaches 100 iterations. Is it possible to allow the blocks to be at different iterations? It can be more efficient to avoid blocking. However, there is no discussion about the difference between synchronous and asynchronous methods.
4. There is no discussion about the memory consumption of master node. How much GPU memory is needed for the master node? Will its memory consumption be linearly increase as the total number of Gaussians increases?
questions: questions: NA
limitations: limitations: NA
paper_summary: paper_summary: This paper proposes a distributed training strategy for 3dgs in large-scale scenes. The scene is evenly splitted into K blocks, but also maintain the global scene representation. Then the optimization of the scene is transferred to a condition optimization solved by the classic   ADMM. The results demonstrate their effectiveness and efficiency.
strength_weakness: strength_weakness: 1. The scene splitting is somehow tailored for bird view images. As for the extending scenes with surround views, such as autonomous driving, a training image in one block could see a large ratio of point cloud in other blocks.

2. It would be better to modify some representations in the paper. 

a. line 82, cone sampling of mip-nerf is not designed for the representation enhancement for outdoor scenes.

b. line 98, "leveraging xxx performance for xxx reconstruction" seems confusing.

c. line 4 of the fig.2, there are a redundant 'the' in sentence "a copy the the global 3D Gaussians".

3. It would be better to highlight the best performance in Table 2, 4.
questions: questions: 1. How to load the global gaussians? Does the method work when a single GPU can not load the global scene (main node)?

2. As the different splitting could lead to different overlapping regions and different ADMM problems, does it matter?
limitations: limitations: As discussed in the Question 1.
paper_summary: paper_summary: DoGaussian incorporates the 'divide-and-conquer' approach and introduces the ADMM algorithm into the 3DGS training process for large-scale 3D reconstruction tasks, reducing training time by 6+ times compared to the original 3DGS. Specifically, DoGaussian first splits the scenes into K local blocks of similar sizes and then maintains a global 3DGS node to ensure consistency through consensus on the K shared blocks. During the inference stage, DoGaussian moves all shared blocks and queries only the global block to improve rendering efficiency.
strength_weakness: strength_weakness: 1. **Artifacts in Teaser.** There are noticeable artifacts in the teaser, particularly in the picture located in the bottom right corner. It would be beneficial for the authors to provide an explanation of these artifacts and address them accordingly.
2. **Suitable for Street Scenes.** In the experiments section, all experiments are conducted on aerial datasets, but reconstructing street data is also an important problem. Can the authors demonstrate DoGaussian's applicability using the San Francisco Mission Bay dataset from Block-NeRF[1] or Block_A from the MatrixCity[2] dataset?
3. **GPU Memory Problem.** DoGaussian appears to be a system paper that utilizes a distributed approach to improve training efficiency by placing the global 3DGS on a main node and some local 3DGS on other nodes. One potential reason other works do not use this strategy could be GPU memory limitations. All datasets used by the authors are processed by 3DGS on a single GPU, which does not truly qualify as 'large-scale.' It would be beneficial for the authors to demonstrate that DoGaussian can be applied to larger datasets, such as the aerial and street data of big city in MatrixCity, which is used in NeRF-XL[3].

[1] Block-nerf: Scalable large scene neural view synthesis.

[2] Matrixcity: A large-scale city dataset for city-scale neural rendering and beyond

[3] NeRF-XL: Scaling NeRFs with Multiple GPUs
questions: questions: There are three questions regarding the weaknesses mentioned above:

1. The authors need to explain the artifacts in the teaser.
2. It would be better to conduct experiments on street datasets and larger datasets.
3. I’m also curious to know if the final results would be better using the visibility-aware splitting strategy of VastGaussian.

I would be happy to raise my score if the authors can address all my questions.
limitations: limitations: The authors discuss the limitation in the appendix A.8.

Comments: title: Minor Typo
Thanks for your reply
Thanks for your reply
Thanks for your reply
Thanks for your reply
Thanks for your reply
comment: There is a minor typo in our attached PDF: The bottom-left images should be swapped in Fig.2 of the attached file, and the full model handles the inconsistency issue in the division boundary. We will include the corrected results in the supplementary of our revised paper.

Again, we thank all reviewers for their insightful suggestions and discussion.
Thanks for your reply and support of our work. We are very grateful for your insightful suggestions and will revise our paper accordingly.
Thanks for your rating. We are very grateful for your insightful suggestions and support of our work. We will update our paper accordingly as suggested in our revised version.
Thanks for your reply. I will maintain my original score.
Thanks for your reply. I will keep my rating.
We are very grateful for your insightful suggestions and support of our work. We are happy to see that our rebuttal has addressed most of your concerns.
We are grateful for your insightful suggestions and happy our rebuttal has addressed your concerns. We will update the paper with all the experiments and details mentioned.
Thanks for your reply and answers. Most of my concerns are addressed. Although the limitation in street scenes exists currently, the contribution of this paper for bringing the condition optimization into large scale scene learning is clear. So I keep my original score.
Thanks for your reply and effort. All my concerns have been addressed. I keep my original score.