Title: LP-3DGS: Learning to Prune 3D Gaussian Splatting
Venue: NeurIPS 2024
Accepted: yes
Keywords: Novel view synthesis

Gaussian splatting

Learn to prune
Abstract: Recently, 3D Gaussian Splatting (3DGS) has become one of the mainstream methodologies for novel view synthesis (NVS) due to its high quality and fast rendering speed. However, as a point-based scene representation, 3DGS potentially generates a large number of Gaussians to fit the scene, leading to high memory usage. Improvements that have been proposed require either an empirical pre-set pruning ratio or importance score threshold to prune the point cloud. Such hyperparameters require multiple rounds of training to optimize and achieve the maximum pruning ratio while maintaining the rendering quality for each scene. In this work, we propose learning-to-prune 3DGS (LP-3DGS), where a trainable binary mask is applied to the importance score to automatically find a favorable pruning ratio. Instead of using the traditional straight-through estimator (STE) method to approximate the binary mask gradient, we redesign the masking function to leverage the Gumbel-Sigmoid method, making it differentiable and compatible with the existing training process of 3DGS. Extensive experiments have shown that LP-3DGS consistently achieves a good balance between efficiency and high quality.

LP-3DGS: Learning to Prune 3D Gaussian Splatting

Abstract

Recently, 3D Gaussian Splatting (3DGS) has become one of the mainstream methodologies for novel view synthesis (NVS) due to its high quality and fast rendering speed. However, as a point-based scene representation, 3DGS potentially generates a large number of Gaussians to fit the scene, leading to high memory usage. Improvements that have been proposed require either an empirical preset pruning ratio or importance score threshold to prune the point cloud. Such hyperparameters require multiple rounds of training to optimize and achieve the maximum pruning ratio while maintaining the rendering quality for each scene. In this work, we propose learning-to-prune 3DGS (LP-3DGS), where a trainable binary mask is applied to the importance score to automatically find a favorable pruning ratio. Instead of using the traditional straight-through estimator (STE) method to approximate the binary mask gradient, we redesign the masking function to leverage the Gumbel-Sigmoid method, making it differentiable and compatible with the existing training process of 3DGS. Extensive experiments have shown that LP-3DGS consistently achieves a good balance between efficiency and high quality.

1 Introduction

Novel view synthesis (NVS) takes images and their corresponding camera poses as input and seeks to render new images from different camera poses after 3D scene reconstruction. Neural Radiance Fields (NeRF) (Mildenhall et al. [2021]) uses multi-layer perceptron (MLP) to implicitly represent the scene, fetching the transparency and color of a point from the MLPs. NeRF has gained considerable attention in the NVS community due to its simple implementation and excellent performance. However, in order to obtain a point in the space, NeRF needs to perform an MLP inference. Each pixel rendered requires processing a ray and there are many sample points along each ray. Consequently, rendering an image requires a large amount of MLP inference operations. Thus, rendering speed becomes a major drawback of the NeRF method.

Besides NeRF, explicit 3D representations are also widely used. Compared to NeRF, the advantage of point-based scene representation is that it is well-supported by modern GPU rendering, enabling fast render speed. 3D Gaussian Splatting (3DGS) (Kerbl et al. [2023]) achieves both good quality and high rendering speed, making it a hot topic in the community. 3DGS uses 3D Gaussian models with color parameters to fit the scene and develops a training framework to optimize the model parameters. However, the number of points required to reconstruct the scene is enormous, usually in the millions. In practice, each point has dozens of floating-point parameters, which makes 3DGS a memory-intensive method.

Some recent works have attempted to mitigate this problem by pruning the points, such as LightGaussian (Fan et al. [2023]), RadSplat (Niemeyer et al. [2024]), and Mini-Splatting (Fang and Wang [2024]). These methods follow a similar pruning approach through defining an importance score for each Gaussian point and prune the points with such importance score below a preset empirical threshold. However, a major drawback of these methods is that the preset threshold must be manually tuned through multiple rounds of training process to identify the favorable pruning ratio to minimize the number of Gaussian points while keeping the rendering quality. To make matters worse, such number of points may vary depending on different scenes, which requires manual pruning ratio searching for each scene. For example, the blue and red lines in Figure 1 show the rendering quality of Kitchen and Room scenes, respectively, in MipNeRF360 scenes (Barron et al. [2022]), with sweeping 12 different pruning ratios (i.e., 12 rounds of training) following the prior RadSplat (Niemeyer et al. [2024]) and Mini-Splatting (Fang and Wang [2024]) method. It is clearly seen that a smaller pruning ratio will not hamper the rendering quality, and the rendering quality will start to decrease with much more aggressive pruning ratios. Both scenes exhibit an optimal pruning ratio region that could maximize the pruning ratio and maintain the rendering quality. It could also be seen that the ideal pruning ratio differs for these two scenes.

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In this paper, we propose a learning-to-prune 3DGS (LP-3DGS) methodology where a trainable mask is applied to the importance score. Notably, it is compatible with different types of importance scores defined in prior works. Instead of a preset threshold to determine the 3DGS model pruning ratio, as illustrated by the red triangle symbol in Figure 1, our method aims to integrate with existing 3DGS model training process to learn the favorable pruning ratio for minimizing the model size while maintaining the rendering quality. Since the traditional hard-threshold-based binary masking function is not differentiable, a recent prior work, Compact3D (Lee et al. [2023]), leverages the popular straight through estimator (STE) (Bengio et al. [2013]) to bypass the mask gradient for adaption to the backpropagation process. However, this approach often results in suboptimal pruning ratios. In contrast, in our work, we propose to redesign the masking function leveraging the Gumbel-Sigmoid activation function to make the whole masking function differentiable and integrate with the existing training process of 3DGS. Consequently, LP-3DGS automatically minimizes the number of Gaussian points for each scene with just a single round of training.

In summary, the technical contributions of our work are:

To address the effortful tuning of 3DGS pruning ratios, we propose a learning-to-prune 3DGS (LP-3DGS) methodology that leverages the differentiable Gumbel-Sigmoid activation function to embed a trainable mask with different types of existing importance scores

designed for pruning redundant Gaussian points. As a result, instead of fixed model size, LP3DGS could learn an favorable Gaussian point size for individual scene with only one-time training.

We conducted comprehensive experiments on state-of-the-art (SoTA) 3D scene datasets, including MipNeRF360 (Barron et al. [2022]), NeRF-Synthetic (Mildenhall et al. [2021]), and Tanks & Temples (Knapitsch et al. [2017]). We compared our method with SoTA pruning methods such as RadSplat (Niemeyer et al. [2024]), Mini-Splatting (Fang and Wang [2024]), and Compact3D (Lee et al. [2023]). The experimental results demonstrate that our method can enable the model to learn the favorable pruning ratio and that our trainable mask method performs better than the STE mask.

2 Related Work

Neural radiance fields (NeRFs) NeRFs (Mildenhall et al. [2021]) targets to represent the scene in multilayer perceptrons (MLPs) based on multi-view image inputs, enabling high-quality novel view synthesis. Due to its advancement, numerous follow-up works improved it in either rendering quality (Barron et al. [2021, 2022]) or efficiency(Müller et al. [2022], Chen et al. [2022], Fridovich-Keil et al. [2022]).

Although NeRF models demonstrate impressive rendering capabilities across numerous benchmarks, and considerable efforts have been made to enhance training and inference efficiency, they typically still face challenges in achieving fast training and real-time rendering.

Radiance Field Based On Points. In addition to implicit representations, several works have focused on volumetric point-based methods for 3D presentation (Gross and Pfister [2011]). Inspired by neural network concepts, (Aliev et al. [2020]) introduced a neural point-based approach to streamline the construction process. Point-NeRF (Ding et al. [2024]) further applied points for volumetric representation, enhancing the effectiveness of point-based methods in radiance field modeling.

Gaussian Splatting 3D Gaussian Splatting (3DGS) (Kerbl et al. [2023]) represents a significant advancement in novel view synthesis, utilizing 3D Gaussians as primitives to explicitly represent scenes. This approach achieves state-of-the-art rendering quality and speed while maintaining relatively short training time. A series of methods have been introduced to improve the rendering quality through using regularization for better optimization, including depth map (Chung et al. [2023], Li et al. [2024a]), surface alignment (Guédon and Lepetit [2023], Li et al. [2024b]) and rendered image frequency (Zhang et al. [2024]). However, the extensive number of Gaussians required for scene representation often results in a model that is too large for efficient storage. Recent research has focused on compression methods to enhance the efficiency of this representation. Notably, several studies (Fan et al. [2023], Fang and Wang [2024], Niemeyer et al. [2024]) have proposed using predefined scores as pruning criteria to keep Gaussians that significantly contribute to rendering quality. Compact3D (Lee et al. [2023]) introduces a method that applies a trainable mask on scale and opacity to each Gaussian and utilizes a straight-through estimator (Bengio et al. [2013]) for gradient updates. LightGaussian (Fan et al. [2023]) employs knowledge distillation to reduce the dimension of spherical harmonics. Additionally, (Fan et al. [2023], Lee et al. [2023]) also explored quantization techniques to further compress model storage. The previously proposed pruning methods primarily rely on predefined scores to determine the importance of each Gaussian. These approaches present two main challenges: first, whether the criteria accurately reflect the importance of the Gaussians, and second, the need for a manually selected pruning threshold to decide the level of pruning. In this work, we address these issues by introducing a trainable mask activated by a Gumbel-sigmoid function, applied to the scores derived from prior methods or directly to the scale and opacity of each Gaussian for more flexibility. Our approach automatically identifies the balance between the pruning ratio and rendering quality, eliminating the need to test on various pruning ratios.

3 Methodology

The conventional pruning methods leveraging predefined importance score require pruning ratio as a manually tuned parameter to reduce the size of Gaussian points in 3DGS. To seek for a favorable

pruning ratio, these methods may need to perform multiple rounds of training for each individual scene, which is inefficient. Motivated by this, we propose a learning-to-prune 3DGS (LP-3DGS) algorithm which learns a binary mask to determine the favorable pruning ratio for each scene automatically. Importantly, the proposed LP-3DGS is compatible with various types of pruning importance scores. In this section, we will: 1) introduce the preliminary of the original 3DGS and recap different importance metrics for pruning that are proposed by prior works, and 2) present the proposed learning-to-prune 3DGS algorithm.

3.1 3DGS Background

3DGS Parameters 3DGS is an explicit point-based 3D representation that uses Gaussian points to model the scene. Each point has the following attributes: position p ∈ R 3 , opacity σ ∈ [0 , 1] , scale in 3D s ∈ R 3 , rotation represented by 4D quaternions q ∈ R 4 and fourth-degree spherical harmonics (SH) coefficients k ∈ R 48 . In summary, one gaussian point has 59 parameters. The center point X of a Gaussian model is represented by p and covariance matrix Σ is denoted by s and q . The SH coefficients model the color as viewed from different directions. The parameters of the Gaussians are optimized through gradient backpropagation of the loss between the rendered images and the ground truth.

Rendering on 3DGS In order to render an image, the first step is projecting the Gaussians to 2D camera plane by world to camera transform matrix W and Jacobian J of affine approximation of the projective transform. The covariance matrix of projected 2D Gaussian is

The projected Gaussians would be rendered as splat (Botsch et al. [2005]), the color of one pixel could be rendered as

Where i is the pixel index, j is the Gaussian index and N is the number of the Gaussians in the ray. c j is the color of the Gaussian calculated by SH coefficients, α j = (1 -exp -σ j δ j ) , σ j is the opacity of the point and δ j is the interval between points. T j = ∏ j -1 k =1 (1 -α k ) is the transmittance from the start of rendering to this point. G 2D j is the 2D Gaussian distribution.

Adaptive Density Control of 3DGS At the start of training, the Gaussians are initialized using Structure-from-Motion (SfM) sparse points. To make the Gaussians fit the scene better, 3DGS applies an adaptive density control strategy to adjust the number of Gaussians. Periodically, 3DGS will grow Gaussians in areas that are not well reconstructed, a process called "densification." Simultaneously, Gaussians with low opacity will be pruned.

3.2 Importance Metrics for Pruning

A straightforward way to prune the Gaussians is by sorting them based on a defined importance score and then removing the less important ones. Consequently, one of the main objective of prior 3DGS pruning works is to define an effective importance metric.

RadSplat (Niemeyer et al. [2024]) defines the importance score as the maximum contribution along all rays of the training images, written as

Where α r i · T r i is the contribution of Gaussian G i along ray r . RadSplat performs pruning by applying a binary mask according to the importance score, where the mask value for Gaussian G i is

Where t prune ∈ [0 , 1] is the threshold of score magnitude for pruning, 1 [ · ] is the indicator function.

Image

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Another recent work, Mini-Splatting (Fang and Wang [2024]), uses the cumulative weight of the Gaussian as the importance score, which can be formulated as:

Where K is the total number of rays intersected with Gaussian G i , ω ij is the color weight of Gaussian G i on the j -th ray.

3.3 Learning-to-Prune 3DGS

The overall LP-3DGS learning process is shown in the Figure 2. In general, it mainly can generally be divided into two stages:1) densification stage, and 2) learning-to-prune stage. Following the original 3DGS, densification stage applies an adaptive density control strategy to gradually increase the number of Gaussians. As revealed by prior pruning works (Lee et al. [2023], Niemeyer et al. [2024]), 3DGS contains a significant number of redundant Gaussians. Subsequently, in the learning-to-prune stage, the proposed LP-3DGS learns a trainable mask upon a previously defined importance metric to compress the number of Gaussians with an favorable pruning ratio automatically. Specifically, to learn a binary mask, we first initialize a real-value mask m i for each point i , and then adopt the Gumbel-sigmoid technique to binarize the mask value differentially.

Gumbel-Sigmoid based Trainable Mask The binarization operation for real-value mask in pruning typically involves a hard threshold function, determining the binary mask should be 0 or 1. However, such hard threshold function is not differentiable during backpropagation. To address this issue, popular straight through estimator (STE) method (Bengio et al. [2013]) is widely used, as it skips the gradient of the threshold function during backpropagation. Such process may create to a gap between trainable real-value mask and binary mask. As shown in Figure 3(a), the trainable mask values exhibit certain ratios across the entire range from 0 to 1 after Sigmoid function, which can be inaccurate when further converting to binary mask via a hard threshold function. To better optimize the trainable mask towards binary values, we propose to apply Gumbel-Sigmoid function to learn the binary mask.

The Gumbel distribution is used to model the extreme value distribution and generate samples from the categorical distribution (Gumbel [1954]). This property is then utilized to create the GumbelSoftmax (Jang et al. [2016]), a differentiable categorical distribution sampling function. The sample of one category is given by:

Where τ is the input adjustment parameter, g i is sample from Gumbel distribution. Inspired by the Gumbel-Softmax, we treat learning the binary mask of each point as a two-class category problem. Thus, we replace the Softmax function to Sigmoid function, referring to Gumbel-Sigmoid:

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By using such Gumbel-Sigmoid function, the output value is either close to 0 or 1, as shown in Figure 3, allowing it to be integrated as an approximation of a binary masking function. More importantly, this function remains differentiable, thus can be integrated during backpropagation.

Moreover, to prune the selected Guassians practically according to the learned binary mask, we further apply the mask value on opacity, which can be mathematically formulated as

where S i is the defined importance score of each Gaussian point. The closer the mask value is to 0, the less corresponding Gaussian point contributes to the rendering. In practice, after learning the trainable mask, a one-time pruning is applied to the corresponding Gaussian points with mask value of 0.

Sparsity regularization In order to compress the model as much as possible, we apply a L1 regularization term (Lee et al. [2023]) to encourage the trainable mask to be sparse, which can be formulated as:

Upon that, the final loss function is defined as:

L L 1 is the L1 loss between rendered image and ground truth. L ssim is the ssim loss. λ ssim and λ m are two coefficients.

Moreover, we find that the trainable mask can be effectively learned in just a few hundred iterations, compared to the thousands required for the overall training process. In practice, the mask learning function is activated for only 500 iterations. Once the mask values are learned, we follow the 3DGS training setup to further fine-tune the pruned model while maintaining the same total number of training iterations. The detailed hyper parameters are described in the later experiment section.

4 Experiments

4.1 Experimental Settings

Dataset and Baseline We test our method on two of the most popular real-world datasets: MipNeRF360 dataset (Barron et al. [2022]), which contains 9 scenes, and the Train and Truck scenes from the Tanks & Temples dataset (Knapitsch et al. [2017]). We also evaluate our method on the NeRF-Synthetic dataset (Mildenhall et al. [2021]), which includes 8 synthetic scenes. In this section, we only present the results on MipNeRF360 dataset, rest of them are listed in appendix A. In this paper, we use the SoTA RadSplat (Niemeyer et al. [2024]) and Mini-Splatting (Fang and Wang [2024]) as the baselines, both of which propose different pruning importance scores. First, we evaluate the performance of these two methods under various pruning ratios. Since neither method is open-sourced at the time of writing, we reproduced them based on the provided equations. For each pruning ratio, we calculate the corresponding threshold based on the magnitude of the importance scores and prune the Gaussians with scores below this threshold. Note that each pruning ratio requires one round of training. We use peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al. [2018]) as rendering evaluation metrics.

Implement Details The machine running the experiments is equipped with an AMD 5955WX processor and two Nvidia A6000 GPUs. It should be noted that our method does not support multiGPU training. We ran different experiments simultaneously on two GPUs. We train each scene under every setting for 30,000 iterations and with the mask training occurring from iteration 19,500 to 20,000, updating the importance score every 20 iterations. The value of τ in Equation 7 is 0.5 and the coefficient λ m of mask loss is 5e-4.

4.2 Experimental Results

Quantitative Results The blue lines in Figure 4 show the results of sweeping pruning ratios using RadSplat and Mini-Splatting for the Kitchen and Room scenes. Results for other scenes in the MipNeRF 360 dataset are presented in Appendix A. The result of the learned LP-3DGS model size and rendering quality is indicated by red triangles.

The quantitative results fluctuate at lower pruning ratios but generally stabilize around a certain value. After surpassing that point, the rendering quality decreases significantly. It's worth noting that this critical point varies for different scenes. Rather than manually searching for the favorable pruning ratio, it clearly shows our LP-3DGS method could learn the favorable model size in conjunction with the scene learning process, with only one-time training. The Table 1 lists the quantitative results of all scenes in MipNeRF360 dataset. It clearly shows that each scene converge into different model size leveraging our LP-3DGS method while maintaining almost the same rendering quality. The pruning ratio varies based on what importance score is used, but LP-3DGS effectively identifies the ideal pruning ratio for the corresponding score.

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Training Cost Table 2 shows the training cost of LP-3DGS on MipNeRF360 dataset. In our setup, after 20000th iteration, the model is pruned based on the learned mask values. The number of Gaussian points will be significantly reduced, resulting in the later stages of training taking much less time than in the non-pruned version. Even with the embedding of the mask learning function, the overall training cost is comparable to that of the vanilla 3DGS. In most cases, the peak training memory usage is slightly higher because training the mask requires more GPU memory. However, after pruning, the 3DGS model size becomes much smaller, leading to a significant improvement in rendering speed, measured in terms of FPS.

4.3 Ablation Study

A recent prior work, Compact3D (Lee et al. [2023]) proposes to leveraging the straight-through estimator (STE) to train a binary mask based on the opacity and scale of Gaussian parameters. To conduct a fair comparison between STE based mask and our LP-3DGS, we perform two ablation

studies, one involves replacing the STE mask in Compact3D with our method, and the other applies the STE mask to the importance score of RadSplat. The formula of STE mask is

∇ / means stop gradients, 1 [ · ] is the indicator function and f ( · ) is sigmoid function, ϵ is masking threshold.

Comparison with Compact3D We first apply the Gumbel-sidmoid activated mask, instead of STE mask, on the opacity and scale of gaussians in the same manner as proposed in Compact3D. The threshold ϵ in Equation 11 and mask loss coefficient follows the default settings in Compact3D. Table 3 shows the comparison between two methods.

In most cases, our LP-3DGS learns a higher pruning ratio, except for Stump, Garden and Flowers scene. In terms of rendering quality, our LP-3DGS outperforms Compact3D using the STE based mask achieving even smaller model sizes in most scenes.

STE Mask on Importance Score We also apply STE mask on the pruning importance score to compare with our method. The Equation 8 would be rewriten as

where M is shown in Equation 11. The same as mentioned before, the parameters for STE mask are default values in Compact3D.

Table 4 shows that under the same settings, after applying the mask to the importance score, the STE mask compresses the mode too much and the performance drops a lot. Trainable mask keeps the gradient of the mask and the comressed model has a more reasonable size.

5 Discussion and Conclusion

Broader Impact and Limitation LP-3DGS compresses the 3DGS model to an ideal size in a single run, saving storage and computational resources by eliminating the need for parameter sweeping to find the favorable pruning ratio. However, the limitation of this work is that the rendering quality after pruning varies depending on the the definition of importance scores.

Conclusion In this paper, we present a novel framework, LP-3DGS, which guides the 3DGS model learn the best model size. The framework applies a trainable mask on the importance score of the gaussian points. The mask is trained for a specific period and used to prune the model once. Our method compressed the model as much as possible without significantly sacrificing performance and is capable to achieve the favorable compression rate for different test scenes. Compared with the STE mask method, ours achieves better performance.

Acknowledgments and Disclosure of Funding

Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0076. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government.

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A Appendix / supplemental material

Code: https://github.com/dexgfsdfdsg/LP-3DGS.git

A.1 Experiment Results on MipNeRF360 Dataset

Ground Truth

3DGS

RadSplat

Mini-Splatting

Bicycle

Counter

Kitchen

Room

Garden

Flowers

Treehill

Bicycle

PSNR

↑

SSIM

↑

LPIPS

↓

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

23.0

23.5

24.0

24.5

25.0

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.60

0.65

0.70

0.75

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.25

0.30

0.35

0.40

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

23.5

24.0

24.5

25.0

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.625

0.650

0.675

0.700

0.725

0.750

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.25

0.30

0.35

0.40

LPIPS

Mini-Splatting

LP-3DGS

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

26

28

30

32

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.825

0.850

0.875

0.900

0.925

0.950

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.20

0.25

0.30

0.35

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

27

28

29

30

31

32

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.850

0.875

0.900

0.925

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.20

0.25

0.30

0.35

LPIPS

Mini-Splatting

LP-3DGS

Counter

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

25

26

27

28

29

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.800

0.825

0.850

0.875

0.900

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.20

0.25

0.30

0.35

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

26

27

28

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.82

0.84

0.86

0.88

0.90

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.20

0.25

0.30

0.35

LPIPS

Mini-Splatting

LP-3DGS

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

25.0

25.5

26.0

26.5

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.675

0.700

0.725

0.750

0.775

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.25

0.30

0.35

0.40

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

25.0

25.5

26.0

26.5

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.650

0.675

0.700

0.725

0.750

0.775

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.25

0.30

0.35

0.40

LPIPS

Mini-Splatting

LP-3DGS

Garden

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

24

25

26

27

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.65

0.70

0.75

0.80

0.85

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.15

0.20

0.25

0.30

0.35

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

25

26

27

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.70

0.75

0.80

0.85

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.15

0.20

0.25

0.30

0.35

LPIPS

Mini-Splatting

LP-3DGS

Flowers

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

20.0

20.5

21.0

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.475

0.500

0.525

0.550

0.575

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.40

0.45

0.50

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

20.0

20.5

21.0

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.45

0.50

0.55

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.40

0.45

0.50

LPIPS

Mini-Splatting

LP-3DGS

Treehill

RadSplat

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

21.0

21.5

22.0

22.5

23.0

PSNR

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.54

0.56

0.58

0.60

0.62

0.64

SSIM

RadSplat

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.35

0.40

0.45

0.50

LPIPS

RadSplat

LP-3DGS

Mini-Splatting

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

21.0

21.5

22.0

22.5

23.0

PSNR

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.56

0.58

0.60

0.62

0.64

SSIM

Mini-Splatting

LP-3DGS

0.0

0.2

0.4

0.6

0.8

1.0

Pruning Ratio

0.35

0.40

0.45

0.50

LPIPS

Mini-Splatting

LP-3DGS

A.2 Experiment Results on NeRF Synthetic Dataset

A.3 Experiment Results on Truck & Train Scenes

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Peer reviews:
comments: SUMMARY:
The paper proposed a pruning method for Gaussian Splatting training, which employ a learnable mask to find optimal pruning rate.

STRENGTHS:
The paper is well-written and the proposed method is easy to understand.

WEAKNESSES:
* The proposed method use a regularization loss to encourage the model to prune, so that the weight parameter is an important balancing factor. The discussion on how to set such parameter is missing.

* Figure 2 is not clear enough for me to well understand the proposed idea. In Figure 3, why pattern like (b) is better than (a)?

* Experiments section use existing works for comparison, but they are all self-implemented. The performance in their original paper should be included for reference.

* The author claim the proposed method can find optimal pruning ratio. Based on my observation, the conclusion is not solid. First, what is definition of optimal? Second, not all the subfigures in Fig. 4 & 6 support this conclusion.

QUESTIONS:
Please see the "weaknesses".

LIMITATIONS:
No potential negative social impact.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 2
DATE: 2024-07-10

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work introduces LP-3DGS, aiming to compress 3DGS by replacing the previously manually set threshold with a learning-to-prune scheme.  In particular, LP-3DGS learns a binary mask to automatically prune 3DGS, where such a mask is regularized with the Gumbel-Sigmoid technique. Experiments on three benchmarks showcase the soundness of the introduced methods.\n\nSTRENGTHS:\n* Applying Gumbel-Sigmoid to regularize the binary mask is reasonable.\n* Extensive experiments are conducted on several existing benchmarks.\n* The paper is well-structured and easy to follow.\n\nWEAKNESSES:\n* Limited technical contributions. This work seems to be a direct application of Gumbel-Sigmoid, which is a general engineering trick (https://github.com/AngelosNal/PyTorch-Gumbel-Sigmoid) to approximate discrete sampling in a differentiable manner. It needs to be clarified what the main technical insights this work aims to bring to the 3DGS compression community. To me, replacing the threshold setting with the Gumbel-Sigmoid is too intuitive to hit the standard of a top-tier conference.\n\n* It is difficult to know whether the learned binary mask achieves the “optimal Gaussian point size”. This work demonstrates that it learns the “optimal” solutions by plotting several line charts without any theoretical analysis. In some cases, LP-3DGS did not find the best balance, e.g., Fig. 4 Mini-Splatting on Kitchen. Besides, LP-3DGS seems to lose the flexibility of finding better solutions compared to its baseline, e.g., RadSplat can set a smaller ratio to compress further while maintaining reasonable visual quality.\n\n\n* Lack of discussions with some recent related works. Several more recent approaches in the 3DGS compression community need discussion, and it would be better to add some comparisons with them to understand the advantages of LP-3DGS better.\n  * Girish, Sharath, Kamal Gupta, and Abhinav Shrivastava. \"Eagles: Efficient accelerated 3d gaussians with lightweight encodings.\" arXiv:2312.04564.\n  * Lu, Tao, et al. \"Scaffold-gs: Structured 3d gaussians for view-adaptive rendering.\" CVPR2024.\n  * Chen, Yihang, et al. \"HAC: Hash-grid Assisted Context for 3D Gaussian Splatting Compression.\" arXiv:2403.14530.\n\nQUESTIONS:\nPlease kindly refer to the [Weaknesses].\n\nLIMITATIONS:\nPlease kindly refer to the [Weaknesses].", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-13"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method to optimally prune Gaussians that do not participate in the rendering or optimizing process of the 3D Gaussian Splatting 3D reconstruction algorithm. The key idea in this paper is to use a Gumbel-sigmoid function instead of the standard Sigmoid function to optimize a binary mask based on transmittance of each splatted Gaussian. Experimental results show that by doing so the number of Gaussians can be reduced without losing reconstruction quality, keeping a near optimal balance between quality and computational speed. As a result, higher frame rate can be obtained for rendering.\n\nSTRENGTHS:\n-\tThe idea to use the Gumbel-function is interesting because it allows to naturally binarize the input values while keeping differentiability. \n-\tResults show that higher frame rate can be achieved without losing accuracy or training time. The ablation study is also good because it shows the advantage of optimizing the mask values compared to hard thresholding.\n\nWEAKNESSES:\n-\tExcept for replacing the sigmoid function with the Gumbel-Sigmoid function it seems that there is no other novel technical point in the paper. From the results it seems that a threshold value of 0.6 would be better than the naïve 0.5. I am wondering how the ablation study changes if using different threshold.\n-\tIn the experiments, no comparisons to other methods that focus on optimizing number compressing the model. For example, comparison with LightGaussian would be interesting. It seems from the Figure 4 that the proposed method performs slightly worse than mini splatting.\n-\tWhat is the meaning of the “pruning ratio” for the proposed method in Figure 4? It seems to be different for the different datasets. However, as far as I understood, the proposed method does not use a pruning ratio: l. 194 => pruning […] points with mask values of 0. This is confusing.\n-\tThere is no significant gain in accuracy, training time or memory consumption. The only significant gain is in rendering speed. This is interesting but because original 3DGS is already quite fast, in practice I am not sure the impact is high. For example if using a simple threshold of 0.5 in Compact3D how does frame rate compares?\n-\tWriting can be brushed up.\no\tL.176-178 is not correct.\no\tIn figure 4, it seems legends are wrong in the lines for Mini-splatting => blue is described as RadSplat.\no\tTables are not easy to read. Add some special fonts like bold or underline to emphasize best and second-best results.\n\nQUESTIONS:\n-\tClarify Figure 4 and explain what the meaning of the pruning ratio for the proposed method is.\n-\tAdd more comparative experiments with other compact 3DGS methods.\n\nLIMITATIONS:\n-\tLimitations are properly discussed in the conclusion section.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-13"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nWhereas other works set a fixed pruning ratio or threshold, this paper introduces a method to learn how to prune Gaussians from a scene while retaining high image fidelity. Different scenes have a drop in fidelity at different pruning percentages and the goal of this work is to remove the need to train the model multiple times while searching for a pruning percentage near, but before, that drop. Specifically this work uses a Gumbel-Sigmoid — which is a 2-class Gumbel softmax followed by a Sigmoid function —  to enable a differentiable mask that can learn to prune Gaussians during training. This mask is then applied to set the opacity of each Gaussian. Gaussians where the mask goes to 0 are pruned. Evaluations are performed on 2 real world datasets — MipNerf 360 and Tanks & Temples — and one synthetic dataset — NeRF-Sythetic.\n\nSTRENGTHS:\nS1: The writing in this work is quite clear. The methodology is straightforward to understand and the explanations appear to be detailed enough to be able to replicate experiments\n\nS2: This method seems useful to practitioners who are low on resources and want to quickly fit and compress a 3D-GS model.\n\nWEAKNESSES:\n**Main Weaknesses:**\n\nW1: This paper uses the terms “optimal” and “best” to describe the pruning ratio found by learning. Specifically a soft definition of the optimal pruning ratio is given in line 41: “minimize the number of Gaussian points while keeping the rendering quality.” But this method does not “keep” the rendering quality — image quality metrics decrease after pruning. Generally the terms “optimal” and “best” are used to describe maximal or minimal points in some meaningful measure. In the domain of pruning 3D-GS models, a more appropriate definition of optimal pruning would be the highest possible compression that can be applied to the model while retaining rendering quality to some percent of the original rendering quality.\n\nW2: It would be helpful to also provide analysis on pruning threshold vs. image quality metrics. It’s possible that there exists a pruning threshold for RadSplat and/or Mini-Splatting that prunes a large percent of Gaussians while retaining image quality. \n\nW3: Table 2: Minutes isn’t a great metric here. FLOPs or MACs over training would be a lot better. Other works that want to compare to this method will need to use exactly this manuscript’s architecture to replicate its results.\n\n\n\n**Other minor considerations:**\n\nMC1: There are still several hyper parameters that haven’t been ablated. This is mostly fine, but it would be good to know how big of an impact these parameters have:\n- Gumbel $\\tau$\n- $\\lambda_m$\n- Applying the pruning earlier/later than 20000 epochs\n\nMC2: It would be interesting to ablate equation 8 by removing $S_i$. Can you simply just learn $m_i$ parameter without computing an importance score?\n\n\n**Cosmetic issues:**\n\nC1: line 46, line 50, line 62: could -> can\n\nC2: $T$ in eq. 7 should be a $\\tau$\n\nC3: Tables 1 and 2, move the metric to the first column for clarity (like tables 4 and 5)\n\nQUESTIONS:\nMy biggest concern for this manuscript is that the use of terms “optimal” and “best” is misleading. This method can find a good pruning ratio in one-shot, but it’s not clear that this ratio is optimal. I’m rating this manuscript a borderline reject for now because I strongly think this wording needs to change. I will raise my score if the authors can provide a detailed description of how they will update this wording in their rebuttal.\n\nI would also like to see W2 and W3 addressed, but these are likely computationally expensive and aren’t as important to me as W1.\n\nLIMITATIONS:\nOnce the wording in this manuscript is changed, I think the main limitations will be addressed.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-14"}