1. Bibliographic Information

1.1. Title

1000+ FPS 4D Gaussian Splatting for Dynamic Scene Rendering

1.2. Authors

Yuan Yuheng, Qiuhong Shen, Xingyi Yang, Xinchao Wang

• Affiliation: National University of Singapore (NUS)

1.3. Journal/Conference

Preprint (arXiv)

• Note: While currently a preprint, the quality and scope suggest submission to top-tier computer vision conferences (e.g., CVPR, ECCV). The "Published at" date provided (March 2025) indicates this is cutting-edge research.

1.4. Publication Year

2025

1.5. Abstract

This paper addresses the efficiency bottlenecks of 4D Gaussian Splatting (4DGS), a popular method for digitally reconstructing moving (dynamic) scenes. While 4DGS produces high-quality visuals, it suffers from massive storage requirements and slow rendering speeds. The authors identify two main causes: (1) Short-Lifespan Gaussians (points that exist only briefly, creating data bloat) and (2) Inactive Gaussians (points processed during rendering that don't actually contribute to the image). To solve this, they propose 4DGS-1K. This framework introduces a Spatial-Temporal Variation Score to prune (remove) unnecessary short-lived points and a Key-frame Temporal Filter to skip inactive points during rendering. The result is a method that runs at over 1000 Frames Per Second (FPS), reduces storage by 41x, and maintains visual quality comparable to the original method.

1.6. Original Source Link

• Source: https://arxiv.org/abs/2503.16422v1
• PDF: https://arxiv.org/pdf/2503.16422v1.pdf

2. Executive Summary

2.1. Background & Motivation

In the field of Computer Vision, Novel View Synthesis (NVS) aims to generate new camera angles of a scene based on a set of recorded images. While static scenes are well-handled by current technologies, dynamic scenes (videos with moving objects) present a much harder challenge.

• The Problem: Traditional methods like NeRF (Neural Radiance Fields) are too slow for real-time applications. A newer method, 4D Gaussian Splatting (4DGS), introduced an explicit way to represent dynamic scenes using millions of 4D points. However, 4DGS is extremely inefficient. It often generates millions of redundant "flickering" points to represent motion, leading to gigabytes of storage usage and rendering speeds that struggle to meet high-frame-rate demands on standard hardware.
• The Gap: Existing compression methods focus on static 3D scenes and fail to address the temporal redundancy (unnecessary data over time) unique to 4DGS.

2.2. Main Contributions / Findings

The authors propose 4DGS-1K, a streamlined framework designed to make 4DGS viable for real-time applications.

1. Identification of Redundancy: The paper provides a deep analysis showing that 4DGS relies heavily on "transient" Gaussians (points that appear and disappear instantly) to model motion, which is inefficient.

2. Spatial-Temporal Pruning: They propose a new scoring system that evaluates not just how much a point contributes to the image (spatial), but how stable it is over time (temporal). Points that are "flickering" or low-impact are permanently removed.

3. Temporal Filtering: They introduce a mechanism to "mask out" points that are technically present in the scene but effectively invisible for a sequence of frames, preventing the graphics card from wasting power on them.

4. Performance Leap: The method achieves 1000+ FPS rendering (a 9x speedup over vanilla 4DGS) and reduces storage from ~2GB to ~50MB per scene (a 41x reduction), without significant loss in visual fidelity.

   The following figure (Figure 1 from the original paper) summarizes this leap in performance, comparing the storage and speed of the proposed method against the original 4DGS:

   该图像是对比图，左侧展示了传统4DGS的性能指标，内存使用为2.16GB、渲染帧率为103、PSNR为33.16dB；右侧展示了改进后的4DGS-1K性能指标，内存使用为53MB、渲染帧率为1088、PSNR为33.06dB。右侧的散点图显示了不同方法的PSNR和计算消耗。

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

To understand this paper, a novice needs to grasp three core concepts:

1. Gaussian Splatting (3DGS): Imagine painting a 3D scene not with polygons (triangles), but with millions of 3D ellipsoids (blobs) called "Gaussians." Each Gaussian has a position, shape (covariance), color, and opacity. The final image is created by "splatting" (projecting) these blobs onto the screen and blending them. This is the explicit representation, which is faster to render than neural networks.
2. 4D Gaussian Splatting (4DGS): This extends 3DGS to handle time. Instead of just x, y, z, each Gaussian has a time dimension $t$. A 4D Gaussian can move, rotate, and change shape over time. When you want to render a specific moment (e.g., t=2.5s), the 4D Gaussian is "sliced" to create a standard 3D Gaussian valid for that specific instant.
3. Rasterization: This is the process of converting the mathematical 3D/4D Gaussians into pixels on your screen. A major bottleneck in 4DGS is that the computer often processes millions of Gaussians during rasterization, even if many of them are transparent or hidden at that specific moment.

3.2. Previous Works

• NeRF-based Dynamic Methods (e.g., DyNeRF, HyperReel, K-Planes): These use neural networks to predict color and density. While accurate, they are computationally heavy and usually render at low frame rates (often < 30 FPS).
• 3D Gaussian Splatting (3DGS): The foundation of this paper. It revolutionized static scene rendering with real-time speeds.
• 4D Gaussian Splatting (4DGS): The direct baseline. It achieved high-quality dynamic rendering but introduced the storage and speed issues this paper solves.
• Compression Methods (e.g., Compact3D, Mini-Splatting): Previous attempts to shrink Gaussian models focused on spatial compression (e.g., merging nearby points). They did not account for temporal redundancy (points that are unnecessary over time).

3.3. Differentiation Analysis

The core innovation of 4DGS-1K compared to works like Compact3D or MEGA is its focus on Time.

• Others: Compress by reducing the precision of numbers (quantization) or removing spatially small points.
• 4DGS-1K: Asks "Does this point exist long enough to be useful?" and "Is this point visible right now?" This temporal awareness allows it to remove vast amounts of data that other methods preserve.

4. Methodology

4.1. Principles

The methodology is built on two key observations regarding inefficiency in standard 4DGS:

1. Massive Short-Lifespan Gaussians: 4DGS tends to "cheat" by creating Gaussians that exist for a split second to fix a small error in one frame, then vanish. This creates a "flickering" effect in the data and bloats file size.

2. Inactive Gaussians: Even if a Gaussian is permanent, it might be behind the camera or transparent for 90% of the video. Standard 4DGS still calculates its position for every frame, wasting computing power.

   The following figures (Figure 2 and Figure 3 from the original paper) illustrate this redundancy. Figure 2a shows that most Gaussians have a very short time variance ($\Sigma_t$), and Figure 3 shows these short-lived points cluster around moving edges:

   该图像是图表，展示了4DGS与改进模型在不同指标上的比较。图(a)显示了随$\Sigma_t$值变化的百分比，图(b)展示了不同时间戳下的活跃比例，图(c)则反映了随时间戳变化的激活IoU。红线表示4DGS的结果，蓝色和青色线分别表示改进模型有无过滤器的效果。这些对比揭示了改进模型在减少临时高斯和提高渲染效率上的优势。

   该图像是图表，展示了ext{Gaussians}在动态场景中的分布特征。左侧和右侧分别显示了不同情况下的ext{Gaussians}分布，主要集中在移动物体的边缘区域。

The solution, 4DGS-1K, implements a two-stage pipeline: Global Pruning (Step 1) and Local Filtering (Step 2), as shown in the system overview below (Figure 4 from the original paper):

该图像是示意图，展示了研究中的两种关键技术：瞬态高斯剪枝（Transient Gaussian Pruning）和时间滤波（Temporal Filter）。图左侧显示了不同时间点的高斯分布，强调了如何通过剪枝短寿命的高斯以减小计算冗余。图右侧则展示了在不同时间帧中如何利用滤波去除非活跃高斯，从而提升渲染效率。这些技术共同促进了4D高斯渲染方法的高效性和速度。

4.2. Core Methodology In-depth

4.2.1. Preliminary: 4DGS Representation

Before optimizing, we must understand how 4DGS works. A 4D Gaussian is defined by a mean $\mu = (\mu_x, \mu_y, \mu_z, \mu_t)$ and a covariance matrix $\Sigma$.

Step 1: Slicing (4D to 3D) To render a frame at time $t$, 4DGS computes a "conditional" 3D Gaussian. The spatial mean ($\mu_{xyz|t}$) and covariance ($\Sigma_{xyz|t}$) at time $t$ are derived using this formula:

$$\begin{array} { r l } & { \mu _ { x y z | t } = \mu _ { 1 : 3 } + \Sigma _ { 1 : 3 , 4 } \Sigma _ { 4 , 4 } ^ { - 1 } ( t - \mu _ { t } ) } \\ & { \Sigma _ { x y z | t } = \Sigma _ { 1 : 3 , 1 : 3 } - \Sigma _ { 1 : 3 , 4 } \Sigma _ { 4 , 4 } ^ { - 1 } \Sigma _ { 4 , 1 : 3 } } \end{array}$$

• Explanation:
  • $\mu_{1:3}$: The spatial center (x,y,z).
  • $\mu_t$: The center time of the Gaussian.
  • $\Sigma_{1:3,4}$: Describes how space correlates with time (velocity/deformation).
  • This formula essentially asks: "Given that we are at time $t$, where is this Gaussian located in 3D space?"

Step 2: Calculating Opacity Even if a Gaussian has a position at time $t$, it might be invisible. Its visibility (opacity) is determined by a temporal Gaussian distribution $p_i(t)$:

$$\begin{array} { c } { \alpha _ { i } = p _ { i } ( t ) p _ { t } ( u , v | t ) \sigma _ { i } } \\ { p _ { i } ( t ) \sim \mathcal { N } ( t ; \mu _ { t } , \Sigma _ { 4 , 4 } ) } \end{array}$$

• Explanation: $\alpha_i$ is the final opacity. It depends on $\sigma_i$ (base opacity) and how close the current time $t$ is to the Gaussian's "peak time" $\mu_t$. If $\Sigma_{4,4}$ (often denoted as $\Sigma_t$) is very small, the Gaussian is only visible for a tiny fraction of a second.

4.2.2. Pruning with Spatial-Temporal Variation Score

The goal is to permanently delete Gaussians that are useless. The authors define a score $S_i$ that combines Spatial importance (Does it cover pixels?) and Temporal stability (Does it last long?).

Component A: Spatial Score ($S^S$) This measures how much a Gaussian contributes to the image. It sums the alpha contributions across all pixels and all training views:

$$S _ { i } ^ { S } = \sum _ { k = 1 } ^ { N H W } \alpha _ { i } \prod _ { j = 1 } ^ { i - 1 } ( 1 - \alpha _ { j } )$$

• Explanation: This looks at the rendering equation. $\alpha_i$ is the opacity of the current Gaussian. The term $\prod (1-\alpha_j)$ represents the transparency of everything in front of it. If a Gaussian is fully occluded (behind a wall), this term is 0, so its score is 0.

Component B: Temporal Score ($S^T$) This is the novel part. The authors want to penalize "unstable" Gaussians. They look at the second derivative of the temporal probability $p_i(t)$. A high second derivative means the opacity spikes and drops sharply (short lifespan).

The second derivative $p_i^{(2)}(t)$ is calculated as:

$$p _ { i } ^ { ( 2 ) } ( t ) = ( \frac { ( t - \mu _ { t } ) ^ { 2 } } { \Sigma _ { t } ^ { 2 } } - \frac { 1 } { \Sigma _ { t } } ) p _ { i } ( t )$$

• Intuition:

  • $\Sigma_t$ represents the duration. If $\Sigma_t$ is tiny (short life), $\frac{1}{\Sigma_t}$ becomes huge, making the derivative magnitude large.

  • Large derivative = Unstable/Flickering Gaussian.

    To convert this derivative into a usable score (where 1 is good and 0 is bad), they normalize it using the tanh function:

$$\mathcal { S } _ { i } ^ { T V } = \sum _ { t = 0 } ^ { T } \frac { 1 } { 0 . 5 \cdot \operatorname { t a n h } ( \Big | p _ { i } ^ { ( 2 ) } ( t ) \Big | ) + 0 . 5 }$$

• Explanation:

  • If $|p^{(2)}|$ is large (unstable), $\tanh$ approaches 1, the denominator becomes $0.5(1)+0.5=1$, so the score is lower relative to a sum over time? Actually, let's look closer. If derivative is 0 (stable), $\tanh(0)=0$, denominator is 0.5, score term is 2. If derivative is huge, $\tanh \approx 1$, denominator is 1, score term is 1.

  • Wait, the paper says "assign a higher temporal score to Gaussians with a longer lifespan."

  • Let's re-read: "Large second derivative magnitude corresponds to unstable... low second derivative indicates smooth."

  • Formula: If derivative is 0 (smooth), term is $1/0.5 = 2$. If derivative is huge (unstable), term is $1/1 = 1$. So stable Gaussians accumulate higher scores. Correct.

    They also weigh this by the Gaussian's volume $\gamma(S^{4D})$ to prefer larger Gaussians: S_i^T = S_i^{TV} \gamma(S_i^{4D})

Final Pruning Metric The total score multiplies the spatial and temporal components, summed over time:

$$\boldsymbol { S _ { i } } = \sum _ { t = 0 } ^ { T } \boldsymbol { S _ { i } ^ { T } } \boldsymbol { S _ { i } ^ { S } }$$

Gaussians with the lowest $S_i$ are deleted.

4.2.3. Fast Rendering with Temporal Filtering

After pruning, we still have many Gaussians. However, at any specific time $t$, only a subset are "active" (visible). Instead of checking every Gaussian for every frame (which involves complex matrix math), the authors use a Key-frame approach.

1. Select Key-frames: Choose timestamps $t_0, t_1, ...$ at intervals (e.g., every 20 frames).
2. Generate Masks: For each key-frame $t_i$, render the scene and record which Gaussians actually contributed to a pixel. This creates a visibility mask $m_{i}$.
3. Union of Masks: Since objects move continuously, a Gaussian visible at $t_0$ is likely visible at $t_1$. They create a combined mask for the interval by taking the union of masks from adjacent key-frames ($t_{left}$ and $t_{right}$).
4. Filtered Rasterization: When rendering a test frame $t_{test}$, the system loads only the Gaussians listed in the combined mask of its nearest key-frames. This dramatically reduces the number of Gaussian decompositions calculated (Eq 1).

5. Experimental Setup

5.1. Datasets

The authors evaluated 4DGS-1K on two standard benchmarks for dynamic scene synthesis:

1. Neural 3D Video Dataset (N3V):
   • Source: Real-world recordings.
   • Content: 6 scenes (e.g., "Flame Salmon", "Sear Steak") captured by multi-camera rigs.
   • Characteristics: Complex lighting, fire, smoke, and intricate motions.
   • Resolution: High resolution ($2704 \times 2028$), evaluated at half-res.
2. D-NeRF Dataset:
   • Source: Synthetic (computer-generated).
   • Content: 8 scenes (e.g., "Lego", "T-Rex").
   • Characteristics: $360^{\circ}$ object rotation with deformation.

5.2. Evaluation Metrics

1. PSNR (Peak Signal-to-Noise Ratio):
   • Definition: Measures the pixel-level accuracy of the generated image compared to the ground truth. Higher is better.
   • Formula: PSNR = 10 \cdot \log_{10} \left( \frac{MAX_I^2}{MSE} \right), where MSE is Mean Squared Error.
2. SSIM (Structural Similarity Index Measure):
   • Definition: Measures perceived quality by comparing structural information (luminance, contrast) rather than just pixel differences. Range [0, 1], higher is better.
3. LPIPS (Learned Perceptual Image Patch Similarity):
   • Definition: Uses a pre-trained neural network (like VGG or AlexNet) to measure how similar two images look to a human. Lower is better (0 means identical).
4. FPS (Frames Per Second):
   • Definition: Rendering speed. The authors distinguish between "FPS" (total pipeline) and "Raster FPS" (just the drawing part).
5. Storage: The disk space required to save the trained model (MB).

5.3. Baselines

• 4DGS (Vanilla): The original method this paper improves upon.
• NeRF-based: DyNeRF, HyperReel, K-Planes (to show speed superiority).
• Gaussian-based: Dynamic 3DGS, 4D-RotorGS, Compact3D, MEGA (concurrent compression works).

6. Results & Analysis

6.1. Core Results Analysis

The experimental results demonstrate a massive efficiency gain. On the N3V dataset, 4DGS-1K reduces the model size from 2085 MB (Vanilla 4DGS) to 50 MB (Ours-PP), a 41x reduction. Simultaneously, the rendering speed jumps from 118 FPS to 1092 FPS.

Critically, the visual quality (PSNR) remains almost identical (31.91 dB vs 31.87 dB). In some synthetic scenes (D-NeRF), 4DGS-1K actually outperforms the original 4DGS because pruning removes "floaters" (visual noise/artifacts) that the original model failed to clean up.

The following are the results from Table 1 of the original paper, comparing performance on the N3V dataset:

The qualitative results (Figure 5 from the original paper) visually demonstrate that the method retains high-frequency details (like text on a steak or scales on a dinosaur) despite the heavy compression:

该图像是图表（图5），展示了在Sear Steak场景和Trex场景中，4DGS及其改进方法的定性比较。可以看到，相较于4DGS，我们的方法在存储和帧率上均有显著提升，同时保持了视觉质量。

6.2. Ablation Studies

The authors performed an ablation study (Table 3) to verify that both Pruning and Filtering are necessary.

• Filter Only: Improves speed (561 FPS) but drops quality significantly (PSNR 29.56) because the filter misses some short-lived Gaussians if they aren't pruned first.

• Pruning Only: Reduces storage and improves speed slightly (600 FPS) by reducing the total count.

• Combined: Achieves the best balance (1092 FPS, PSNR 31.88). The pruning removes short-lived Gaussians, which makes the temporal filter more robust (since remaining Gaussians are stable and visible across longer intervals).

  The following are the results from Table 3 of the original paper:

  ID	Method\Dataset			PSNR↑	SSIM↑	LPIPS↓	Storage(MB)↓	FPS↑	Raster FPS↑	#Gauss↓
  	Filter	Pruning	PP
  a				31.91	0.9458	0.0518	2085	90	118	3333160
  b	✓			31.51	0.9446	0.0539	2091	242	561	3333160
  c	✓ (Large Δt)			29.56	0.9354	0.0605	2091	300	561	3333160
  d		✓		31.92	0.9462	0.0513	417	312	600	666632
  e	✓	✓		31.88	0.9457	0.0524	418	805	1092	666632
  f	✓ (Large Δt)	✓		31.63	0.9452	0.0524	418	789	1080	666632
  g	✓	✓	✓	31.87	0.9444	0.0532	50	805	1092	666632

Additionally, Figure 10 and Figure 11 show how the performance changes with different pruning ratios and key-frame intervals, helping to identify the optimal parameters:

该图像是图表，展示了在不同修剪比例下，针对Cook Spinach、Cut Roasted Beef和Sear Steak三种场景的PSNR变化。横轴为修剪比例，纵轴为PSNR(dB)，其中红点表示默认设置的结果。

该图像是一个图表，展示了不同关键帧间隔下，三种不同场景（Cook Spinach, Cut Roasted Beef, Sear Steak）的PSNR（dB）变化。图中对比了使用微调和不使用微调的过滤器在不同间隔下的表现，并标注了默认设置参数。

7. Conclusion & Reflections

7.1. Conclusion Summary

4DGS-1K successfully democratizes high-fidelity dynamic scene rendering. By identifying that "flickering" Gaussians are the root cause of inefficiency, the authors devised a method to mathematically detect and remove them (Pruning) and ignore irrelevant ones during drawing (Filtering). This results in a system that is lightweight (50MB) and extremely fast (>1000 FPS), making 4DGS practical for VR, AR, and mobile applications where it was previously too heavy.

7.2. Limitations & Future Work

• Preprocessing Overhead: The paper notes that calculating the masks and pruning scores takes additional time after training. Optimizing this preparation phase is a future goal.
• Scene Dependency: The optimal pruning ratio (e.g., removing 80% vs 90% of points) depends on the specific scene. A cluttered scene might need more points than a simple one. The authors suggest that finding an automatic way to determine this ratio is an open challenge.
• Generalizability: The method is tailored specifically for the 4DGS representation. Future work could explore if these temporal pruning concepts apply to other dynamic representations like TensorRF.

7.3. Personal Insights & Critique

• Critique of Innovation: The use of the second derivative of opacity as a proxy for "Gaussian stability" is a brilliant, mathematically grounded insight. It moves beyond simple heuristics (like "is opacity low?") to a deeper understanding of the signal's behavior over time.
• Practicality: The shift from 118 FPS to 1092 FPS is not just an incremental improvement; it is a paradigm shift. It moves the technology from "offline rendering" to "high-refresh-rate VR/Gaming" territory.
• Potential Issue: The method relies on "fine-tuning" after pruning to recover quality. This implies that the pruning does damage the scene initially, and the network must work to repair holes. If the pruning is too aggressive, fine-tuning might fail to recover fine details.