4DGCPro: Efficient Hierarchical 4D Gaussian Compression for Progressive Volumetric Video Streaming
Authors: Zihan Zheng
Zhenlong Wu
Houqiang Zhong
Yuan Tian
Ning Cao
Lan Xu
Jiangchao Yao
Xiaoyun Zhang
Qiang Hu
Wenjun Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Volumetric Video
Dynamic 3DGS
Progressive Streaming
4D Reconstruction
Progressive Compression
Primary area: applications

Abstract: Achieving seamless viewing of high-fidelity volumetric video, comparable to 2D video experiences, remains an open challenge. Existing volumetric video compression methods either lack the flexibility to adjust quality and bitrate within a single model for efficient streaming across diverse networks and devices, or struggle with real-time decoding and rendering on lightweight mobile platforms. To address these challenges, we introduce 4DGCPro, a novel hierarchical 4D Gaussian compression framework that facilitates real-time mobile decoding and high-quality rendering via progressive volumetric video streaming in a single bitstream. Specifically, we propose a perceptually-weighted and compression-friendly hierarchical 4D Gaussian representation with motion-aware adaptive grouping to reduce temporal redundancy, preserve coherence, and enable scalable multi-level detail streaming. Furthermore, we present an end-to-end entropy-optimized training scheme, which incorporates layer-wise rate-distortion (RD) supervision and attribute-specific entropy modeling for efficient bitstream generation. Extensive experiments show that 4DGCPro enables flexible quality and variable bitrate within a single model, achieving real-time decoding and rendering on mobile devices while outperforming existing methods in RD performance across multiple datasets.

4DGCPro: Efficient Hierarchical 4D Gaussian Compression for Progressive Volumetric Video Streaming
Zihan Zheng', Zhenlong Wu', Houqiang Zhong?, Yuan Tian Ning Cao
Lan Xu JJingchao Yao Xiaoyun Zhang' Qiang Hu²; Wenjun Zhang Cooperative Medianet Innovation Center, Shanghai Jiaotong University' Department of Electronics, Shanghai Jiaotong University? Shanghai AI Lab"
Cloud platform department, E-surfing Vision Technology Co., Ltd. School of Information Science and Technology. ShanghaiTTech University
0.24MB/30.04dB
31.18dB
0.10MB
Tnblet
1920 44FPS
Desktop
Bitstream
Frame
Frume
Figure 1: Left: Our method enables progressive streaming of hierarchical 4D Gaussians within single bitstream, where incremental enhancement layers (e.g., +0. 10MB) gradually improve visual quality (e.g., from 30.04dB to 31. 31.18BB) with minimal bitrate overhead. Right: The streamed content is adaptively decoded and rendered in real-time on various devices (e.g., tablets 44FPS, desktops 58FPS) by dynamically selecting layers (L.1-1.6) based on available bandwidth and compute.
Abstract
Achieving seamless viewing of high- fighfiidlityy volumetric video, comparable to 2D video experiences, remains an open challenge. Existing volumetric video compres- sion methods either lack the flexibility to adjust quality and bitrate within single model for efficient streaming across diverse networks and devices, or struggle with real-time decoding and rendering on lightweight mobile platforms. To address these challenges, we introduce 4DGCPro, a novel hierarchical 4D Gaussian compression framework that facilitates real-time mobile decoding and high-quality rendering via progressive volumetric video streaming in a single bitstream. Specifically, we propose perceptually-weighte and compression-friennty friendll hierarchical 4D Gaussian representation with motion-aware adaptive grouping to reduce temporal redundancy, preserve coherence, and enable scalable multi-level detail streaming. Furthermore, we present an end-to-end ontrope-optimized training scheme, which incorporates layer-wise rate-distortion (RD) supervision and attribute-specific en- tropy modeling for efficient bitstream generation. Extensive experiments show that 4DGCPro enables flexible quality and multiple bitrate within single model, achieving real-time decoding and rendering on mobile devices while outperforming existing methods in RD performance across multiple datasets.
The corresponding author is Qiang Hu(qiang hu @ @sj.u.cdu.cn)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
Volumetric video enables immersive 3D experiences with free-viewpoint navigation, but streaming and rendering high-quality long sequences with large motions remains challenging, especially on lightweight devices like mobile phones. Compared to 2D video, volumetric content demands higher bandwidth, storage, and real-time decoding capabilities, making fixed-bitrate solutions inadequate to handle the variability across heterogeneous devices and network conditions. Therefore, the core challenge lies in achieving real-time, high-fidelity playback with low computational cost, while enabling scalable and progressive streaming under constrained resources.
Traditional volumetric reconstruction methods. including surface estimation 88) point clouds [57]. meshes [8]] light field [28] 44] and depth-based techniques [60] [79], struggle to faithfully capture the geometric complexity and temporal dynamics of real-world scenes. Neural radiance field (NeRF)
40 address these limitations by modeling view-dependent appearance without relying on explicit geometry, enabling photorealistic rendering. While extensions [49 30 12
78 adapt NeRF to dynamic scenes, they remain constrained by the difficulty of handling long sequences and efficient streaming. Some works [66 67 73 81 80] compress dynamic NeRF's to enable streaming, but the high computational cost of decoding and rendering limits their practicality in real-time applications.
24 14
Recent work on 3D Gaussian Splatting (3DGS) [27] introduces an explicit scene representation using anisotropic Gaussian primitives with real-time, differentiable rasterization, achieving unprecedented rendering speed and visual quality. Subsequent studies [34 72 19 (7) extend 3DGS to dynamic
scenes by incorporating temporal attributes into Gaussian parameters, but require full-sequence pre-loading during training and rendering, limiting streaming practicality. Alternative approaches 18 16 model temporal Gaussian variations via deformable fields or residual tracking to enable streamable representations, yet incur substantial bandwidth overhead. A few studies
[38 61
20 26 25 69 have explored compression for dynamic 3DGS. For example, 4DGC [20] jointly optimizes representation and entropy models via RD loss, improving efficiency but struggling with high decoding latency and poor robustness to large motions due to rigid modeling. More fundamentally, existing dynamic Gaussian compression methods lack the flexibility to adjust video quality and bitrate within a single model, and typically require separate models for each bitrate, leading to high storage costs and limited adaptability under varying network and device conditions.
To tackle the above challenges, we propose 4DGCPro, novel hierarchical 4D Gaussian compression approach for progressive volumetric video streaming. As illustrated in Fig. [ our method achieves multiple bitrate using single model and enables real-time decoding and high-fidelity rendering on lightweight devices for large-motion sequences. We realize this through three key innovations. First, we introduce a perceptually-weighte hierarchical Gaussian representation for keyframes, guided by significance metric that combines geometric volume and opacity. This enables scalable representation across detail levels and establishes the foundation for dynamic modeling. Second, we propose hicrarchical motion modeling strategy, where motion in subsequent frames is decomposed into rigid transformations and residual deformations to capture large displacements and preserve temporal coherence. We further adopt motion-awan adaptive Gaussian grouping to handle topological changes and long-term dynamics, ensuring compact and consistent temporal representation.
Third, we propose joint entropy- -uttopy-op training and progressive coding framework for effi- cient and scalable bitstream generation. Specifically, we introduce layer-wise rate-distortion (RD) supervision into the training pipeline using differenniable quantization and attribute-specific entropy modeling. For keyframes, we utilize FFT-accelerated Gaussian kernel density estimation (KDE) for precise bitrate prediction of Gaussian attributes, with hierarchical Gaussian optimization guided by per-layer RD trade-offs. For inter- framme we apply caiasiianndistibutiin based entropy estimation and temporal consistency constraints to maintain compactness and coherence. After training, we quantize attributes and convert multi-layer representations into stacked 2D single-channel maps, which are encoded with 2D codecs into a progressive bitstream, enabling scalable real-time decoding and rendering via hardware video codecs and shaders. Experimental results show that our 4DGCPro supports multiple bitrates using a single model and achieves state-of-the, the-art RD performance across various datasets. Compared the SOTA method HPC [80), our approach achieves 3x compression rate without quality degradation, while enabling real-time decoding and rendering on mobile devices.
In summary, contributions are as follows:
2

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We propose 4DGCPro, a novel framework for progressive volumetric video streaming that supports multiple bitrates with a single compact model, enabling real-time decoding and rendering on mobile devices with superior RD performance.
We introduce a compact hierarchical 4D Gaussian representation with motion aware adaptive grouping for scalable and high-fidelity modeling of dynamic scenes.
We present an end-to-end cntropy-optimiin training scheme with layer-wise RD supervision and attribute-specifie entropy modeling, enabling fine-grained RD optimization across layers and better overall compression.
2 Related Work
2.1
NeRF-based Volumetric Video Modeling
NeRF 440 have revolutionized 3D scene representation using differentiable volume rendering with implicit neural representations. While recent advances in static scene representation (2H4] 7 39
41 52 53
have improved compactness and reconstruction speed, several works have extended these methods to dynamic scenes. blsw- approaches [32 33 construct 3D features from monocular video, reducing data collection complexity but requiring additional priors for complex scenes. Deformation field methods [10]
warp dynamic frames into a canonical space to capture temporal features, yet suffer from slow training and rendering. To accelerate performance, adopt explicit 4D radiance field representations based structured volumetric decompositions (e-g., voxel grids, multi-plane projections, tensor factorizations), yet these unified frameworks remain incompatible with streaming scenarios.
45
49
[5]
recent methods [12 [4 14 5 58
31 47
63 65
2.2 3DGS-based Volumetric Video Modeling
enable photorealistic static scene reconstruction through their efficiency and physical interpretability. with recent extensions dynamic scenes. Current dynamic 3DGS approaches mainly follow two paradigms. Some studies 72 76 199 (7] 74 77
3DGS 27 and its variants 22
13
23 6
model Gaussian attributes as temporal functions to create unified dynamic representations, which achieve exceptional RD performance but neglect streaming feasibility. Alternative approaches [3
61
16] employ frame-wise modeling with explicit rigid motion estimation, enabling streamable Gaussian volumetric video at the cost of increased data volume and compromised reconstruction quality. While 3 (69 optimizes the full Gaussian coefficients to model complex motions, its fixed group length leads to error accumulation or data redundancy. Meanwhile, it lacks the capability to support multiple-bitrate selection within a single bitstream. Our approach introduces a compact hierarchical motion-aware Gaussian representation coupled with adaptive Gaussian grouping that dynamically responds to topological changes and achieves multiple bitrate using single model.
18
2.3 Volumetric Video Compression
Volumetric video compression is crucial for reducing massive data requirements, where traditional approaches employ octree [55 (2 and wavelet [42] techniques (later standardized as MPEG-PCC
(50). while subsequent learning-
methods 335
50
15 focus on improved
80 21 have made progress in compressing dynamic NeRF features for storage optimization, they commonly suffer from poor quality and slow decoding/rendering. For instance, HPC (80] employs learned compression for progressive coding of residual feature grids representing dynamic scenes. However, its high decoding latency limits real-time applications. For 3DGS based methods, static scene techniques 443 II] [1) dominate, whereas dynamic scene approaches [26] 25) (00] face inefficiency and single-rate constraints. Our method delivers superior RD performance and computational efficiency using standard video codecs, supporting both streaming for quality adaptation across dynamic bandwidth.
efficiency. While recent advances [66] 67
73
59
48
54
81
real-time decoding and progressive
3 Method
In this section, we present the technical details our 4DGCPro architecture (Fig. 2). The framework begins with a perceptually- hierarchical Gaussian representation for keyframes (Sec. 3.1

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(a) Herarccicaa KeyrarchhcalKeyyrrii Keyframe
Matte Joi
Highhr Devii Levels
Hingarchaee Mution
Rigid Transiormation
H
Residual Deformation
Composition
Residual Deformatio
Representation
Modeling
Reader
[-]
[G]
6/-1
MUP 000
Apr, &
G
f
Liyane Inter
Leaker
Keyframe
Inter-frame
bieg
Threshold T
Group
Group
Group
T
(c) Molion-aware Adaplive e Grouping
Figure 2: Our 4DGCPro framework. (a) prrceptually-weigghe hierarchical 4D Gaussian represen- tation models keyframes at multi-level detail for progressive reconstruction. (b) Hierarchical motion modeling decomposes dynamic scenes into rigid transformations and residual deformations based on the previous frame, while (c) motion motion-aware aware adaptive grouping dynamically adjusts to topological changes enhance temporal consistency and reduce error accumulation. The entire pipeline is end-to-end optimized with layer-wise RD supervision and attribute-spccffi entropy modeling.
which establishes the foundation for dynamic scene characterization and progressive streaming. We then introduce a hierarchical motion modeling approach with adaptive grouping (Sec. 3.2). decomposing motions into rigid transformations and residual deformations. This motion-aware adaptive Gaussian grouping mechanism effectively handles diverse motion patterns in complex scenes. To generate efficient and scalable bitstreams, we incorporate layer-wise RD optimization into the training pipeline through differentiable quantization and attribute-specine entropy modeling, followed by compression using standard 2D video codecs (Sec. 3.3).
3.1 Perceptually- Weighted Hierarchical Gaussian Keyframe Representation
Recall that 3DGS represents scenes explicitly through 3D Gaussians G, defined by set of Iearnable parameters, including center position μ., rotation matrix R representing orientation, spherical har- monic coefficients f for view-dependent appearance modeling, scaling factors s controlling spatial extent, and opacity value The spatial influence at point follows G (x), expressed as:
G(x) = exp (-x(xx 1) (x - 14)
(I)
The covariance matrix E is constructed through Σ Rss"R" With af being the projection of the opacity of the i-th Gaussian onto the image plane and c, denoting the color of the i-th Gaussian in the viewing direction, the pixel color is computed by differentiable splatting of N ordered Gaussians as follows:
i-1 c = Σ caa', SEN
(1--a) j=1
When reconstructing long-duration dynamic scenes, we first reconstruct high-quality keyframes to serve as references for subsequent inter-frames. Inspired by y [6), we initialize keyframe 3D Gaussians through NeuS2-based [70] surface mesh extraction. After pre-training, low-opacity Gaussians are pruned to achieve compact representations. While this optimized 3DGS delivers high-fidelity reconstruction, its substantial data footprint becomes problematic for smooth viewing under fluctuating bandwidth conditions. We therefore propose a perceptually-weighhe Gaussian representation guided by significance metric V, which serves as the basis for progressive transmission and rendering. The proposed metric V analytically evaluates each Gaussian's 's visual importance through two geometrically goouuddd attributes: (I) spatial volume S, representing the 3D volume occupied by the Gaussian and computed as rabe (where b, are its scale parameters along the three principal axes), which reflects its structural contribution to the scene geometry; and (2) opacity which determines its perceptual weight in final rendering. These orthogonal factors are integrated with the weight A
hicrarchical
V = a S.

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Keyframe
Inter-Sramee
Soalt
Upacity
Opaelty
12
0.6EMB3228.156
1.22MB/29.
-15
2.4
50
Group Size S0: Error Accumolaation
Group Size S: Data Redundancy
(b) Conssian Atmihutte
Residunl Attribates
Analysis of Diffirent Group Size Figure 3: Analysis of group size and attributes distributions. (a) Large groups suffer from error accumulation while small groups exhibit data redundancy. (b) Keyframe Gaussian attributes display irregular spatial distributions, whereas (c) residual attributes follow Gaussian distributions.
Distribution
Distribution
After sorting all Gaussians in descending order using our significance metric, we partition them into L hierarchical layers G = {G' The base layer G' preserves essential scene structures, while subsequent layers progressively enhance details. This hierarchical representation facilitates adaptive streaming, where the client dynamically selects the optimal number of layers to decode based on network conditions and computational resources. This approach ensures smooth playback while efficiently balancing transmission overhead and reconstruction fidelity across diverse network environments.
Progressive Rendering. Our method supports progressive rendering from single compressed representation, enabling scalable visual output with adjustable levels of detail. Starting from the base layer (1 1), which contains essential structural and appearance information, each subsequent Gaussian layer incrementally refines the reconstruction. Specifically, when decoding up to level I, only the Gaussians up that layer (denoted by the index set N are used for rendering. The color c¹ at this stage is computed as:
i- c'= c'a ( NE
(4)
5=1
Each additional layer introduces a compact of Gaussians that enhance detail without redundant transmission. This hierarchical refinement strategy allows the model to adapt dynamically to available computational and bandwidth resources, balancing reconstruction quality and efficiency in real time. The result is scalable, high-fidelity rendering system capable of maintaining seamless visual enhancement under varying resource constraints, all within a unified bitstream.
3.2 Hierarchical Motion Modeling with Adaptive Grouping
Building upon the hierarchical keyframe Gaussian representation, we employ it as reference basis for training subsequent inter-frames. Our proposed hicrarchical motion modeling strategy effectively captures large-scale complex motions while maintaining temporal coherence through decomposition of frame differences into rigid transformations and residual deformations. We futher introduces adaptive Gaussian grouping, which dynamically responds varying scene changes to achieve dual benefits: enhanced representation fidelity and reduced model size for efficient streaming.
motion- aware notion-aware
Rigid Transformation. To estimate the rigid transformations of Gaussians between frames, utilize the Gaussian positions p4-1 = {/|اト} from the previous frame as input and predicts both translation Au, (A and rotation AR, = (AR) The module first employs multi-resolution hash grid H. [H with Ln levels capture motion features h, at different scales through hash coding as:
(5) where interp(-) refers the hash grid interpolation operation. Subsequently, h, is input into two lightweight MLPs, namely tf and &R, to calculate the translation Aμr; and rotation AR, for each Gaussian:
h = (b!a --- = finterp(r(_.,H
A = 15" (b)), AR = (h))
(6)
In this manner, the position and rotation of frame can determined using the equations μ p + Aut and R, AR(R_
5

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Residual Deformation. Existing motion- awarre 3DGS streaming methods 20 61 primarily focus on rigid motion simulation and Gaussian compensation, which often fail to accommodate object deformation and frequently introduces visual artifacts and temporal instability. To address these limi- tations, our approach incorporates residual deformation framework following rigid transformation. The framework learns Gaussian deformations via adaptive scaling, opacity and color adjustments while predicting attribute residuals (As;, Day. Af)) relative to parameters of t-l frame, ensuring both local detail preservation and temporal stability.
s = = + As/, af = a + Say, f'= Af..
(7)
By combining both rigid transformations and residual deformations, method effectively captures both large displacements and subtle scene variations, significantly reducing visual artifacts while maintaining temporal coherence.
Motion-aware Adaptive Gaussian Grouping. For long-sequenee dynamic scenes with substantial motion, using only the initial frame as reference becomes inadequate due to accumulating scene variations. Meanwhile, as shown in Fig. 3īa), fixed-length group structures inevitably introduce two competing artifacts: error accumulation across frames in large groups, and data redundancy in small groups due to repeated parameter transmission. We address this through motion-aware adaptive Gaussian grouping, where the group size is dynamically determined by rigid transformation results. When the average Gaussian translation Aue; exceeds a predefined threshold Tus indicating substantial scene changes, initiate new group with an updated reference frame. This adaptive grouping strategy automatically adjusts to motion intensity, employing shorter groups during rapid changes for better reference quality, while maintaining longer groups for stable segments optimize compression efficiency. The resulting representation achieves both accuracy and compactness by balancing temporal coherence with adaptive topology updates.
In summary, our 4DGCPro dynamically structures the scene into variable-length groups for ef- ficient temporal modeling. For a group starting at frame T with length N, we sequentially rep- resent as Gr, [Ap,, AR,, Af,, Ast, Aar TT+N- where GT is the keyframe Gaussian and (Apr, AR, Af,, A8,, A are the hierarchical residual attributes. This design optimally exploits frame-frame similarities while preserving reconstruction quality under complex motions.
3.3 End-to-end Entropy-optimizee Training
We propose an end-to-end entropy-optimized training scheme, which attains the optimal RD per- formance by incorporating layer-wise RD supervision and atrribute-ppecific entropy modeling. To facilitate gradient entropy modeling method to accurately estimate the bitrates of diverse attributes. Furthermore, we carry out progressive compression with 2D codecs on the hierarchical representation of Gaussians, enabling scalable real-time decoding and rendering. Next, we will introduce keyframe optimization, inter-keyframe optimization, and progressive bitstream generation in details.
we utilize differentiable quantization along with attribute-specific
Keyframe Optimization. During the optimization process of keyframes, we first use Leotor supervision term to pretrain the Gaussians:
Leolor (1 >sim))lc, c/l1 + CD
(8)
where Cg and è denote the ground truth and reconstructed colors respectively, and Assim weights the D-SSIM[36 metric. After pre-training and pruning, we hierarchically organize Gaussians and perform joint entropy-optimized hierarchical training to maximize the RD performance per level. To ensure differentiable gradient flow and enhance quantization robustness, we implement uniform
noise injection u ~ U 2q 2q to simulate quantization effects with step size q. Additionally, we introduce entropy estimation of Gaussian attributes into our loss function to improve compression efficiency. As shown in Fig. Bb), keyframe Gaussian attributes exhibit irregular spatial distributions, necessitating KDE-based density estimation. Our implementation first computes the cumulative distribution function (CDF) through Silverman-rule bandwidth selection and FFT convolution, then obtains the probability density function (PDF) via numerical differentiation of the CDF:
(P = PeDr (ū + - (
(9)
To ensure optimal RD performance at each level, the keyframe optimization loss function Lksy is formulated as weighted sum of per-level losses Cley. where each level's loss combines photometric

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8. 1OMB
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0.94MB
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Figure 4: Qualitative comparison on our 4DGCPro and HiFi4G 226 datasets against ReRF 80 3DGStream [6]] and v 69).
[66], HPC
term L co and a rate term Crate, key"
Key Σ Xcyyyy =
Σ
X ACColor + Arate key frate key k
(10)
1=1
1=1
(1
1lc -6'112 + Ausim ADsim-
(11)
C Fay key
1
E
log2 (PeMF(()))
(12)
N
Here, Loster measures the photometric difference between the ground truth and the Gaussian rendering results at level I, L jey denotes the entropy estimated via KDE from Gaussian attributes at the same level. Arate key is the weight of the entropy loss, and X is the weight parameter for the loss at different levels. With this training objective, we obtain the keyframe Gaussians that achieve the optimal RD performance at each level.
Inter-frame Optimization. Building upon the hierarchically trained Gaussians of keyframes, optimize subsequent Gaussians within each group. Since Gaussian positions and rotations are particularly crucial for rendering quality, we only employ simulated quantization deliberately exclude entropy constraints and rely solely on Ceotor for supervision.
In the residual deformation stage, maximize both accuracy and compactness each level, maintain hierarchical supervision by augmenting color constraints with both entropy loss L inter and temporal loss C.eg As illustrated Fig. c(), we validate the Gaussian distribution of residual attributes, which allows us simplify the entropy estimation merely calculating the mean and variance of residuals, significantly streamlining training. To further enhance temporal coherence, we impose the temporal loss residual attributes, explicitly enforcing fiter-frame consistency. This deliberate smoothness constraint not only improves reconstruction quality but also reduces residual magnitudes during subsequent coding, ultimately optimizing storage efficiency. Thus, the training objective Linter for this stage can be summarized as:
Linter
Σ X Clatce
X (C Arate inter Crate inter + >regFlegg
(13)
C inter
Σ
log2 (P)))
(14)
N
AEIA
C
Σ
1
(15)
where C denotes the inter-frame loss for the 1-th layer of Gaussians, while CL inter and L are weighted by Arate_imter inter and Arg. respectively. Through this joint antropy-optimizz training framework. we obtain a compact yet high-fidelity hierarchical 4D Gaussian representation, enabling efficient volumetric video compression for storage and transmission.
Efficient Progressive Bitstream Generation. Once the training is completed, we explicitly separate Gaussians at different levels and implement differential quantization for Gaussian attributes, where

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Table I: Quantitative comparison on our 4DGCPro, HiF14G [26 and N3DV B1 datasets. Our
method achieves the best rendering quality against other methods, achieving progressive rendering results within one single model.
4DGCPro
HiF14G 26
N3DV(31
Method
PSNR,
Size (MB)*
PSNR,
Size
PSNR,
Size
SSIMI
SSIM
(MB) +
SSIM
(MB) +
(dB)
(dB)
(dB)
ReRF 66
27.37
0.947
1.70
30.30
0.977
0.97
29.71
0.918
0.77
HPC 80
27.68
0.948
1.08
34.14
0.987
0.72
3DGStream 61
21.08
0.837
8.1
21.02
0.946
8.1
31.54
0.942
8.10
4DGC 20
21.48
0.850
0.97
21.05
0.946
0.94
31.58
0.943
0,50
HiCoM 16
24.65
0.926
2.61
29.37
0,968
1.94
31.17
0.939
0.70
V 69
28.11
0.955
1.60
36.26
0,994
0.92
Ours(High)
29.47
0.963
1.31
36.38
0,995
0.75
31.64
0.944
0.64
Ours(Mid)
28.68
0.958
0.66
35.48
0.991
0.37
31.14
0.938
0.43
Ours(Low) 27.69
0.952
0.33
34.62
0.988
0.19
30.68
0.926
0.21
Ours Full wlo Rate Estimation
w/o Aduptive Group Modeling
w/o Significance Metric
RcRF
HPC
44DGC
Va
30
30
27
20
32
222
25
(MB/Frame)
0.5
1,0
1.5
0.5
1.0
0.5
1.5
(a) Dance
(b) Coser
(c) Actorl Greeting
(d) Coffee martini
Figure 5: Rate-distorticn curves across various datasets. Rate-distortion curves not only illustrate the superiority of our method compared the multiple-bitratee approaches ReRF [66], HPC 80) 4DGC
20 and v [69]. but also demonstrate the efficiency of various components within our method.
employ 6 or uint32 precision for position information due to its higher sensitivity to errors while using uint8 for all other attributes. Since each Gaussian parameter contains multiple channels, carefully flatten each feature channel into separate 2D single-channel image while strictly preserving the 2D spatial continuity. The flattened feature images are systematically arranged into temporal sequences by aligning same same-group. same-level, and same-channel features. These sequences are then compressed using an H.264 video encoder, enabling scalable real-time decoding and rendering via hardware video codecs and shaders. These bitstreams are transmitted collectively, enabling clients to selectively receive and decode different quality levels for adaptive rendering, thereby supporting smooth quality transitions, flexible viewing experiences, and real-time presentation.
4 Experiments
To comprehensively evaluate our method, conducted experiments two kind of distinct datasets: (1) the N3DV dataset [31] featuring subtle motions with background, and (2) the HiFi4G dataset [26] containing complex motions without background. We additionally captured new dataset using 81 synchronized Z-CAM cinema cameras 3840x2160, recording diverse performances including dance, sports, and instrument playing. Our dataset contains not only solo performances but also multi-person interactions, which poses higher demands on the modeling method. We further introduce the detailed experimental settings in Sec. A
4.1 Comparison
To validate the effectiveness of the proposed method, we compare it against several SOTA approaches including NeRF-based methods ReRF [66], HPC [80] and 3DGS-based methods 3DGStream [61]. 4DGC [20]. HiCoM [T6]. v [69) presenting results in Fig.
can be observed that due the limitations of the finite neural representation of NeRF when dealing with complex motions, both ReRF [66] and HPC (80) produce blurry results and over- weer-smothinng. Meanwhile, 3DGStream [61] is limited to modeling only rigid motion of Gaussians and relies exclusively on the first frame as universal reference across all frames. This leads to severe enror accumulation over time, particularly in regions with motion, causing pronounced visual artifacts. Due to its inability to capture non- rigid deformations and significant displacements, the approach produces inconsistencies. including trajectory fragmentation and residual errors propagated from previous frames. Compared with

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Table 2: The BD-PSNR results of our 4DGCPro, HPC with ReRF [66] on different datasets.
80
4DGC
20
and V
66
when compared
Dataset
4DGCPro
226
N3DV
Method
HPC
4DGC
v
Ours
HPC
4DGC
V
Ours
HPC
4DGC
V
Ours
BD-PSNR(dB)
3.42
-6.15
1.90
4.20
5.84
-9.10
7.19
7.87
1.99
2.07
Table 3: Complexity comparison of our method with dynamic scene compression methods, ReRF
666. HPC [80]. 4DGC (20] and v [69] 4DGCPro dataset.
Time
6c
2DGC
v 69
HPC[8D
Ours Mid
High
Mid
Low
High
Low
Encode(ms)
820
2700
390
3300
2870
2420
408
205
102
Decode(ms)
61
94
20
121
103
90
29
19
12
Train(min)
42.73
0.83
0.97
93
93
93
4.3
4.3
4.3
Render(ms) 52
5.6
2.8
231
167
110
3.1
2.5
2.2
v 669,
our method achieves better reconstruction quality while reducing the model bitrate, and can render multi-quality reconstruction results from a single model. We further provide more demonstrations of our method in Sec. [B.
For quantitative comparison, as demonstrated in Tab. I our method achieves superior performance compared to other approaches on diverse datasets. On the 4DGCPro dataset, our method achieves superior performance across all quality levels: the high-quality model attains the best PSNR (29.47dB) and SSIM (0.963) with compact size (1.31MB): the medium-quality version maintains high PSNR performance (28.68dB) with improved compression (0.66MB); while the low-quality configuration further reduces model size to 0.33MB while retaining competitive quality (27.69dB). Notably, our framework supports multiple bitrates within a single model while outperforming baselines on all metrics. The rate-distortion superiority of our approach is further demonstrated in Fig. and quantitatively validated through BD-PSNR measurements in Tab. 2] Our method achieves consistent RD improvements across all datasets and bitrates, with BD-PSNR gains of 4.20dB, 7.87dB, and 2.07dB over ReRF on the 4DGCPro, HiFi4G, and N3DV datasets, respectively. These results significantly exceed those of other compared methods, including HPC (3.42dB on 4DGCPro) and v (I.90dB on 4DGCPro). The superior RD performance demonstrates the effectiveness of our significance metric, adaptive grouping, and entropy modeling strategies.
As validated in Tab. 3 our method demonstrates exceptional computational efficiency across all quality levels. The medium-quality configuration achieves 19ms decoding and 2.5ms rendering per frame, enabling real-time performance at over 52 FPS, while even the high-quality setting maintains practical efficiency with 29ms decoding and 3.1ms rendering. As shown in Tab. 7 our approach also delivers remarkable performance on lightweight devices: on mobile platforms, the complete pipeline requires only 43ms for high-quality rendering, reduced to 39ms and 34ms for medium and low quality, demonstrating real-time decoding and rendering capability even under strict resource constraints.
These results collectively demonstrate that our method achieves the best trade-off between recon- struction quality, compression ratio, and computational efficiency among all compared approaches. The progressive coding capability further enhances practical applicability, enabling adaptive quality adjustment based on available computational resources and bandwidth constraints.
4.2 Ablation Studies
We conducted four ablation studies to evaluate the effectiveness of each component of our method. These experiments focus on the significance metric, motion-aware adaptive Gaussian grouping, the number of Gaussian layers, and joint entropy-optimizer training. Using the full model as the baseline, we first ablated the components of the significance metric, including the weight parameter Ag. We then compared our adaptive grouping strategy against different fixed group lengths. The third experiment examines the impact of different number of Gaussian layers. Finally, we assessed various entropy modeling methods and underscored the importance of simulated quantization.
Tab. presents ablation results for the significance metric and adaptive grouping strategy. The left section evaluates the significance metrie for low-level Gaussians. Compared to our full model (27.69dB), using only opacity or volume leads to clear performance degradation (26.71dB and 25,83dB, respectively). Simply multiplying these two factors also causes a significant PSNR drop of -L.33dB, Furthermore, improper weighting of xy results in measurable PSNR reductions ranging

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Table 4: Ablation studies of our perceptually-weighhed hierarchical Gaussian representation and
adaptive Gaussian grouping.
Significance Metric PSNR(dB) Size(MB))
Group Size
BDBR(%))
BD-PSNR(dB)]
w/o Opacity w/o Volume Multiplication
26.71
0.39
48.37
-0,96
25.83
0,38
5
11.81
-0.25
26.36
0.33
10
16.34
-0.32
Aw = 10a
27.51
0.34
15
14.95
-0.33
AØ 10a
27.57
0.35
20
11.42
-0.34
Ours(Full)
27.69
0.33
25
8.11
-0.31
Table Ablation studies of the number of layers and end-to-end entropy-optimized training scheme.
L BD-PSNR(dB)t Training Time(min))
Training
BDBR(%) BD-PSNR(dB))
4 -0.87
3.1
w/o R-E
32.73
-0.60
5
-0.38
3,5
w/o H-S
61.21
-2.89
4.3
w/o S-Q
4.36
-0.1
7
0.06
4.9
Only KDE
0.58
-0.02
8
0.09
5.5
Only Gaussian
from -0.18dB to -0.12dB. The right section validates our motion-awar adaptive grouping approach. Even the rest-performing fixed group size strategy shows consistent degradation, with minimum BDBR of 8.11 % and a maximum BD-PSNR reduction of -0.25dB, confirming the clear advantage of adaptive grouping method in rate-distortion performance.
Table Sableeexxaminee the impact of the number Gaussian layers and the entropy modeling strategy. The left panel shows that deeper hierarchies (c.g.. L=8) only slightly improve BD-PSNR (up to 0.09dB) at the cost noticeable increase training time (+1.2 min). In contrast, shallower configurations (e.g., L=4) lead to more substantial degradation in BD-PSNE (-0.87dB). The right panel highlights the importance of entropy modeling: omitting ("woo R-E"") introduces redundancy, while removing hierarchical supervision ("w/o H-S") severely degrades the quality of low-level Gaussians, resulting in a BD-PSNR drop -2.89BB. Moreover, the absence of simulated quantization (S-Q) leads to 4.36% % increase in BDBR, confirming its essential role in enhancing resilience quantization erros. For Gaussian parameter modeling, using only KDE estimation ("Only KDE") achieves similar performance but prolongs training by 1.2 minutes per frame, whereas assuming universal Gaussian distribution ("Only Gaussian ") causes training failures. Additional ablation studies are provided in Section B.3
5
Discussion
Limitation, Although 4DGCPro presents an innovative and efficient approach to progressive stream- ing of volumetric video, it has several limitations. First, the Gaussian optimization process suffers from prolonged training times (several minutes) due to hierarchical supervision which leads re- peated rendering passes. Accelerating this procedure remains an essential research objective. Second, our method relies on multi-view video input and faces challenges in sparse-view reconstruction, limiting its applicability in scenarios with insufficient camera coverage. Finally, the current frame- work underperforms in spatially extensive scenes, necessitating further exploration enhance its scalability.
Conclusion. We present 4DGCPro, novel hierarchical 4D Gaussian compression approach for progressive volumetric video streaming. Our framework accomplishes multiple bitrate control within sigle model while supporting both real-time decoding and high-fidelity rendering on mo- bile platforms, even for sequences containing large motion displacements. Our approach begins by constructing a perceptually-
hierarchical Gaussian representation using the importance metric. We then model inter-frame Gaussians by rigid transformations and residual deformations, enhanced by a motion-aue awarre adaptive Gaussian grouping strategy for efficient sequence- wide model- ing. Furthermore, we introduce joint entropy-optimized training and progressive coding framework, employing attribute-specific entropy modeling to ensure precise and efficient optimization. Thanks to its multiple bitrate capability, 4DGCPro enables progressive streaming and high-efficiency decod- ing/rendering across multiple quality levels, making ideal for sandwidth-flutuaal scenarios. This work establishes critical foundation for broader volumetric video adoption.
10

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Acknowledgements
This work is supported by National Natural Science Foundation of China (62571322, 62431015. 62271308), STCSM (242R1432000, 2451 I 106902, 2451 1 106900, 22DZ2229005), 111 plan (BP0719010), and State Key Laboratory UHD Video and Audio Production and Presentation.
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Figure 6: Gallery of our results. 4DGCPro delivers real-time figh-fidelity rendering of scenes across
challenging motions, such "playing instruments", "dancing" and "playing sports".
Level
Level 2
Level 3
Level 4
Level
Level 6
Figure 7: Multi-bitrate results of our method under single bitstream.
This appendix provides additional material to supplement the main text. will first introduce implementation details in Sec. A Then provide additional experimental results in Sec. B
A Implementation Details
Our code is primarily based on the open-source codes of 3DGS 27 and y [69 and is also inspired by 3DGStream (TT and 4DGC 20). In the initialization phase, due to the limitations of the NeuS2 (70] method, it is challenging to obtain high-quality surface meshes for scenes with backgrounds, making difficult to initialize Gaussians effectively. Therefore, on the N3DV dataset, initialize Gaussians based on the results of COLMAP. Additionally, we observed that in scenes with multiple interacting people, NeuS2 may occasionally fail capture all individuals. To enhance the stability of our method, we train the NeuS2 network parameters of each keyframe to learn residuals from a pre- trainedd,,, known-correct NeuS2 network. During the pre-training phase of key frames, we first train for 12,000 steps under the setting of Assim 0.2. In the Gaussian pruning phase, we remove 40% of the Gaussians with lower opacity on HiFi4G dataset (26 and 4DGCPro dataset but not remove any Gaussians on N3DV dataset [31] During the hierarchical process, we set X 1 x 10 to ensure a balance between volume and opacity, and divide the Gaussians into
still
layers. Regarding the motion-aware adaptive Gaussian grouping, we have selected different тμ values for different
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PSNR
28
26
24
High
Mid
Low
Frame Number
2000
Figure 8: The results of our method on long sequences. We show that the performance of our method does not decrease the number of frames increases.
Table 6: PSNR performance stability across three runs, Results are reported as the mean and standard deviation from three runs the 4DGCPro dataset.
Method
Dancel
Dance2
Coserl
Coser2
Boxing
Bandl
Mean
(Hig))
31.79 #0.37
29.78
=a.1
29.84
#0.18
25.65
+0.24
32.54 #006
27.19 #0.15
29.47 #0.8
Ours(Mid)
30.66 +0.28
29.05
=0.4
29.39
40.1
25.40 40.11
30.65 =000
26,93 #0.10
28.68 4022
Ours(Low)
29.26 #0.17
27.97
=00
28.60
#008
25.06
10.15
28.99 =005
26.23 #008
27.69 4014
datasets: T₁ 0.0025 for 4DGCpro, T₁ = 0.001 for HiFi4G, and Ty 0.01 for N3DV. Then, conduct end-to-end entropy training on keyframes for 1,500 steps with the supervision of 005/l, 1<
A
1, 1 and \yate_ko key 10-7 In the subsequent inter-frame Optimization,, we set
Arate_inte = x 10 Areg = 1 10-3, and train for 800 and 2,000 steps in the rigid transformation and residual deformation phases respectively. During the compression process, we have adopted different precisions for the compression of positions depending on the dataset. Since the Gaussian positions in the N3DV dataset have larger range, have quantized the Gaussian positions of the N3DV dataset using uint32 precision and compressed all attributes with qp = 10. For the other two datasets, have applied u precision and qp 20. The H.264 encoder was configured using the x264 library with the following settings: I/P-frames only (no B-frames), 3 reference frames, color space in YUV4:4:4, and preset set "medium."
Our experimental setup includes an Intel(R) Xeon(R) W-2245 CPU running at 3.90 GHz and an RTX 3090 graphics card. In the experiment, conducted evaluations the 4DGCPro and N3DV datasets. Also, we selected the Greeting and Umbrella sequences from the HiFi4G dataset. We selected the 48th view as the test view in the HiFi4G and 4DGCPro datasets, while the Oth view was chosen in the N3DV dataset. Due to the relatively high resolution of the HiFi4G and 4DGCPro datasets, downsample them by factor of 2 for training. In the experimental results, we reproduce and run the comparison methods on the HiFi4G and 4DGCPro datasets, and the results on the N3DV dataset are reported in the papers of 4DGC and HiCOM (16). Additionally, since the HPC [80] and v methods cannot operate properly on datasets with backgrounds, we do report their metrics the N3DV dataset.
total of 12 sequences from
B
Additional Experimental Results
B.1
Addition Demonstrations of 4DGCPro
In this section, we additionally present some results of our method to comprehensively demonstrate the advantages of our method as much as possible. First of all, in Fig. 6 the render gallery of our method is shown. It can be seen that our method can achieve high-quality reconstruction for scenarios
Table 7: Runtime analysis on multiple platforms of rendering.
Platform
Desktop Mid
Tablet Mid
Phone
High
Low
High
Low
High
Mid
Low
Decoding(ms)
24
17
11
27
22
10
35
27
19
Rendering(ms)
2.6
2.3
2.1
16
14
11
43
39
34
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Table 8: Quantitative comparison of average PSNR values(dB) and model size(MBB across all
sequences in the 4DGCPro dataset.
Method
Dancel
Dance2
Coserl
Coser2
Boxing1
Bandl
Mean
ReRF
30.01/0.98
26.30/2.17
27.30/1.32
24.35/1.99
31.12/1.44 .46
26.35/2.10
27.57/1.70
HPC
30.78/0.83
26.95/0.92
26.90/0.86
24.01/1.29
31.00/1.15
26,45/1.42
27.68/1 188/1.08
3DGStream
22.65/8. 10
18.45/8.10
23.62/8. 10
19.64/8.10
23.49/8.10
18.62/8.10 100
21.08/8. 10
4DGC
22.53/0.85
19.77/1.00
24.28/0.96
19.06/0.94
24.06/0.84
19.18/1.20
21 48800999
HiCoM
25.06/1.62
23.81/1.72
24.55/2.07
21.51/3.87
28.87/2.92
24.07/3.47
24.65/2.6
V
31.37/1.10
29.19/1.11
29.52/1.45
18.97/1.85
32.58/1.61
27.11/2.46
28. 28/11/1.60
Ours(High)
31.79/0.89
29.78/0.78
29.84/1.19
25.65/1.80
32.54/1.33
27.19/1.88
29.47/1.31
Ours(Mid)
30.66/0.45
29.05/0.39
29.39/0.60
25.40/0.91
30.65/0.66
26,93/0.94
28. 28.68/0.66
Ours(Low)
29.26/0.22
27.97/0.21
28.60/0.30
25.06/0.45
28.99/0.33
26.23/0.47
27.69/0.33
Table 9: Quantitative comparison across two sequences in the HiFi4G dataset.
Greeting
Umbrella
Mean
Method
PSNR,
Size
PSNR,
Size (MB)
PSNR,
Size
(dB)
(MB)*
(dB)
(dB)
(MB)*
ReRF
29.90
0.96
30.69
0.98
30.30
0.97
HPC
35.47
0.75
32.81
0.69
34.14
0.72
3DGStream
21.38
8.10
20.65
8.10
21.02
8.10
4DGC
20.94
0.99
21.15
0.89
21.05
0.94
HiCoM
29.12
1.70
29.61
2.18
29.37
1.94
V
37.06
0.89
35.45
0.95
36.26
0.92
Ours(High)
37.21
0.68
35,52
0.81
36.38
0.75
Ours(Middle)
36.83
0.34
34.13
0.39
35,48
0.37
Ours(Low)
35.96
0.17
33.28
0,20
34.62
0.19
with many complex motions. Fig. 7 shows the multi-bitrate results our method under a single bitstream. From the figure, it can be observed that due to the high effectiveness of our hierarchical representation and layerwise supervision, 4DGCPro maintains excellent rendering quality at each level of the results. Fig. 8 presents the multi-bitrate results of our method in long sequence. Our method can maintain a very high reconstruction quality in long sequences. As illustrated in Fig. 9 present supplementary qualitative results for scenes from the N3DV [3]] dataset. These visual outcomes vividly showcase the resilience of our approach in accurately capturing and effectively representing dynamic scenes. In addition, to verify the stability of the method, conducted multiple experiments under the same setting and reported the fluctuations the results, as shown in Tab.
We also conducted efficiency analysis of our 4DGCPro across multiple platforms. The test platforms consist of an Ubuntu desktop PC featuring an Intel 19-10X20X processor and an NVIDIA GeForce RTX 3090 GPU, an Apple iPad powered by an Apple M2 processor, and Apple iPhone equipped with an A15 Bionic processor. As presented in Tab. 7 we detail the time consumption of each thread within the rendering pipeline. During the decoding process, on the desktop, multi threaded decoding combined with CUDA memory copying takes between 11ms and 24ms. For Apple's mobile devices, leveraging parallel decoding via compute shaders, these devices achieve decoding time consumption comparable to that of the desktop (22ms on the tablet and 27ms on the phone). Regarding the rendering thread, the desktop with CUDA-enable device demonstrates extremely rapid rendering speed (2.3ms), while mobile devices are also capable of rendering at a satisfactory frame rate (14ms and 39ms).
B.2 Additional Comparison Results
We present the quantitative results for each scene from three datasets respectively in Tab. 8 and to provide more detailed comparison. We categorize the datasets into two groups: large- motion, background-free datasets such as 4DGCPro and HiFi4G (26). and small-motion, background- containing datasets like N3DV [I.. Our method demonstrates a distinct advantage the former group, which can be attributed to its precise motion modeling capabilities. In contrast, methods like 3DGStream 611 and 4DGC 20 perform poorly. Specifically, they completely loses modeling ability after processing only a very short sequence due to the emror accumulation. This shortcoming stems from inherent limitations of using only the first frame as a reference and being capable of modeling only rigid motion. Notably, v [69] shows subpar performance on the coser2 sequence.
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Table 10: Quantitative comparison of average PSNR values(dB) and model size(MB) across all
sequences the N3DV dataset.
Coffee
Cook
Cut
Flame Salmon
Flame Steak
Sear
Method
Mean
Martini
Spinach
Beef
Steak
ReRF
26.24/0.79
31,23/0.84
31.82/0.81
26.80/0.78
32.08/0.91
30.03/0.51
29.71/0.77
3DGStream
27.96/8.00
32.88/8.05
32.99/8.11 19
28.52/8.07 07
33.41/8.19
33.58/8. 16
31.54/8. 11
HiCoM
28.04/0.80
32.45/0.60
32.72/0.60
28.37/0.90
32.87/0.60
32.57/0.60
31.17/0.70
4DGC
27.98/0.58
32.81/0.44
33.03/0.47
28.49/0.51
33.58/0.44
33.60/0.50
31,58/0.49
Ours(High)
27.9170.64
32.93/0.67
33.1070.61
28.73/0.61
33.7770.65
33.72/0.66
61.64
(urs(Mid)
27.63/0.43
32.30/0.45
32.51/0.41
28.28/0.45 43
33.09/0.43
33,03/0 44
31.14/0.43 43
Ours(Low)
26.88/0.21
31.95/0.22
32.17/0.20
27.95/0.21
32.49/0.20
32.64/0.23
30.68/0.21
Table 11: Results of more ablation studies.
High
Mid
Low
Ablation Studies
PSNR(dB)
Size(MB)
PSNR(aB)
Size(MB)
PSNR(dB)
Size(MM)
Wi Motion Decomposition
28.84
1.31
28.17
0.66
27.04
0.33
w/o Layer-wise Supervision
29.53
1.33
26.49
0.67
24.98
0.34
Ours Full
29.47
1.31
28.68
0.66
27.69
0.33
The reason lies in the fact that NeuS2 [70 fails to initialize the two interacting objects correctly during the training process, resulting in only portion of the image being successfully modeled. Our approach addresses this issue by introducing residual NeuS2. Within the N3DV dataset, given the small motion amplitudes, 3DGStream and 4DGC achieve good results. Nevertheless, method still manages to deliver comparable performance.
B.3 Additional Ablation Studies
In this section, conducted additional experiments to validate the efficacy of motion decomposition and layer-wise wise supervision, as shown in Tab. [T] The results reveal that motion decomposition enables precise modeling of dynamic scenes by distinctly separating the processes of rigid transformation and residual deformation. However, simultaneously training these two components makes the positions of Gaussians less accurate and increases the training difficulty, and accurate results cannot be obtained with the same number training steps. Regarding layer-wise supervision, while has a marginal impact the reconstruction quality of complete Gaussians, it yields substantial boost in the quality of lower-level Gaussians.
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Figure 9: Qualitative results of scenes from N3DV dataset. Frames shown are the t0th 1h 150th th and th from the test video.
26


Reviews:
[{"review_id": "XWxSwGu4Uq", "reviewer": "Reviewer_LFeZ", "summary": "This paper introduces 4DGCPro, a 4D Gaussian compression framework designed for progressive volumetric video streaming. Specifically, the proposed method comprises three key components: (1) a perceptually-weighted; (2) a motion-aware adaptive grouping strategy; and (3) a joint entropy-optimized training scheme. Experimental results demonstrate that 4DGCPro outperforms the included baselines rate-distortion performance.", "questions": "- The proposed ideas appear somewhat incremental, as intra-frame and inter-frame coding are standard practices, and progressive layer coding (also known as scalable coding) is well-established. Additionally, the \"motion-aware adaptive Gaussian grouping\" resembles common strategies in video compression that employ intra-frame coding during scheme changes. It would be helpful if the authors could elaborate more on what specific novel designs or adaptations they introduce for 4D Gaussian compression in this work to clarify its distinct contributions.\n\n- The authors describe the framework as a variable-rate model. In learned image and video compression, a variable-rate model typically means the ability to encode inputs at arbitrary target bitrates within a continuous range. However, in this work, the multiple bitrates seem to arise solely from discrete multi-layer coding. In other words, the model supports only a few fixed rates rather than truly continuous variability. Therefore, the use of the term \"variable rate\" may need reconsideration.\n\n- In traditional scalable coding, although multi-rate options exist, coding efficiency is often lower than single-layer coding because information may be redundantly transmitted across layers. This paper does not report a comparison between single-layer and multi-layer coding results, which is important for understanding trade-offs.\n\n- The paper employs H.264 as a video encoder, but lacks details on its configuration, such as whether P-frames or B-frames are used, the number of reference frames, or whether YUV or RGB color coding is applied.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\nThis paper integrates several established techniques from learned video compression into the domain of 4D Gaussian compression. Notably, it incorporates intra-frame and inter-frame coding, as well as residual motion coding, into a unified framework tailored for volumetric video.\n\nWeaknesses:\n- The proposed ideas appear somewhat incremental, as intra-frame and inter-frame coding are standard practices, and progressive layer coding (also known as scalable coding) is well-established. Additionally, the \"motion-aware adaptive Gaussian grouping\" resembles common strategies in video compression that employ intra-frame coding during scheme changes. It would be helpful if the authors could elaborate more on what specific novel designs or adaptations they introduce for 4D Gaussian compression in this work to clarify its distinct contributions.\n- The authors describe the framework as a variable-rate model. In learned image and video compression, a variable-rate model typically means the ability to encode inputs at arbitrary target bitrates within a continuous range. However, in this work, the multiple bitrates seem to arise solely from discrete multi-layer coding. In other words, the model supports only a few fixed rates rather than truly continuous variability. Therefore, the use of the term \"variable rate\" may need reconsideration.\n- Details regarding progressive rendering are limited. \n- The term “interp” in Equation 5 should be defined.\n- In traditional scalable coding, although multi-rate options exist, coding efficiency is often lower than single-layer coding because information may be redundantly transmitted across layers. This paper does not report a comparison between single-layer and multi-layer coding results, which is important for understanding trade-offs.\n- Table 3 reports complexity measurements, but the hardware or platform used for these measurements is not specified in the main paper and should be included.\n- The paper employs H.264 as a video encoder, but lacks details on its configuration, such as whether P-frames or B-frames are used, the number of reference frames, or whether YUV or RGB color coding is applied.", "was_revised": true, "final_justification": "Since the authors have addressed all my concerns during the rebuttal stage, I have raised my score. I hope the authors will incorporate the necessary revisions in the final paper based on the comments from the rebuttal stage.", "rebuttal": "Thank you for acknowledging our work as \"outperforms the included baselines\" and for providing numerous helpful suggestions. Next, we will respond to each of the weaknesses and questions you have raised one by one, and we commit to incorporating the following revisions into the final version of the paper.\n## Novelty and Contributions beyond Conventional Coding Strategies (W1&Q1)\nWe sincerely thank the reviewer for this insightful comment. While some high-level concepts such as intra-/inter-frame coding and progressive transmission are common in video compression, we would like to clarify that our work introduces **novel and tailored adaptations specifically for 4D Gaussian compression**, which differ significantly from traditional pixel-domain compression. Our key innovations include:\n\n(1) **Joint Representation-Compression Framework for 4D Gaussians**. Traditional video compression techniques operate in the **2D pixel domain**, while our work directly compresses **spatiotemporal 3D Gaussian representations**. This requires rethinking how motion, hierarchy, and entropy modeling are designed. Unlike conventional pipelines, we propose a **deeply coupled framework** that unifies representation learning and compression-aware optimization of 4D Gaussians. This is a challenging and relatively underexplored direction, with few studies providing systematic solutions.\n\n(2) **Fine-Grained Motion Modeling at the Representation Level**. Unlike traditional video codecs that model motion at the **pixel or block level**, our method explicitly decomposes motion on the **Gaussian primitive level** into rigid transformations (position and rotation) and residual deformations (scale, opacity, color, etc.). This dual-level modeling better captures complex dynamic behaviors and leads to improved reconstruction fidelity. To validate its effectiveness, we conducted an ablation study replacing our motion model with that of V³[1] within our pipeline. This substitution resulted in a PSNR drop from **31.64dB** to **31.50dB** on the N3DV dataset, confirming the advantage of our motion decomposition design.\n\n(3) **Motion-Aware Adaptive Grouping for Enhanced Compression Efficiency**. In contrast to traditional video coding that often uses a fixed GOP size, we propose a motion-aware adaptive grouping strategy that **dynamically clusters Gaussian primitives based on the estimated motion magnitude in 3D space**. This adaptive grouping dynamically adjusts group boundaries according to scene motion intensity, enabling better temporal consistency and compression efficiency across frames with varying motion. As demonstrated in the middle section of Table 4, our method achieves a significant improvement in rate-distortion performance over fixed-size grouping, with a minimum BD-PSNR gain of **+0.25dB**.\n\n(4) **Single-Model Bitrate Scalability with Minimal Redundancy**. Unlike traditional scalable video coding, which often suffers from inter-layer redundancy due to repeated information across layers, our method introduces a **Perceptually-Weighted and Residual-Aware Hierarchical Gaussian Representation with layer-wise RD supervision**. This design ensures that each layer contributes non-overlapping and perceptually significant details, minimizing redundancy and enhancing coding efficiency. This is the **first framework that supports multiple bitrates within a single unified model** for 4D Gaussian compression, eliminating the need for model retraining and excessive storage typically required in prior works. We validate our multi-layer design by comparing it with a single-layer baseline. 4DGCPro achieves comparable RD performance (**29.47dB at 1.31MB** vs. **29.50dB at 1.27MB**), confirming that our progressive scheme retains high quality while offering scalability.\n\n(5) **Attribute-Specific RD-Aware Entropy Modeling**. We further go beyond standard entropy coding by tailoring **distribution-specific estimators** for each Gaussian attribute. For example, we use **KDE-based entropy modeling** for keyframe Gaussians (with high variance) and **Gaussian-based modeling** for inter-frame Gaussians. This novel design leads to improved RD efficiency and is verified via ablation studies (Section 4.2), where removing this entropy design causes BD-PSNR to drop by **0.60dB**.\n\n## Usage of the term \"variable rate\" (W2&Q2)\nWe understand your concern regarding the use of the term \"variable-rate model.\" To clarify, our model allows for flexibility in bitrate selection, but rather than offering truly continuous bitrate variability, it provides a set of discrete bitrate options based on the **multi-layer coding structure**. Specifically, the model uses a **6-layer structure** that corresponds to different quality/detail levels, and within each layer, we adjust the **QP parameters** (ranging from 1 to 25) during the compression phase to allow for fine-grained bitrate variation. This enables flexible bitrate choices across these fixed levels, effectively offering a **6x25** range of possible bitrates.\n\nWe agree that \"variable-rate\" may imply continuous bitrate variability, which is not the case here. Therefore, we will revise the terminology in the paper to \"**multiple bitrate**\"  to more accurately describe the nature of the model’s bitrate flexibility.\n## Progressive Rendering Details (W3)\nWe appreciate your concern regarding the details of progressive rendering. Our process begins with the base layer ($l$=1), which contains essential scene information. As additional layers are progressively decoded, we merge them with the previously decoded layers to refine the visual quality. Specifically, each layer adds extra detail, and only a small amount of additional data (Gaussians) is needed for the next layer ($l$+1), enhancing the rendering quality.\n\nBy dynamically adjusting the level of detail based on computational and bandwidth resources, we maintain a balance between quality and efficiency. This approach enables scalable, high-fidelity visualization while ensuring real-time performance within resource constraints. We will expand on these details in **Subsection 3.1** of the revised manuscript, particularly on how layers are combined and rendered.\n## interp(·) (W4)\nIn our work, interp(·) refers to the **hash grid interpolation operation**, which is used to map points in the hash grid to corresponding values during the encoding process. We will include this definition in the revised manuscript.\n## Single-layer and multi-layer coding results (W5&Q3)\nWe have conducted experiments comparing single-layer coding with our 4DGCPro (multi-layer coding) on our dataset. Our results show that 4DGCPro achieves comparable RD performance to single-layer coding, with only a slight difference in quality (**29.47dB at 1.31MB** vs. **29.50dB at 1.27MB**). This is primarily due to our **compact hierarchical Gaussian representation**, which effectively reduces redundancy both between layers and across frames. In particular, we apply a residual learning-based representation to model the residuals between layers and across frames, ensuring that each layer captures unique, non-redundant information. This minimizes the redundant information that typically arises in multi-layer coding, thus maintaining high compression efficiency.\n\nAdditionally, we introduce **layer-wise RD supervision** to refine the optimization process, ensuring that each layer contributes optimally to the overall representation. As a result, despite the typical trade-offs associated with multi-layer coding, our approach significantly reduces redundancy and maintains high efficiency, achieving performance similar to single-layer encoding.\n\nWe will include these detailed comparisons and further explanations on compression efficiency in the revised manuscript to provide a clearer understanding of the trade-offs involved.\n|        | PSNR/dB | Size/MB |  \n|:------: |:------: |:------: |  \n| Single-layer   | 29.50   | 1.27    |  \n| Multi-layer    | 29.47   | 1.31    |  \n\n## Experimental setup (W6)\nThank you for your suggestion. The details of our experimental setup, including the hardware and platform used, are provided in **Line 264** and **Lines 533-534**. We will ensure that these details are more clearly highlighted in the revised manuscript.\n\n## H.264 configuration (W7&Q4)\nWe thank the reviewer for pointing this out. The H.264 encoder was configured using the x264 library with the following settings: **I/P-frames only** (no B-frames), **3 reference frames**, color space in **YUV4:4:4**, and preset set to \"**medium**.\" We will include these details in the main paper to ensure reproducibility.\n\n[1] V³: Viewing Volumetric Videos on Mobiles via Streamable 2D Dynamic Gaussians, SIGGRAPH Asia 2024"}, {"review_id": "tdCXOt8naG", "reviewer": "Reviewer_kNfk", "summary": "This paper presents 4DGCPro, a compact 4D Gaussian representation that requires only a small storage size for streaming volumetric videos. To achieve this, it models the rigid transformation of Gaussians in the key frames to define translation and rotation of Gaussians for subsequent frames. Moreover, it also models temporal residuals for remaining attributes, such as scale, opacity, and color. To minimize redundancy in these residuals, it conducts entropy-optimized training for each attribute. Furthermore, it can effectively represent the deformation by grouping frames based on the magnitude of the Gaussian translation. Experimental results demonstrate that the proposed method achieves superior rendering quality with minimal storage usage compared to existing efficient 4D Gaussian approaches.", "questions": "- Although this work highlights a hierarchical representation of 4D Gaussians, this paper does not provide detailed optimization schemes, such as initialization and different supervision for each level, and experiments for validating the effectiveness of the hierarchical structure with varying numbers of levels. Please provide more details for hierarchical representation with analysis on the results.\n\n- The authors have investigated that the proposed significance score enhances the rendering quality. However, there is no comparison with existing importance scores introduced by existing compact 3D Gaussian approaches, LightGaussian [NeurIPS'24], EAGLES [ECCV'24], Mini-Splatting [ECCV'24], and Taiming-3DGS [SIGGRAPH Asia'24].\n\n- Moreover, what is the detailed definition of spatial volume in L145?\n\n- As mentioned in the weaknesses, this framework is closely similar to V$^3$. Can you provide technical contributions different from V$^3$ for better understanding? \n\n- To validate the effectiveness of motion-aware adaptive grouping, it could be helpful to provide an ablation study on the adaptive grouping strategy.\n\n- Minor typo in L147: are are", "limitations": "- Despite the superior performance, this framework only shows limited technical advancements compared to V$^3$.\n\n- Also, more detailed experiments and analysis need to be added to validate the effectiveness of the proposed method.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 2, "significance": 4, "originality": 2, "strengths_and_weaknesses": "### Strengths\n\n- The proposed motion-aware adaptive grouping enables dividing entire frames into optimal sub-groups for varying scenes.\n- Experimental results show that 4DGCPro outperforms the rendering quality of V$^3$, SOTA 4D Gaussian representation while the high-bitrate variant of this method requires a smaller storage size than V$^3$.\n\n---\n\n### Weaknesses\n\n- This method is closely similar to V$^3$ which introduces the definition of hash grid-based Gaussian translation, attributes residual modeling, and a grouping strategy for input frames.\n\n- While the authors propose a hierarchical representation, they do not provide any details for optimization and analysis on the hierarchical structure.\n\n- The papers need to improve the overall writing.", "was_revised": true, "final_justification": "During the rebuttal period, the authors have addressed all of my concerns regarding the clarification of the technical contributions, hierarchical representation, and significance metrics. Therefore, I raise my final rating to positive.", "rebuttal": "Thank you for acknowledging our work as \"dividing entire frames into optimal sub-groups\" and \"SOTA 4D Gaussian representation\". Going forward, we will respond to each of the weaknesses and questions you have raised one by one, and we commit to incorporating the following revisions into the final version of the paper.\n## Technical contributions (W1&Q4) \nWhile our framework shares the high-level goal of compressing dynamic 3D Gaussian representations with V³, our method introduces several substantial technical innovations that differentiate it from V³ in terms of motion modeling, grouping, bitrate scalability, and entropy coding:\n\n(1) **Motion-aware Adaptive Gaussian Grouping**. Unlike V³ which adopts a fixed group size, we propose a motion-aware adaptive grouping strategy that dynamically adjusts group boundaries based on scene motion magnitude. This allows better temporal consistency and compression efficiency across varying motion intensities. As shown in the middle part of Table 4, our method significantly improves RD performance compared to fixed-size grouping, achieving a minimum BD-PSNR gain of **+0.25dB**.\n\n(2) **Motion Decomposition**. Unlike V³, which estimates motion solely via position offset and subsequently fine-tunes other attributes, our method explicitly decomposes motion into rigid transformations (position + rotation) and residual deformations (scale, opacity, color, etc.). This dual-level modeling allows better handling of complex dynamics and improves reconstruction fidelity. To verify this, we replaced our motion strategy with that of V³ in our pipeline, which led to a PSNR drop from **31.64dB** to **31.50dB** on the N3DV dataset as shown in the below table, confirming the effectiveness of our fine-grained motion decomposition.\n| |PSNR(dB)|\n|:-:|:-:|\n|V³'s motion modeling|31.50|\n|Ours|31.64|\n\n(3) **Beyond V³: Single-Model Bitrate Flexibility**. Our framework introduces a Perceptually-Weighted Hierarchical Gaussian Representation with layer-wise RD supervision and is the **first to support variable bitrates within a single unified model** for 4D Gaussian compression. This progressive structure enables smooth adaptation to bandwidth variations and device constraints during volumetric video streaming. In contrast, **V³ lacks this flexibility**, as it requires training and storing **separate models for each target bitrate**, leading to higher storage overhead and limited adaptability in practical streaming scenarios. \n\n(4) **Attribute-Specific Entropy Modeling**.   Unlike V³, which does not incorporate entropy supervision for keyframes during training, our method adopts an RD-aware, attribute-specific entropy coding strategy. Specifically, we employ **KDE-based modeling for keyframes** to better capture their complex and diverse attribute distributions, and **Gaussian-distribution modeling for inter-frame residual attributes**. This tailored approach enables more accurate entropy estimation, thereby improving overall RD performance. To assess its effectiveness, we conducted an ablation study by removing entropy supervision for keyframes, i.e., adopting V$^3$'s setting, and observed a clear performance drop: the BD-PSNR on the HiFi4G dataset decreased **0.20dB** compared to our full method. This result highlights the critical role of entropy supervision in our design. \n||BD-PSNR(dB)|\n|:-:|:-:|\n|w/o keyframe entropy supervision|-0.20|\n## Clarification and Analysis of Hierarchical Representation (W2&Q1)\nThank you for your insightful comment.  We provide the requested clarifications below, focusing on our initialization strategy, layer-wise supervision, and empirical analysis with varying numbers of hierarchy levels.\n\n(1) **Initialization Strategy**. We adopt a principled approach to initialize the hierarchical structure. Specifically, after pre-training a full-resolution 3DGS model (see Lines 209–213), we sort all Gaussians in descending order using our significance metric defined in Eq. 3, which balances geometric visibility and photometric opacity. These Gaussians are then evenly divided into $L$ layers to form the initial hierarchy. To validate this design, we additionally experimented with an alternative metric that replaces the summation in Eq. 3 with multiplication. This variant significantly underweights Gaussians with low volume but high opacity, resulting in blurred reconstructions and a **-1.33dB BD-PSNR drop**, confirming the effectiveness of our proposed initialization scheme.\n\n(2) **Layer-wise Rate-Distortion Supervision**.  As described in Subsection 3.3, we design an **end-to-end layer-wise RD supervision strategy** that explicitly optimizes each level in both Keyframe and Inter-frame stages. For each layer, we compute the entropy of attributes and the photometric loss independently, ensuring that each layer contributes non-redundant, high-value information. As shown in the right part of Table 4, disabling this layer-wise supervision and applying global supervision to all layers will cause a **61.21% increase in BDBR** and a **2.89dB drop in BD-PSNR**, demonstrating that our layer-wise scheme is crucial for maintaining compression efficiency and reducing redundancy.\n\n(3) **Analysis with Varying Number of Layers**. To analyze the impact of the number of layers $L$, we conducted experiments with different settings (see table below). Using $L$=6 as baseline, we found that fewer layers (e.g., $L$=4) degrade BD-PSNR by up to **0.87dB**, while increasing $L$ beyond 6 yields marginal gains but increases training time significantly (e.g., *+1.2 min/frame*). We therefore select $L$=6 as the best trade-off between efficiency and RD performance.\n|| BD-PSNR(dB) | Training Time(min)|\n|:-:|:-:|:-:|\n|L=4|-0.87|3.1|\n|L=5|-0.38|3.5|\n|L=6|-|4.3|\n|L=7|0.06|4.9|\n|L=8|0.09|5.5|\n## Comparison with Existing Significance Metrics (Q2)\nWe have conducted **additional experiments comparing our proposed significance metric** with those adopted by recent compact 3D Gaussian approaches, including LightGaussian, EAGLES, Mini-Splatting and Taiming-3DGS. The results are summarized in the table below.\n- **LightGaussian** computes a dynamic, view-dependent importance score considering volume, opacity, and light transmittance. It offers a **+0.07 dB BD-PSNR gain**, but at the cost of **+1.1 min/frame** pre-training time.\n- **EAGLES** uses static rendering weights as significance. It is efficient but less adaptive to motion and occlusion, resulting in a **-0.15 dB drop in BD-PSNR**.\n- **Mini-Splatting** adopts blending weights but lacks generalization to dynamic scenes (**BD-PSNR: -0.13 dB**, **+3.6 min/frame overhead**).\n- **Taiming-3DGS** combines geometric and perceptual saliency terms. It improves quality slightly (**+0.03 dB**), but adds high training complexity due to multi-view evaluations.\n\nIn contrast, our proposed metric, based on a simple combination of volume and opacity, is **lightweight, scene-agnostic, and efficient**, achieving **comparable or better RD performance without incurring extra training cost**. By avoiding dependence on rendering feedback or multi-view saliency, our method is particularly suitable for scalable 4D Gaussian streaming under constrained resources.\n||BD-PSNR(dB)|Training Time(min)|\n|:-:|:-:|:-:|\n|LightGaussian|0.07|4.5|\n|EAGLES|-0.15|3.6|\n|Mini-Splatting(Imp1)|-0.12|7.1|\n|Taiming-3DGS|0.03|4.3|\n|4DGCPro|-|3.5|\n## Clarification of Spatial Volume Definition (Q3)\nIn the context of Gaussian representations, the \"spatial volume\" refers to the 3D volume that a Gaussian occupies in the 3D space, which is calculated as $\\dfrac{4}{3}\\pi abc$, where $a$, $b$, and $c$ correspond to the scale parameters (standard deviations) along the three principal axes of the Gaussian.  \n## Effectiveness of Motion-Aware Adaptive Grouping (Q5)\nWe agree that validating the motion-aware adaptive grouping strategy is important. In fact, Table 4 of our manuscript already provides an ablation study comparing our adaptive grouping method against multiple fixed group sizes (5,10,15,20,25). Across these settings, our adaptive strategy consistently demonstrates better RD performance, indicating its effectiveness under various scene dynamics.\n\nTo further strengthen this analysis, we have conducted an additional experiment comparing our adaptive grouping to a degenerate case of GOP size = 1 (i.e., treating every frame independently with no temporal grouping). This setting performs even worse, with a BD-PSNR degradation of  **-0.96dB**, which underscores the importance of appropriately grouping frames with coherent motion.\n\nWe also explored the sensitivity of our method to the grouping threshold hyperparameter $\\tau_u$, by testing values of 0.002 and 0.003. Both resulted in noticeable RD performance drops (**−0.07dB** and **−0.10dB** BD-PSNR, respectively), suggesting that our chosen default ($\\tau_u$ = 0.0025) provides a good trade-off between motion sensitivity and compression performance.\n## Minor Typo (Q6)\nThank you for pointing this out. We will correct the duplicated word \"are\" in the revised version.\n##  Writing Quality (W3)\nThank you for your suggestion. We will improve the overall writing in the revised version. Specifically, we will enhance the clarity of technical descriptions, reorganize the methodology section for better logical flow, and polish the language throughout the paper to improve readability and presentation quality.\n\n(1) **More technical details**. We will provide a more detailed introduction to progressive rendering. Additionally, we will elaborate further on the initialization strategy based on significance metric sorting, layer-wise rate-distortion supervision, and the selection of hyperparameter $L$ that balances RD performance and training efficiency.\n\n(2) **More terminology explanations and typo fixes**. We will clarify the definitions of spatial volume and interp(·) in the main text. Meanwhile, we will remove the redundant \"are\" in Line 147."}, {"review_id": "xLh2kvFfA9", "reviewer": "Reviewer_kU2V", "summary": "This paper proposes a hierarchical compression approach for progressive volumetric video streaming using the 3D Gaussian Splatting (3DGS) representation. The proposed residual-based representation and adaptive grouping strategy are interesting and could provide useful insights for future research in this area. The experimental results demonstrate its superiority compared with other methods.", "questions": "1. It would be better to illustrate equation 3 with more context.\n2. Incorporating the suggested baseline will strengthen the paper.\n3. Providing a more in-depth ablation study on the weakness part will enhance the paper quality.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n1. The proposed residual-based representation and adaptive grouping strategy are interesting and show promise for progressive streaming.\n2. The decision to directly apply an off-the-shelf H.264 codec for compression, rather than relying fully on learned entropy coding, is another interesting design choice. This makes the system more compatible with existing hardware and supports faster decoding.\n\nWeakness:\n1. Clarity is a major concern, and several parts require more detailed explanation:\n(1) In Equation 3, what exactly does “spatial volume $\\mathcal{S}$” refer to?\n(2) Why is Equation 3 formulated as a weighted sum, with $\\lambda_\\Phi$ as a trade-off parameter? The motivation and implications of this formulation are not sufficiently discussed.\n(3) The paper lacks discussion on how Gaussians are partitioned into $L$ layers. Is it done uniformly or based on specific criteria?\n2. Experimental concerns: \n(1) A key ablation study is missing: the case without residual modeling (i.e., equivalent to setting Group=1). This should be included, for example, in Table 4.\n (2) The paper does not compare with QUEEN [A], which is a relevant baseline for compression of Volumetric Video Streaming.\n3. Inconsistency in claims: In line 161, the paper claims the method “… effectively captures large-scale complex motions …”, yet in the limitations section (line 315), it says the method “underperforms in large-scale scenes.” This appears contradictory. A clear analysis is needed to explain why the method performs well or poorly in large-scale scenes, better supported by visual results.\n4. In Figure 4, the qualitative image for 3DGStream appears to be from a different timestamp than the other methods, making the comparison less meaningful.\n5. Minor issues:\n(1) Line 147: duplicated word “are”s.\n(2) Line 202: “a” should be “an”.\n(3) Line 220 & Equation (9): Please unify the terminology—should it be PDF or PMF?\n\n[A] Girish S, Li T, Mazumdar A, et al. Queen: Quantized efficient encoding of dynamic gaussians for streaming free-viewpoint videos[J]. Advances in Neural Information Processing Systems, 2024, 37: 43435-43467.", "was_revised": true, "final_justification": "Overall, the proposed framework is a good solution for dynamic Gaussian Splatting and show potential ability to integrate the development from video compression. Given the current status and the comments, I prefer to raise the score but the paper needs to be carefully polished according to the comments.", "rebuttal": "Thank you for recognizing our work as \"interesting and show promise for progressive streaming\", \"superiority\" and \"more compatible with existing hardware and supports faster decoding\". We will now address each of the weaknesses and questions you have raised one by one, and we commit to incorporating the following revisions into the final version of the paper.\n\n## Clarity (W1&Q1) \nThank you for your valuable feedback. We appreciate your concerns regarding the clarity of certain parts of the paper, and we will address each of your points in detail:\n\n(1) **Spatial Volume in Equation 3**. In the context of Gaussian representations, the \"spatial volume\" refers to the three-dimensional volume that a Gaussian occupies in the 3D space, which is calculated as $\\dfrac{4}{3}\\pi abc$, where $a$, $b$, and $c$ are the three dimensions of the Gaussian’s scale. This volumetric measure quantifies the spatial influence of a Gaussian, contributing to its visual significance in the scene. \n\n(2) **Why is Equation 3 Formulated as a Weighted Sum?** Eq.3 is formulated as a weighted sum of spatial volume $S$ and opacity $\\alpha$ because these two attributes contribute independently to the visual significance of a Gaussian. Specifically, $S$ reflects the spatial extent of a Gaussian in 3D space, while $\\alpha$ quantifies its visual prominence in rendering. Both factors influence the final reconstruction quality, but in different and complementary ways.\n\nA weighted sum is used to preserve their respective contributions while allowing flexible trade-offs. In contrast, a multiplicative formulation would overly suppress Gaussians with small volume but high opacity, leading to loss of fine details. To balance the influence of $S$ and $\\alpha$, we introduce a tunable trade-off parameter $\\lambda_{\\Psi}$.\n\nWe further conducted ablation studies to validate this design choice. As shown in the table below, using a multiplicative form or removing $\\lambda_{\\Psi}$ altogether leads to significant performance degradation, with BD-PSNR drops of **-1.33 dB** and **-2.06 dB**, respectively. These results confirm the necessity of the weighted formulation and the role of $\\lambda_{\\Psi}$ in achieving robust performance.\n|| BD-PSNR(dB) |\n|:-:|:-:|\n| Multiplication | -1.33 |\n| w/o $\\lambda_{\\Psi}$ | -2.06|    \n\n(3) **How Gaussians Are Partitioned into Layers**. The partitioning of Gaussians into layers is based on their importance scores, computed using a significance metric that jointly considers spatial volume $S$ and opacity $\\alpha$. After sorting all Gaussians in descending order by their importance scores, we uniformly divide them into $L$=6 hierarchical layers. This strategy ensures that each layer captures a progressively finer level of scene detail, facilitating scalable reconstruction.\n\nWe chose $L$=6 based on empirical validation: as shown in the table below, using fewer layers degrades RD performance (e.g., BD-PSNR drops of **-0.87dB** and **-0.38dB** for smaller $L$), while increasing $L$ beyond 6 offers marginal gains at the cost of increased training complexity (**+0.6/+1.2 min** per frame). This confirms that our choice strikes a favorable trade-off between rate-distortion efficiency, visual quality, and training cost.\n||BD-PSNR(dB)|Training Time(min)|\n|:-:|:-:|:-:|\n|L=4|-0.87|3.1|\n|L=5|-0.38|3.5|\n|L=6|-|4.3|\n|L=7|0.06|4.9|\n|L=8|0.09|5.5|\n## Experimental Concerns (W2&Q2)\nWe thank the reviewer for their insightful comments. Below, we address each of the points raised:\n\n(1) **Ablation Study for Residual Modeling (Group=1)**. We acknowledge that an important ablation study without residual modeling was missing in our initial submission. To address this, we have now conducted the experiment by setting Group=1, which removes the residual modeling step. This condition reflects a scenario where each frame is modeled independently, without the temporal consistency enforced by residual deformations. The results are shown in Table below. Specifically, when comparing this configuration with our full method, we observe a **48.37% increase in BDBR** and a **-0.96dB drop in BD-PSNR**. This demonstrates the significant redundancy in Gaussian information when residual modeling is not used, which in turn leads to a noticeable degradation in compression efficiency and visual quality. These results highlight the importance of residual modeling in preserving temporal consistency and reducing redundancy.\n|Group Size|BDBR(%)|BD-PSNR(dB)|\n|:-:|:-:|:-:|\n|1|48.37|-0.96|\n\n(2) **Comparison with QUEEN**. We have compared our method with QUEEN under the same experimental settings. The results are shown in the table below. As can be seen from the comparison, our method achieves better reconstruction quality while maintaining a significantly lower bitrate. Specifically, for the N3DV dataset, our method outperforms QUEEN in both PSNR and SSIM, while reducing the file size from **0.75 MB** (QUEEN) to **0.73 MB**. For the Immersive dataset, we observe a similar trend, where our method achieves a PSNR of **30.23dB** and SSIM of **0.947**, compared to QUEEN’s PSNR of **29.40dB** and SSIM of **0.917**, while also reducing the file size from **1.79 MB** to **1.34 MB**. Additionally, a key advantage of our method is its ability to render multi-quality reconstruction results from a single model. This capability enables flexible quality scaling based on network conditions and computational resources, which is particularly beneficial for adaptive streaming scenarios. \n\n||N3DV PSNR(dB)|N3DV SSIM|N3DV Size(MB)|Immersive PSNR(dB)|Immersive SSIM|Immersive Size(MB)|\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|QUEEN|32.19|0.946|0.75|29.22|0.915|1.79|\n|Ours|32.23|0.947|0.73|29.40|0.917|1.34|\n## Inconsistency in claims (W3)\nWe apologize for any confusion caused by the repeated use of the term “large-scale.” To clarify, in Line 161, \"large-scale complex motions\" refers to **intense, complex object motions** within a scene, where our method excels. Thanks to our precise motion modeling and adaptive grouping, 4DGCPro performs particularly well with highly dynamic motions. In contrast, \"underperforms in large-scale scenes\" in Line 315 refers to **spatially extensive scenes**, such as city-scale environments, where the method currently lacks optimizations to efficiently handle the large scene size. This is a limitation we aim to address in future work.\n## Qualitative Result (W4)\nThank you for your valuable feedback. We would like to clarify that all images, including those for 3DGStream, are from the **same timestamp** (the 30th frame). The apparent differences arise from the limitations of the 3DGStream method in handling complex motions, such as large displacements or rapid movements. Specifically, 3DGStream only models rigid motion, and it struggles to capture fast or large motions, such as head rotation, sleeve movement, and  umbrella spinning, which results in motion artifacts like trajectory fragmentation and residual errors from earlier frames. These issues cause visual differences, which are not due to different timestamps but are a result of the method's motion modeling constraints. We will revise the figure caption in the manuscript to include this explanation.\n## Typo Fixes (W5)\nThank you for pointing out these minor issues. We will correct the duplicated word “are” in Line 147 and change “a” to “an” in Line 202. Additionally, we will unify the terminology in Line 220 and Eq.9 to use PMF consistently throughout the manuscript. \n## Ablation Studies (Q3)\nThank you for your insightful suggestion. We have incorporated a comprehensive set of ablation studies that target the core design modules of our framework. Specifically, we evaluate (1) the necessity of temporal grouping, (2) the formulation of the significance metric, (3) the impact of the number of hierarchy levels, (4) the effectiveness of multi-layer coding, and (5) the role of attribute-specific entropy modeling. The results and analyses are summarized below:\n\n(1) **Group Size = 1 (No Temporal Grouping)**. We simulate a frame-by-frame modeling baseline by setting the group size to 1, which disables residual modeling. Compared to our full method, this leads to a **48.37% increase in BDBR** and a **-0.96 dB drop in BD-PSNR,** highlighting the importance of motion grouping and temporal modeling. This result is discussed in our response to W2.\n\n(2) **Significance Metric Design (Eq. 3)**.\nTo verify the necessity of our weighted sum formulation, we compared it against alternatives such as multiplicative fusion and omission of the trade-off weight λΨ. These result in BD-PSNR drops of **-1.33dB** and **-2.06dB**, respectively, demonstrating that our proposed metric more effectively captures Gaussian importance. Detailed discussion can be found in our response to W1.\n\n(3) **Number of Hierarchical Levels**.\nWe conducted additional experiments varying the number of hierarchy levels $L$. The results show that fewer layers (e.g., $L$=3) lead to performance degradation, while increasing $L$ beyond 6 provides negligible gains at the cost of higher training time. Thus, we set $L$=6 as a balanced choice. Please refer to our response to W1 for quantitative results.\n\n(4) **Single-Layer vs. Multi-Layer Coding**. To verify the effectiveness of our residual-aware hierarchical design, we compare our 4DGCPro (multi-layer) against a single-layer coding baseline. Despite introducing layered transmission, our method achieves comparable quality (**29.47dB at 1.31MB** vs. **29.50dB at 1.27MB**), confirming that our hierarchical representation avoids inter-layer redundancy. This is enabled by our residual learning and Gaussian significance-based sorting. \n\n(5) **Attribute-Specific Entropy Modeling**.\nWe also ablated our entropy coding strategy by removing KDE-based supervision from keyframes. The result is a BD-PSNR drop of **0.20dB**, affirming the benefit of attribute-specific modeling for capturing distributional variations across key and inter-frames."}, {"review_id": "oSPJDCyhjn", "reviewer": "Reviewer_NqUw", "summary": "This paper presents 4DGCPro, a novel compression framework for volumetric video streaming that addresses several key challenges in the field. The work tackles the persistent issues of inflexible bitrate adaptation and computational constraints that have limited the practical deployment of high-quality volumetric video on mobile platforms. The proposed solution introduces a hierarchical 4D Gaussian representation combined with motion-aware adaptive grouping, which effectively reduces temporal redundancy while maintaining visual coherence. A significant contribution is the end-to-end entropy-optimized training scheme that incorporates both rate-distortion supervision and attribute-specific entropy modeling. The framework's ability to support quality and bitrate adaptation within a single model represents an important advancement toward making volumetric video more practical for real-world applications.", "questions": "1. Why was H.264 chosen over more efficient standards (e.g., H.265) or learning-based compression methods for encoding the Gaussian attributes?\n\n2. During training, rotation attributes are included in the entropy estimation for keyframes, but are excluded for inter-frames. What is the technical rationale behind this design decision?\n\n3. For the 4K HiFi4G dataset, did 4DGCPro train on the original high-resolution dataset, or was downsampling applied beforehand?", "limitations": "Yes.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths: \n\n1.This paper presents the first hierarchical 4D Gaussian compression approach for progressive volumetric video streaming, with a well-designed architecture that adapts to the heterogeneous capabilities of client devices. It enables adaptive rendering quality selection, ensuring practical applicability in real-world streaming scenarios.\n\n2.The paper uses adaptive grouping to handle topological changes and long-term dynamics, ensuring compact and consistent temporal representation. Layer-wise RD supervision and attribute-specific entropy modeling optimize volumetric video compression for better storage and transmission.\n\n3.The paper provides a thorough evaluation of 4DGCPro, demonstrating its flexibility in supporting variable bitrate and quality within a single model. The method enables real-time decoding and rendering on mobile devices and outperforms existing approaches in RD performance across multiple datasets, showcasing its efficiency and scalability.\n\nWeaknesses:\n\n1.Unlike methods such as 3DGStream, which employ Gaussian compensation for new areas, 4DGCPro lacks dedicated mechanisms to handle emerging content. This could potentially affect the reconstruction fidelity in dynamic scenes with previously unseen regions.\n\n2.It would be beneficial if the authors could include ablation studies on the QP setting. This would provide additional insights into its influence on the overall performance and help strengthen the evaluation of the method.", "was_revised": true, "final_justification": "After carefully reviewing the rebuttal and the discussion with other reviewers, I strongly support the acceptance of this paper. The authors have provided thorough and well-reasoned responses that fully address the concerns raised during the initial review.\n\nResolved Issues:\n1. The authors clarified how their motion-aware adaptive grouping handles emerging content through dynamic keyframe updates. While not explicitly inserting new Gaussians, their approach provides effective modeling of previously unseen regions.\n2. The QP ablation studies are comprehensive and show a clear understanding of bitrate-quality trade-offs, which adds practical value for streaming applications.\n3. The decision to use H.264 instead of H.265 or learning-based codecs is well-justified in terms of latency, deployment ease, and reconstruction quality.\n4. The rotation entropy design choice and layer partitioning mechanism were clearly explained and supported by experiments.\n\nInnovation and Impact:\n1. The paper presents the first hierarchical 4D Gaussian compression framework tailored for progressive volumetric video streaming, which is both novel and timely in its ability to support scalable streaming with a single unified model.\n2. The proposed attribute-specific entropy modeling, motion decomposition, adaptive grouping, and multi-layer Gaussian representation reflect strong innovation beyond conventional video coding schemes.\n3. This work offers a well-designed and scalable solution with practical value, and I believe it will be a useful reference for the community, especially in areas involving real-time neural rendering, streaming, and compact 4D representation.\n\nConclusion:\nIn summary, this paper introduces a novel and well-executed framework that addresses a highly relevant problem with both theoretical and practical contributions. The rebuttal further strengthened the submission, and I confidently recommend Accept.", "rebuttal": "Thank you for your positive feedback on our paper and for highlighting its strengths, including \"the first hierarchical 4D Gaussian compression approach for progressive volumetric video streaming\", \"a well-designed architecture that adapts to the heterogeneous capabilities of client devices\", \"compact and consistent temporal representation\" and \"efficiency and scalability\". We will now address each of the weaknesses and questions you have raised one by one, and we commit to incorporating the following revisions into the final version of the paper.\n\n## Unseen Regions (W1)\nAlthough we have not designed a process for adding Gaussians, our motion-aware adaptive grouping strategy enables the modeling of emerging content. When new regions appear in the scene, the motion of Gaussians becomes intense, triggering the switch to a new keyframe as the subsequent reference. While this strategy does not directly add new Gaussians, it models emerging regions by reperforming keyframe modeling when new objects appear for accurate representation. As evidenced by the results on the N3DV dataset, our method still maintains competitive performance, achieving better reconstruction quality than 3DGStream under storage conditions of less than **1/12**.\n\n## QP setting (W2)\nWe have supplemented ablation experiments with different QP settings on the 4DGCPro dataset, and the results are shown in the table below. Combined with the experimental phenomena, it can be seen that different QP settings have a significant impact on the performance of 4DGCPro: Low QP (0, 10) preserves fine Gaussian parameters, with reconstruction quality close to lossless but large data volume (**+1.05MB** for QP=0, **+0.61MB** for QP=10), which is suitable for scenarios requiring high image quality; Medium QP (20) achieves a balance between quality and compression ratio with less information loss, making it the default choice; High QP (30) leads to excessive information loss during compression due to excessive quantization intensity, resulting in a significant decline in quality (**-0.97dB**). By adjusting the QP value, 4DGCPro can provide multiple discrete bitrates, adapting to streaming scenarios with fluctuating bandwidth.\n\n## Coding Methods (Q1)\nThrough experiments, we found that the encoding and decoding time consumption of H.265 is greater than that of H.264: encoding takes approximately **3.1 times** longer, and decoding takes about **1.7 times** longer. More importantly, H.265 causes more information loss (**-3.4 dB**) during the compression of Gaussian features. In contrast, deep learning-based encoding methods significantly increase decoding latency, making real-time applications impossible, while also being difficult to integrate into existing pipelines. We will incorporate the above analysis into the final paper.\n\n## Rotation Entropy (Q2)\nWe have conducted additional ablation experiments to illustrate the rationality of the training scheme selection. The reconstruction of keyframes does not rely on motion information from other frames. Performing entropy estimation for rotation features in keyframes can effectively reduce the size of Gaussians (**-0.03MB**) with almost no impact on reconstruction quality. However, introducing this in motion modeling will affect the accuracy of rigid transformation estimation, leading to a decrease in reconstruction quality (**-0.2dB**).\n|                              | PSNR(dB) | Size(MB) |\n|:------------------------------:|:----------:|:----------:|\n| w/o keyframe rotation entropy estimation | 29.48    | 1.34     |\n| non-keyframe rotation entropy estimation  | 29.27    | 1.30     |\n| Ours                         | 29.47    | 1.31     |\n## Data Process (Q3)\nFollowing the setting in HiFi4G, we first performed 2x downsampling for subsequent reconstruction."}]

Author rebuttal:

Meta-review: The paper received unanimously positive reviews after the rebuttal. While there were originally some concerns regarding experiments, novelty, and presentation, the authors provided extensive experiments and addressed most of the concerns (good job!). The AC agrees with the reviewers and recommmends acceptance. The AC strongly urge the authors to revise the final paper based on the comments from the rebuttal stage.
Decision: Accept (poster)