TRiGS: Temporal Rigid-Body Motion for Scalable 4D Gaussian Splatting
Authors: Suwoong Yeom, Joonsik Nam, Seunggyu Choi, Lucas Yunkyu Lee, Sangmin Kim, Jaesik Park, Joonsoo Kim, Kugjin Yun, +2 more
Organizations: Sogang University · POSTECH · Seoul National University · Electronics and Telecommunications Research Institute · Pusan National University
Recent 4D Gaussian Splatting (4DGS) methods achieve impressive dynamic scene reconstruction but often rely on piecewise linear velocity approximations and short temporal windows. This disjointed modeling leads to severe temporal fragmentation, forcing primitives to be repeatedly eliminated and regenerated to track complex nonlinear dynamics. This makeshift approximation eliminates the long-term temporal identity of objects and causes an inevitable proliferation of Gaussians, hindering scalability to extended video sequences. To address this, we propose TRiGS, a novel 4D representation that utilizes unified, continuous geometric transformations. By integrating SE(3) transformations, hierarchical Bezier residuals, and learnable local anchors, TRiGS models geometrically consistent rigid motions for individual primitives. This continuous formulation preserves temporal identity and effectively mitigates unbounded memory growth. Extensive experiments demonstrate that TRiGS achieves high fidelity rendering on standard benchmarks while uniquely scaling to extended video sequences (e.g., 600 to 1200 frames) without severe memory bottlenecks, significantly outperforming prior works in temporal stability.
Figures & tables
Figure 1: Comparison of temporal modeling for extended dynamic scenes. (Left) While previous methods like FTGS rely on fragmented piecewise linear approximations that force primitives to repeatedly reset, our continuous rigid-body transformations preserve the long-term temporal identity of active Gaussians. (Right) By eliminating the need for unnecessary proliferation, TRiGS maintains a strictly constant, compact memory footprint while sustaining high rendering quality across extended sequences (up to 1200 frames), in stark contrast to baselines that suffer from severe memory bloat and performance drops. (Bottom) Consequently, our approach delivers temporally stable, high-fidelity novel view synthesis without visual degradation or motion artifacts.
Figure 2: Overview of our framework. We comprehensively model the scene dynamics through three key components. First, the motion is parameterized via a hierarchical decomposition using Bézier residuals within an effective temporal window. Second, this Lie algebra representation is mapped to a coupled SE(3) transformation. Third, the transformation is applied relative to a gauge-fixed local anchor ( ai,⊥ ) to ensure stable, articulate deformation. Finally, the deformed primitives are rendered to optimize both photometric and motion regularization objectives.
Method
600 frames
900 frames
1200 frames
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
GIFStream [ 16 ]
23.76
0.877
0.134
23.80
0.871
0.124
24.27
0.874
0.117
4DGS [ 10 ]
24.30
0.860
0.227
23.48
0.851
0.240
23.28
0.851
0.233
Ex-4DGS [ 17 ]
21.61
0.801
0.233
20.93
0.793
0.248
20.45
0.787
0.248
STGS [ 11 ]
24.17
0.844
0.161
23.01
0.864
0.136
25.34
0.734
0.100
LocalDyGS [ 8 ]
25.49
0.858
0.240
23.51
0.838
0.280
24.24
0.884
0.116
Table 1: Quantitative comparison on the SelfCap dataset across 600, 900, and 1200 frame budgets. best , second-best , and third-best results are highlighted in the table. ( ∗ Results from our reproduction, as the official code is not publicly available.)
Figure 3: Qualitative comparison on the SelfCap 1200-frame scenes.
Figure 4: Qualitative results on the N3V dataset.
Method
PSNR ↑
DSSIM 1↓
DSSIM 2↓
LPIPS ↓
HexPlane 2 [ 34 ]
31.71
-
0.014
0.075
K-Planes [ 35 ]
31.63
-
0.018
-
MixVoxels [ 36 ]
31.73
-
0.015
0.064
HyperReel [ 37 ]
31.10
0.036
-
0.096
NeRFPlayer [ 38 ]
30.96
0.034
-
0.111
Deformable-3DGS [ 5 ]
31.15
0.030
-
0.049
Table 2: Quantitative comparison on N3V datasets. best , second-best , and third-best results are highlighted in the table. ( † Results reported in the original paper, using 0.5M initial points.)
Method
600 frames
900 frames
1200 frames
FPS ↑
#Gaussians ↓
MB ↓
FPS ↑
#Gaussians ↓
MB ↓
FPS ↑
#Gaussians ↓
MB ↓
GIFStream [ 16 ]
94
6.47M
1586
98
8.85M
2169
102
11.53M
2825
4DGS [ 10 ]
43
2.51M
4665
43
2.70M
5021
44
2.70M
5015
STGS [ 11 ]
90
1.31M
190
83
2.01M
291
90
2.45M
355
FTGS ∗ [ 18 ]
113
2M
490
110
3M
733
106
4M
977
Ours
116
0.5M
160
111
0.5M
160
120
0.5M
160
Table 3: Efficiency comparison on SelfCap across 600, 900, and 1200 frame budgets.
Configuration
Modeling Choices
Quality Metrics
Efficiency
Trajectory
Anchor
Base Param.
PSNR ↑
SSIM ↑
LPIPS ↓
#Gaussians ↓
MB ↓
Baseline
Linear
None
R3
24.83
0.865
0.162
2.10M
512
Naive SE(3)
Rigid Body
Origin
SO(3)×R3
23.95
0.842
0.198
2.85M
694
Local SE(3)
Rigid Body
Local
se(3)
25.52
0.891
0.125
0.60M
185
Linear + Bézier
Non-linear
None
R3
25.10
0.873
0.145
1.85M
450
Full TRiGS
Non-linear
Local
se(3)
26.05
0.904
0.099
0.50M
160
Table 4: Ablation study of core components in TRiGS on the 1200-frame extended sequence. We evaluate the impact of trajectory modeling, anchor modes, and base parameterization on rendering quality and memory efficiency.
Figure 5: Visual ablation on the SelfCap bike2 scene. Compared to incomplete configurations that suffer from motion artifacts and blurriness, Full TRiGS successfully preserves sharp geometric details and structural integrity.
Configuration
PSNR ↑
SSIM ↑
LPIPS ↓
w/o Gauge Fixing ( ai,⊥ )
25.15
0.880
0.134
w/o Rigid Reg. ( Lrigid )
25.48
0.885
0.128
w/o Motion Smoothness ( Lmotion )
25.66
0.892
0.115
w/o Motion-guided Relocation
25.80
0.897
0.108
Full TRiGS Architecture
26.05
0.904
0.099
Table 5: Ablation study on optimization components in TRiGS. We evaluate the impact of gauge fixing, regularization losses, and relocation strategy on the 1200-frame sequence.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Method
PSNR ↑
DSSIM 1↓
LPIPS ↓
#Gaussians
FTGS (published, 500k)
32.97
0.028
0.043
500k
FTGS (ours, reproduced)
32.80
0.021
0.040
500k
Appendix
Table S1 : Validation of our FTGS reproduction on Neural3DV under the matched 500k-primitive setting. The reproduced FTGS closely matches the published FTGS result while using the same primitive budget, supporting the faithfulness of our implementation.
1200 frames
bike1
bike2
corgi1
corgi2
dance
yoga
avg
PSNR ↑
STGS [ 11 ]
25.95
25.67
24.87
24.97
24.95
24.58
25.16
4DGS [ 10 ]
25.06
24.65
24.35
23.03
23.59
22.15
23.81
FTGS [ 18 ]
25.61
25.92
25.33
23.25
26.12
25.04
25.21
Ours
26.45
26.70
26.25
24.62
26.85
25.43
26.05
SSIM ↑
Appendix
Table S2 : Matched-budget comparison on the 1200-frame SelfCap setting, where all methods are constrained to the same budget of 500k Gaussians. Under this setting, 4DGS and STGS run without OOM on a single RTX 4090 (24GB VRAM), enabling a controlled equal-capacity comparison. Even in this favorable setting for the baselines, TRiGS achieves the best average PSNR/SSIM/LPIPS.
Figure S1 : Qualitative comparison on the bike2 scene across different sequence lengths. Rows denote frame length (1200/900/600), and columns denote methods (GT, Ours, FTGS, STGS).
Figure S2 : Qualitative comparison on the corgi2 scene across different sequence lengths. Rows denote frame length (1200/900/600), and columns denote methods (GT, Ours, FTGS, STGS).
Figure S3 : Qualitative comparison on the yoga scene across different sequence lengths. Rows denote frame length (1200/900/600), and columns denote methods (GT, Ours, FTGS, STGS).
High-fidelity reconstruction of dynamic scenes is an important yet challenging problem. While recent 4D Gaussian Splatting (4DGS) has demonstrated the ability to model temporal dynamics, it couples Gaussian motion and geometric attributes within a single covariance formulation, which limits its expressiveness for complex motions and often leads to visual artifacts. To address this, we propose VeGaS, a novel velocity-based 4D Gaussian Splatting framework that decouples Gaussian motion and geometry. Specifically, we introduce a Galilean shearing matrix that explicitly incorporates time-varying velocity to flexibly model complex non-linear motions, while strictly isolating the effects of Gaussian motion from the geometry-related conditional Gaussian covariance. Furthermore, a Geometric Deformation Network is introduced to refine Gaussian shapes and orientations using spatio-temporal context and velocity cues, enhancing temporal geometric modeling. Extensive experiments on public datasets demonstrate that VeGaS achieves state-of-the-art performance.
Yi Zhang, Yulei Kang, Jiangxin Sun +3
Sun Yat-sen University · University of Trento · Huazhong University of Science and Technology +1
Temporal retiming, the ability to reconstruct and render dynamic scenes at arbitrary timestamps, is crucial for applications such as slow-motion playback, temporal editing, and post-production. However, most existing 4D Gaussian Splatting (4DGS) methods overfit at discrete frame indices but struggle to represent continuous-time frames, leading to ghosting artifacts when interpolating between timestamps. We identify this limitation as a form of temporal aliasing and propose RetimeGS, a simple yet effective 4DGS representation that explicitly defines the temporal behavior of the 3D Gaussian and mitigates temporal aliasing. To achieve smooth and consistent interpolation, we incorporate optical flow-guided initialization and supervision, triple-rendering supervision, and other targeted strategies. Together, these components enable ghost-free, temporally coherent rendering even under large motions. Experiments on datasets featuring fast motion, non-rigid deformation, and severe occlusions demonstrate that RetimeGS achieves superior quality and coherence over state-of-the-art methods.
Realistic reconstruction of dynamic 4D scenes from monocular videos is essential for understanding the physical world. Despite recent progress in neural rendering, existing methods often struggle to recover accurate 3D geometry and temporally consistent motion in complex environments. To address these challenges, we propose MotionScale, a 4D Gaussian Splatting framework that scales efficiently to large scenes and extended sequences while maintaining high-fidelity structural and motion coherence. At the core of our approach is a scalable motion field parameterized by cluster-centric basis transformations that adaptively expand to capture diverse and evolving motion patterns. To ensure robust reconstruction over long durations, we introduce a progressive optimization strategy comprising two decoupled propagation stages: 1) A background extension stage that adapts to newly visible regions, refines camera poses, and explicitly models transient shadows; 2) A foreground propagation stage that enforces motion consistency through a specialized three-stage refinement process. Extensive experiments on challenging real-world benchmarks demonstrate that MotionScale significantly outperforms state-of-the-art methods in both reconstruction quality and temporal stability. Project page: https://hrzhou2.github.io/motion-scale-web/.
Haoran Zhou, Gim Hee Lee
Department of Computer Science, National University of Singapore