TRiGS: Temporal Rigid-Body Motion for Scalable 4D Gaussian Splatting

Suwoong Yeom; Joonsik Nam; Seunggyu Choi; Lucas Yunkyu Lee; Sangmin Kim; Jaesik Park; Joonsoo Kim; Kugjin Yun

cs.CVApr 1, 2026

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

Abstract

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 ( $a_{i,\perp}$ ) 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
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
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.)

Panel of Figure 3 — Figure 3: Qualitative comparison on the SelfCap 1200-frame scenes.

Panel of Figure 4 — Figure 4: Qualitative results on the N3V dataset.

Method	PSNR $\uparrow$	DSSIM ${}_{1}\downarrow$	DSSIM ${}_{2}\downarrow$	LPIPS $\downarrow$
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
Method	FPS $\uparrow$	#Gaussians $\downarrow$	MB $\downarrow$	FPS $\uparrow$	#Gaussians $\downarrow$	MB $\downarrow$	FPS $\uparrow$	#Gaussians $\downarrow$	MB $\downarrow$
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
Configuration	Trajectory	Anchor	Base Param.	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	#Gaussians $\downarrow$	MB $\downarrow$
Baseline	Linear	None	$\mathbb{R}^{3}$	24.83	0.865	0.162	2.10M	512
Naive SE(3)	Rigid Body	Origin	$SO(3)\times\mathbb{R}^{3}$	23.95	0.842	0.198	2.85M	694
Local SE(3)	Rigid Body	Local	$\mathfrak{se}(3)$	25.52	0.891	0.125	0.60M	185
Linear + Bézier	Non-linear	None	$\mathbb{R}^{3}$	25.10	0.873	0.145	1.85M	450
Full TRiGS	Non-linear	Local	$\mathfrak{se}(3)$	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.

Panel of Figure 5 — 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 $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
w/o Gauge Fixing ( $a_{i,\perp}$ )	25.15	0.880	0.134
w/o Rigid Reg. ( $\mathcal{L}_{rigid}$ )	25.48	0.885	0.128
w/o Motion Smoothness ( $\mathcal{L}_{motion}$ )	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 $\uparrow$	DSSIM ${}_{1}\downarrow$	LPIPS $\downarrow$	#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 $\uparrow$
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 $\uparrow$

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.

Panel of Figure 13 — 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).

Panel of Figure 14 — 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).

Panel of Figure 15 — 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).

Explore similar work

Decoupling Motion and Geometry in 4D Gaussian Splatting
Mar 1, 2026Yi Zhang, Yulei Kang, Jiangxin Sun +34D Reconstruction Dynamic Scene Reconstruction
Sun Yat-sen University · University of Trento · Huazhong University of Science and Technology +1
RetimeGS: Continuous-Time Reconstruction of 4D Gaussian Splatting
Mar 14, 2026Xuezhen Wang, Li Ma, Yulin Shen +24D Reconstruction 3D Gaussian Splatting
HKUST · Netflix Eyeline Labs · HKUST(GZ)
MotionScale: Reconstructing Appearance, Geometry, and Motion of Dynamic Scenes with Scalable 4D Gaussian Splatting
Mar 31, 2026Haoran Zhou, Gim Hee Lee4D Reconstruction Dynamic Scene Reconstruction
Department of Computer Science, National University of Singapore

Mar 1, 2026J/K move · Enter open · S save

Decoupling Motion and Geometry in 4D Gaussian Splatting

Yi Zhang, Yulei Kang, Jiangxin Sun, Beihao Xia+2

Sun Yat-sen University · University of Trento · Huazhong University of Science and Technology+1

4D Reconstruction Dynamic Scene Reconstruction 3D Gaussian Splatting Disentangled Representation Learning

Open paper AskPDF arXiv

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.

Abstract

Explore similar work

Decoupling Motion and Geometry in 4D Gaussian Splatting

RetimeGS: Continuous-Time Reconstruction of 4D Gaussian Splatting

MotionScale: Reconstructing Appearance, Geometry, and Motion of Dynamic Scenes with Scalable 4D Gaussian Splatting