4D Gaussian Ray Tracing (4D-GRT)

• 4D-GRT is a dynamic scene rendering method that leverages 4D Gaussian splatting and differentiable ray tracing to model spatio-temporal deformations and camera-induced effects.
• The framework accurately simulates camera effects like fisheye distortion, depth of field, and rolling shutter using physically-based algorithms and calibrated lens models.
• End-to-end optimization with neural deformation fields enables high-quality renderings at speeds exceeding 100 FPS, facilitating camera-aware data generation for vision research.

4D Gaussian Ray Tracing (4D-GRT) refers to a pipeline for dynamic scene reconstruction and physically accurate rendering that integrates 4D Gaussian Splatting—a spatio-temporal primitive representation—with a physically-based differentiable ray tracing module. The 4D-GRT framework facilitates simulating real camera effects (e.g., fisheye distortion, rolling shutter, depth of field) and supports high-quality, fast rendering for camera-aware computer vision, robotic perception, and photorealistic simulation using dynamic 3D scenes captured from multi-view videos (Liu et al., 13 Sep 2025).

1. Spatio-Temporal Scene Representation via 4D Gaussian Splatting

At the heart of 4D-GRT lies 4D Gaussian Splatting, in which dynamic scenes are modeled as a union of spatio-temporal Gaussian primitives. Each primitive is defined by a mean $\mathbf{\mu} = (\mu_x, \mu_y, \mu_z, \mu_t)$ and a covariance matrix $\mathbf{\Sigma} \in \mathbb{R}^{4\times4}$ constructed as $\Sigma = R S S^\top R^\top$, where $R$ is an arbitrarily rotatable 4D rotation matrix assembled from two quaternions and $S = \text{diag}(s_x, s_y, s_z, s_t)$ encodes anisotropic scaling in all dimensions (Yang et al., 2023). This parametrization allows the modeling of ellipsoidal support regions in spacetime and enables Gaussians to align and rotate non-trivially in both spatial and time domains to capture complex motion and deformation.

Appearance is encoded by coefficients of 4D spherindrical harmonics (Editor’s term: 4DSH), $$Z_{nlm}(t, \theta, \phi) = \cos(\frac{2\pi n}{T} t) Y_{lm}(\theta, \phi)$$, unifying view-dependent appearance and temporal color evolution.

Dynamic deformation is parameterized by a neural deformation field (e.g., HexPlane (Ren et al., 2023)), which maps spatio-temporal coordinates to position, rotation, and scale residuals, implemented as a lightweight MLP operating over six feature planes.

2. Ray Tracing Algorithms with 4D Gaussian Primitives

4D-GRT combines splatting-style volume rendering with hit-based ray tracing for the evaluation of physically-based camera models. Rays are emitted from the specified camera model (pinhole, fisheye, rolling shutter, etc.), and, for each ray, intersections with the space-time Gaussians are efficiently computed.

In the compositing routine, each Gaussian’s opacity at a position $(u, v)$ and time $t$ is defined as

$\alpha_i = \sigma_i\, p_i(t)\, p_i(u, v | t)$

where $p_i(t)$ is the marginal temporal weight and $p_i(u, v | t)$ is the conditional 3D spatial Gaussian projected to image coordinates. Colors are evaluated from the corresponding 4DSH coefficients. Final pixel intensities use a time-extended alpha-blending equation:

$$I(u, v, t) = \sum_i [p_i(t)\, p_i(u, v | t)\, \alpha_i\, c_i(d, t)] \prod_j \left(1 - p_j(t)\, p_j(u, v | t)\, \alpha_j\right)$$

Real-time performance is achieved with hardware-accelerated “k-buffer” marching and efficient Gaussian gating—only the subset of primitives with sufficient temporal support need be evaluated per frame (Liu et al., 13 Sep 2025).

3. Physically-Based Camera Effects Simulation

An innovation of 4D-GRT is native support for simulating real-world sensor effects:

• Fisheye Distortion: Employs a fourth-degree radial polynomial $\theta = k_0 + k_1 r + k_2 r^2 + k_3 r^3 + k_4 r^4$, where $r = \sqrt{x^2 + y^2}$ yields polar angle $\theta$ for ray direction. The distortion coefficients $k_i$ are determined by physical lens calibration (Liu et al., 13 Sep 2025).
• Depth of Field: For each pixel, the system computes the intersection of the ideal ray with the focal plane and samples origins $\mathbf{o'}$ over a circular aperture. The direction $\mathbf{d'}$ is set to $$(\mathbf{p} - \mathbf{o'})/\|\mathbf{p} - \mathbf{o'}\|$$, averaging multiple samples to simulate optical blur.
• Rolling Shutter: Each image row is assigned a unique sensing time $t_r$. Scene deformation fields yield the 3D Gaussians at $t_r$, and rays per row are traced accordingly. For efficiency, rows are chunked, with shared time per chunk, trading accuracy for speed.

This structure enables automated, parameter-controllable simulation of effects such as geometric distortions, spatio-temporal blur, and sensor-induced motion artifacts. Rendering with 4D-GRT yields photorealistic videos conditioned on physically plausible camera models.

4. Training and Optimization

Training the 4D-GRT pipeline proceeds end-to-end. Multi-view video is used to fit the spherindrical harmonic coefficients and deformation parameters of the 4D Gaussians via differentiable rendering losses:

$$\mathcal{L} = \mathcal{L}_1(C_{\nu, t}, \hat{C}_{\nu, t}) + \mathcal{L}_{TV}$$

Color predictions utilize L1 loss; spatial smoothness is regularized via total variation. Deformation networks are often initialized in a “zero deformation” regime to avoid divergence, ensuring static geometry fidelity before dynamic modeling (Ren et al., 2023).

Benchmarks show optimization times as low as ten minutes for moderate-length sequences, and rendering speeds exceeding 100 FPS (or higher when hybrid or disentangled parameterizations are used) (Oh et al., 19 May 2025, Feng et al., 28 Mar 2025).

5. Comparative Analysis and Benchmarks

4D-GRT exhibits superior performance relative to prior volumetric, mesh-based, and rasterization-centric approaches for dynamic scene rendering with camera effects:

Method	Rendering Speed (FPS)	PSNR	Flexible Camera Effects	Real-time?	Storage Efficiency
4D-GRT (proposed)	$>$100	Highest/Better	Native	Yes	Moderate
HexPlane/MSTH	$<$60	Lower	None	Partially	Moderate
3DGS (+ rasterization)	Variable	Lower	Emulated/limited	Often	High

Reported experiments on eight synthetic dynamic scenes with four camera effects confirm 4D-GRT delivers the fastest speeds and competitive or superior visual quality (Liu et al., 13 Sep 2025).

6. Applications, Implications, and Future Directions

4D-GRT is a tool for generating physically accurate, camera-aware video datasets for computer vision, improving sim-to-real transfer in robotics, and enabling camera effect-aware data augmentation for learning-based systems. It supports interactive AR/VR, immersive simulation, and robust photorealistic rendering in dynamic environments. The explicit, interpretable nature of spatio-temporal Gaussian primitives with calibrated camera effects allows precise scientific analysis and reproducibility.

A plausible implication is that expanding the pipeline with adaptive static/dynamic partitioning (Oh et al., 19 May 2025), Wasserstein-constrained temporal regularization (Deng et al., 30 Nov 2024), or semantic segmentation annotation (Ji et al., 5 Jul 2024) will further enhance scalability, realism, and downstream utility. Research directions include integrating global illumination, supporting hybrid mesh/splat representations, and extending the method for interactive scene editing and segmentation tasks.

7. Limitations and Controversies

Storage and memory overhead remain challenges for high-resolution, long-duration dynamic scenes, although anchor-based and hybrid frameworks have produced dramatic efficiency gains approaching $97.8\times$ reduction (Cho et al., 26 Nov 2024). Real-time rolling shutter simulation trades accuracy for efficiency via row chunking, which may produce minor block artifacts except at high chunk rates.

Debate persists on disentangled versus coupled spatio-temporal representations; while disentangled methods are faster, fully coupled formulations can better capture certain motion interactions (Feng et al., 28 Mar 2025). As 4D-GRT is leveraged for sim-to-real transfer and photorealistic simulation, continued scrutiny of its physical accuracy and completeness is warranted.

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4D Gaussian Ray Tracing unifies dynamic spatio-temporal scene modeling with physically accurate camera effect emulation. By extending Gaussian Splatting into four dimensions and integrating ray tracing, it achieves fast, high-fidelity rendering of dynamic environments for camera-aware data generation and vision research.