RDSplat: Advanced 3D Gaussian Splatting

• RDSplat is a framework that extends 3D Gaussian Splatting by integrating advanced noise modeling, radar synthesis, and robust watermarking techniques.
• It employs radar-specific enhancements like FFT-based noise analysis and multipath modeling to generate accurate occupancy maps and synthetic radar imagery.
• The watermarking paradigm uses low-frequency Gaussian selection and adversarial training to ensure message integrity even under diffusion-based editing attacks.

RDSplat refers to a set of technical advancements in the domain of 3D Gaussian Splatting (3DGS), with key instantiations encompassing radar-based neural scene synthesis for autonomous driving and robust digital watermarking resistant to diffusion-based editing. The term has been notably associated with the "RadarSplat" pipeline for radar data synthesis and geometric reconstruction (Kung et al., 2 Jun 2025), as well as a watermarking paradigm explicitly designed to counter modern diffusion editors (Zhao et al., 7 Dec 2025). These methods generally extend the classical GS framework—where scenes are encoded as a set of spatially parameterized, colored Gaussians—through novel formulation, noise modeling, and adversarial optimization techniques.

1. 3D Gaussian Splatting: Principles and Extensions

3D Gaussian Splatting (3DGS) encodes a scene as an ensemble of anisotropic Gaussians $$\mathcal{G} = \{(\mu_i, \Sigma_i, c_i, \alpha_i)\}_{i=1}^N$$, where each primitive is defined by its mean $\mu_i \in \mathbb{R}^3$, covariance $\Sigma_i \in \mathbb{R}^{3\times 3}$, color $c_i$, and opacity $\alpha_i$. Rendering proceeds by projecting each 3D Gaussian to a 2D image plane and aggregating via front-to-back alpha blending. The formulation supports high fidelity and real-time rendering, and is extensible to multimodal sensor data (e.g., radar, LiDAR).

Explicitly, the splatting process for each pixel $x$ aggregates projected Gaussians $G_i^{2D}(x)$ as: $$I(x) = \sum_{i=1}^N \alpha_i \cdot c_i \cdot G_i^{2D}(x)$$ with colors optionally parameterized via spherical harmonics for photorealism. Notable limitations of classical 3DGS include difficulty in modeling lighting variation, physical interactions, and vulnerability to signal-level or semantic editing.

2. RadarSplat: Gaussian Splatting for High-Fidelity Radar Data Synthesis

RadarSplat ("RDSplat" as Editor's term) defines a unified Gaussian-splatting pipeline for FMCW scanning-radar data (Kung et al., 2 Jun 2025). It targets three outputs: realistic novel-view radar image synthesis (signal + noise), dense bird’s-eye-view (BEV) occupancy maps, and 3D Gaussian scene representations for autonomous driving simulation.

Pipeline Overview

• Preprocessing: Radar images are analyzed using Fast Fourier Transform (FFT) on range bins to identify corruption due to receiver saturation ($C = |X[0]|/\sum_{k>0}|X[k]|$), multipath reflection (local peaks $|X[k_m]|$ for $k_m \neq 0$), and speckle noise.
• Denoising & Occupancy Mapping: Noisy beams are Gaussian-smoothed, return peaks are localized, and masks exclude decay regions. A sliding temporal window (size $W=10$) yields denoised BEV occupancy maps $I_{occ}$ for geometric supervision.
• Multipath Modeling: Detected multipath sources $(k_m)$ are mapped to "ghost" distances, reconstructed via inverse FFT and fitted exponential decay, then stored for reprojection in novel viewpoints.
• Gaussian Splatting Representation: The scene is modeled as $N$ explicit 3D Gaussians $$\mathcal{G} = \{G_i : (\mu_i,q_i,S_i,\sigma_i)\}_{i=1}^N$$, with $\sigma_i = \rho_i \cdot \min(\alpha_i + \eta_i, 1)$ explicitly disentangling beam occupancy ($\alpha_i$), reflectance ($\rho_i$) and learned noise probability ($\eta_i$) in each primitive.

Radar-Specific Rendering and Noise Synthesis

Gaussians are projected to spherical radar coordinates, with elevation and azimuth projections, and weighted by antenna gain and radar equation ($R_n^{-4}$ falloff). Spectral leakage from FFT windowing is modeled as a 1D Gaussian blur ($\sigma_w = 0.17$ m). At test time, noise synthesis integrates multipath ghosts, speckle, and saturation events per pose, emulating realistic radar phenomena.

3. Robust Watermarking for 3DGS: RDSplat Paradigm

RDSplat also denotes a watermarking framework explicitly resilient to diffusion-based editing attacks (Zhao et al., 7 Dec 2025). Classical approaches embed watermarks in high-frequency content, which diffusion editors erase; RDSplat circumvents this by targeting low-frequency Gaussians and employing adversarial optimization.

Core Technical Elements

• Low-Frequency Gaussian Selection: For each Gaussian, the maximal view-dependent Nyquist frequency $\hat{\nu}_k$ is computed ($\hat{\nu}_k = \max_{c} f_c/d_c$ over views $c$), selecting primitives below the 25th percentile and visible in sufficient views, as diffusion editors preserve low-frequency structure.
• 3D Covariance Regularization: Low-frequency Gaussians have their covariance convolved with isotropic Gaussian noise ($$\Sigma_k^{\text{reg}} = \Sigma_k + \lambda/\hat{\nu}_k^2 \cdot I$$) to further band-limit their frequency profile.
• Multi-Domain Embedding: Watermarks are embedded by densifying the low-frequency subset, training additional Gaussians to encode the watermark message in both object (3D) and screen (2D) space, with coordinated covariance control and 2D mip filtering ($\tilde{\Sigma}_k = \Sigma_k^{2D} + \tau^2 I$).
• Adversarial Training via Diffusion Proxy: Rather than costly direct backpropagation through real diffusion editors, RDSplat leverages Gaussian blur as a surrogate for low-pass filtering, combining it with standard data augmentations and adversarial GAN regularization to maximize watermark survivability.

Implementation

Two-stage training is employed: classical 3DGS model optimization (unwatermarked), followed by densification and adversarial fine-tuning of watermark carriers. A frozen 2D CNN decoder (HiDDeN style), pre-trained for 48-bit message extraction, supervises watermark recovery. The training objective balances image reconstruction, bit accuracy under augmentation, and perceptual invisibility via R3GAN losses.

4. Quantitative Benchmarks and Empirical Insights

RadarSplat Results

On the Boreas dataset (Kung et al., 2 Jun 2025), RadarSplat outperforms prior radar-neural methods (Radar Fields) by +3.4dB PSNR, 2.6x SSIM, and -40% RMSE in geometric reconstruction. It achieves fast 4.5 FPS rendering of synthetic radar images with explicit modeling of multipath, speckle, and saturation noise sources.

Metric	RadarSplat	Radar Fields
PSNR (dB)	26.06	22.66
SSIM	0.51	0.20
LPIPS	0.37	0.60
RMSE (m)	1.81	3.03
BEV Accuracy	0.91	0.59

Noise modeling ablations show notable drops in signal fidelity without $\eta_i$, occupancy supervision, and spectral leakage correction.

RDSplat Watermarking Results

On Mip-NeRF360, LLFF, and Blender datasets, RDSplat achieves clean bit accuracy of 97.0% and state-of-the-art robustness under both classical signal attacks (average 0.828 bit accuracy vs. 0.764 for GaussianMarker) and diffusion editing (TPR@1%FPR: 0.657 vs. 0.599 for GaussianMarker). Watermark imperceptibility is confirmed via PSNR/SSIM/LPIPS metrics and error maps.

Method	Clean Accuracy	Classical Attack	Diffusion TPR@1%FPR
RDSplat	97.0%	0.828	0.657
GaussianMarker	95.8%	0.764	0.599
GuardSplat	—	0.540	0.511
3DGS+Hidden	—	0.583	0.583

Surrogate blur in adversarial training matches spectral attenuation of real diffusion editors.

5. Limitations and Future Research Directions

For RadarSplat, handling of dynamic scenes is not supported; integrating Gaussian-scene-graph segmentation and physical-wave occlusion is suggested for future work. Hardware generalization and higher scanning rates present additional scalability challenges (Kung et al., 2 Jun 2025).

In watermarking, current pipelines rely on 2D CNN decoders; future developments target fully 3D-native message extraction for greater robustness. Enhanced adversarial proxies and defenses against full 3D reconstruction attacks are also proposed (Zhao et al., 7 Dec 2025).

A plausible implication is that coordinated control of spatial frequency content and adversarial optimization in native 3DGS parameter space can generalize to broader data protection and multimodal scene synthesis scenarios, especially when sensor-specific noise characteristics are present.

6. Context within Related 3DGS and Multimodal Splatting Frameworks

RDSplat approaches fundamentally extend the classical purpose of Gaussian Splatting beyond RGB-based rendering (as in RadSplat (Niemeyer et al., 20 Mar 2024)) and mesh-adapted ray tracing (e.g., REdiSplats (Byrski et al., 15 Mar 2025)), illuminating new use cases in radar simulation, robust provenance encoding, and sensor-specific realism. The explicit disentanglement of occupancy, reflectance, and noise parameters per Gaussian, as well as frequency-aware adversarial watermarking, mark a shift toward domain-adaptive splatting pipelines.

This suggests that future GS-based frameworks will increasingly incorporate sensor physics, active robustness optimization, and hybrid mesh-/density-based representations to meet application needs in autonomous perception, data security, and real-time rendering under challenging environmental conditions.