DehazeGS: 3D Fog Dehazing Framework

• DehazeGS is a novel framework that integrates a physically accurate fog model with explicit 3D Gaussian splatting to reconstruct foggy scenes.
• The method jointly optimizes scene geometry, scattering coefficients, and illumination parameters to recover detailed, clear scene views.
• It outperforms NeRF-based methods by achieving superior PSNR, SSIM, and LPIPS metrics in real-time dehazing and multi-view consistency.

DehazeGS is a novel reconstruction and dehazing framework for 3D scene synthesis under foggy conditions, integrating a physically accurate participating media model into the explicit 3D Gaussian Splatting (3DGS) representation. It enables rendering fog-free views from multi-view foggy image collections by jointly learning geometric, scattering, and illumination parameters. DehazeGS achieves superior fidelity and efficiency compared to NeRF-based and alternative Gaussian-based baselines and supports real-time dehazing with state-of-the-art multi-view consistency and detail preservation (Yu et al., 7 Jan 2025).

1. Physical Principles of Foggy Image Formation

DehazeGS incorporates a physically grounded model of image formation in fog, where image intensity $I$ along a ray results from two additive effects: direct transmission of scene radiance, attenuated by the medium, and airlight, generated by scattering of ambient illumination. The general volume-rendering equation is:

$$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$

where $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$ is the transmittance, $\sigma_t$ is the extinction coefficient ($\sigma_t = \sigma_s + \sigma_a$), $L(D)$ is the surface radiance, and $A_{\infty}$ is the global atmospheric light. Under homogeneous fog (constant extinction $\beta$) and single-scattering, the model simplifies to:

$$I(x) = J(x)\,t(x) + A_{\infty}(1-t(x)), \qquad t(x) = e^{-\beta\,d(x)}$$

with $I(x)$ the observed foggy color, $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$0 the latent clear-scene radiance, $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$1 the atmospheric light (learned), $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$2 the scattering coefficient (learned), and $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$3 the pixel depth.

2. 3D Gaussian Splatting Representation

DehazeGS builds on the 3DGS framework, which describes the volumetric scene geometry using $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$4 anisotropic 3D Gaussians. Each Gaussian $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$5 is characterized by mean $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$6, covariance $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$7 (parametrized as $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$8), opacity $$I = T(0,D)\,L(D) + \int_{0}^{D} T(0,s)\,\sigma_s(s)\,A_{\infty}\,\mathrm{d}s$$9, and color coefficients $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$0 (potentially in a spherical harmonic basis for view dependence). The Gaussian spatial density is:

$T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$1

Rendering proceeds by projecting 3D Gaussians to 2D ellipses and compositing them in depth order using their effective 2D opacities $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$2. The pixel color is:

$T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$3

3. Integrating Physically Based Fog into Gaussian Splatting

DehazeGS extends 3DGS by incorporating the atmospheric scattering model at the per-Gaussian level. Each Gaussian receives a learnable transmittance $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$4, where $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$5 is the depth of its center. For fog simulation:

• Opacity is attenuated: $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$6
• Color is a convex combination of latent color and airlight: $T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$7

Rendering of the foggy image follows the same over-compositing principle:

$T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$8

This integration enables differentiable, physically grounded simulation of scattering and attenuation, facilitating accurate recovery of both scene properties and fog parameters.

4. Joint Optimization and Training Objectives

All scene parameters ($T(a,b)=\exp(-\int_{a}^{b}\sigma_t(u)\,\mathrm{d}u)$9), along with $\sigma_t$0 and $\sigma_t$1, are optimized end-to-end by minimizing a composite loss over multi-view foggy images. The objective includes:

• Reconstruction loss: Combines $\sigma_t$2 distance and D-SSIM between observed and rendered foggy images.

$\sigma_t$3

• Dark/Bright Channel Priors: Impose regularization on the transmittance map $\sigma_t$4 using classical 2D priors and Laplacian smoothing.
• Depth Supervision: Enforces consistency between learned depths and pseudo-depth maps. The total loss is:

$\sigma_t$5

5. Inference and Dehazing Pipeline

After training, dehazing proceeds by neutralizing fog parameters: setting $\sigma_t$6 and omitting the airlight term. Each dehazed Gaussian is recovered by:

$\sigma_t$7

The latent scene is rendered as a standard 3DGS composite:

$\sigma_t$8

This process yields a clear view consistent with the original scene, enabling extraction of fog-free images from foggy multi-view inputs.

6. Experimental Benchmarking and Comparative Analysis

Evaluation encompasses both synthetic fog datasets (four Mip-NeRF scenes with randomized $\sigma_t$9 and $\sigma_t = \sigma_s + \sigma_a$0) and real fog scenes (three indoor scenes captured with professional fog machines). Performance is compared against ScatterNeRF, SeaSplat, vanilla 3DGS, and DehazeNeRF using PSNR (↑), SSIM (↑), and LPIPS (↓).

Method	Iterations	PSNR	SSIM	LPIPS	Training Time
ScatterNeRF	250K	9.8	0.32	0.77	>16 h
SeaSplat	30K	11.8	0.55	0.29	~25 min
3DGS	30K	12.8	0.57	0.31	~5 min
DehazeNeRF	50K	16.3	0.57	0.25	>4 h
DehazeGS	3K	17.7	0.76	0.15	~1.2 min

On synthetic fog, DehazeGS achieves PSNR ≈ 20.3, outperforming SeaSplat (PSNR ≈ 18.8) and matching its real-time efficiency (25 min vs 30 min). DehazeGS consistently demonstrates superior detail recovery, multi-view coherence, and computational speed (Yu et al., 7 Jan 2025).

7. Key Contributions and Implications

DehazeGS introduces several notable advances:

• Physically grounded fog modeling within the explicit 3D Gaussian framework, enabling accurate simulation of scattering and attenuation at the per-Gaussian level.
• Joint learning of scene geometry, appearance, atmospheric scattering coefficient $\sigma_t = \sigma_s + \sigma_a$1, and light $\sigma_t = \sigma_s + \sigma_a$2 from foggy multi-view images, without requiring clear ground-truth supervision.
• Real-time dehazing rendering with enhanced multi-view consistency and fine detail recovery relative to both NeRF-like and prior Gaussian-based approaches. A plausible implication is that this integration of explicit geometry and physical forward-models may generalize to other participating media and image degradation phenomena, enabling efficient, interpretable scene reconstruction in adverse conditions (Yu et al., 7 Jan 2025).