---
title: 'DehazeGS: 3D Fog Dehazing Framework'
url: https://www.emergentmind.com/topics/dehazegs
type: topic
---

# DehazeGS: 3D Fog Dehazing Framework

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 [2501.03659].

## 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, $J(x)$ the latent clear-scene radiance, $A_{\infty}$ the atmospheric light (learned), $\beta$ the scattering coefficient (learned), and $d(x)$ the pixel depth.

## 2. 3D Gaussian Splatting Representation

DehazeGS builds on the 3DGS framework, which describes the volumetric scene geometry using $N$ anisotropic 3D Gaussians. Each Gaussian $G_i$ is characterized by mean $\mu_i \in \mathbb{R}^3$, covariance $\Sigma_i \in \mathbb{R}^{3 \times 3}$ (parametrized as $R_i S_i S_i^T R_i^T$), opacity $\alpha_i \in [0,1]$, and color coefficients $c_i \in \mathbb{R}^3$ (potentially in a spherical harmonic basis for view dependence). The Gaussian spatial density is:
$$
\mathcal{G}_i(x) = \exp\left(-\frac{1}{2}(x-\mu_i)^T\Sigma_i^{-1}(x-\mu_i)\right)
$$
Rendering proceeds by projecting 3D Gaussians to 2D ellipses and compositing them in depth order using their effective 2D opacities $\alpha'_i(x) = \alpha_i \mathcal{G}_i^{2D}(x)$. The pixel color is:
$$
I_{\mathrm{clear}}(x) = \sum_{i=1}^N c_i \alpha'_i(x) \prod_{j<i} \left(1 - \alpha'_j(x)\right)
$$

## 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 $t_i = \exp(-\beta d_i)$, where $d_i$ is the depth of its center. For fog simulation:
- Opacity is attenuated: $\alpha'_{i,\mathrm{fog}} = \alpha_i t_i$
- Color is a convex combination of latent color and airlight: $c_{i,\mathrm{fog}} = c_i t_i + A_{\infty}(1-t_i)$

Rendering of the foggy image follows the same over-compositing principle:
$$
I_{\mathrm{fog}}(x) = \sum_{i=1}^N c_{i,\mathrm{fog}}\,\alpha'_{i,\mathrm{fog}}(x)\,\prod_{j<i}\left(1-\alpha'_{j,\mathrm{fog}}(x)\right)
$$
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 ($\mu_i, \Sigma_i, \alpha_i, c_i$), along with $\beta$ and $A_{\infty}$, are optimized end-to-end by minimizing a composite loss over multi-view foggy images. The objective includes:
- **Reconstruction loss:** Combines $L_1$ distance and D-SSIM between observed and rendered foggy images.
$$
\mathcal{L}_{\mathrm{rec}} = (1-\lambda_{\ell_1})\,\|I_{\mathrm{obs}}-I_{\mathrm{fog}}\|_1 + \lambda_{\mathrm{ssim}}\,\mathrm{D\!-\!SSIM}(I_{\mathrm{obs}}, I_{\mathrm{fog}})
$$
- **Dark/Bright Channel Priors:** Impose regularization on the transmittance map $T(x)$ using classical 2D priors and Laplacian smoothing.
- **Depth Supervision:** Enforces consistency between learned depths and pseudo-depth maps.
The total loss is:
$$
\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{rec}} + \lambda_{D}\mathcal{L}_{\mathrm{DCP}} + \lambda_{B}\mathcal{L}_{\mathrm{BCP}} + \lambda_{d}\mathcal{L}_{d} + \lambda_{d_{\mathrm{rec}}}\,\mathcal{L}_{d_{\mathrm{rec}}}
$$

## 5. Inference and Dehazing Pipeline

After training, dehazing proceeds by neutralizing fog parameters: setting $t_i \rightarrow 1$ and omitting the airlight term. Each dehazed Gaussian is recovered by:
$$
G_{c,i}(x) = \frac{G_{f,i}(x) - A_{\infty}(1-t_i)}{t_i},\quad (t_i \approx 1)
$$
The latent scene is rendered as a standard 3DGS composite:
$$
I_{\mathrm{dehazed}}(x) = \sum_{i=1}^N c_i\;\alpha'_i(x)\;\prod_{j<i}(1-\alpha'_j(x))
$$
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 $\beta$ and $A_{\infty}$) 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 [2501.03659].

## 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 $\beta$, and light $A_{\infty}$** 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 [2501.03659].

Source: https://www.emergentmind.com/topics/dehazegs