Tri-DehazeGS Overview

• Tri-DehazeGS is an advanced framework for reconstructing clean 3D scenes from hazy or foggy images, employing a Scene–Medium Decoupled Gaussian Splatting technique.
• It separates intrinsic scene radiance and participating media, improving reconstruction accuracy with a transmittance-aware optimization schedule. Tri-DehazeGS significantly outperforms existing methods on benchmarks such as RealX3D, Mip-NeRF 360 foggy, and Fog-NeRF, achieving the highest PSNR, SSIM, and LPIPS scores on hazy image reconstructions.
• During its two-stage optimization process, Tri-DehazeGS first uncovers medium representation and then refines the clean scene. This two-step method stabilizes medium estimation before reconciling cascaded gradients in clean reconstructions.
• follow_up_questions
• What is the impact of using spherical harmonics for medium radiance in Tri-DehazeGS?
• How significant is the improvement in PSNR and SSIM metrics when comparing Tri-DehazeGS to other baseline methods like 3D-UIR and BiLaLoRA-GS?
• What are the most critical features of the Dark Channel Prior (DCP) in the first-stage optimization of Tri-DehazeGS?
• How does the use of view-shared tri-plane fields improve the accuracy of medium transparency and scattering?
• Find recent papers about optimization algorithms for medium-representation and scene reconstruction in hazy images.

Tri-DehazeGS is a scene–medium decoupled Gaussian Splatting framework for reconstructing clean 3D scenes from multi-view hazy or foggy images. Introduced in “Tri-DehazeGS: Scene–Medium Decoupled Gaussian Splatting with Transmittance-Aware Optimization” (Jiang et al., 10 Sep 2026), it represents intrinsic scene radiance with explicit 3D Gaussian primitives and participating media with an independent, view-shared tri-plane field. Hazy observations are synthesized through a physical scattering model, while Medium-Decoupled Transmittance Gradient Compensation (MD-TGC) counteracts the suppression of clean-scene gradients in low-transmittance regions. The method extends the physical Gaussian-splatting direction represented by DehazeGS (Yu et al., 7 Jan 2025), but differs from it by explicitly separating the scene and medium representations and by introducing a transmittance-aware optimization schedule.

1. Problem formulation and methodological context

Haze degrades multi-view reconstruction through two coupled effects: attenuation of radiance traveling from scene surfaces to the camera and in-scattering of atmospheric radiance toward the camera. Consequently, a hazy pixel is not a direct observation of intrinsic scene radiance. Tri-DehazeGS describes the observation model as

$$\hat{\mathbf{I}}(\mathbf{p}) = \hat{\mathbf{J}}(\mathbf{p})\hat{T}(\mathbf{p}) + \hat{\mathbf{S}}(\mathbf{p}),$$

where $\hat{\mathbf{J}}$ is clean scene radiance, $\hat{T}$ is medium transmittance, and $\hat{\mathbf{S}}$ is accumulated in-scattered radiance.

The framework identifies two principal difficulties in prior scattering-aware Gaussian and neural rendering approaches. First, image-space degradation estimators associate haze with particular images rather than shared 3D locations, potentially producing view-inconsistent medium estimates. Second, methods that attach medium variables directly to Gaussian primitives couple intrinsic scene attributes—such as geometry, opacity, scale, and view-dependent radiance—with extinction and in-scattered illumination. Different combinations of scene radiance and medium parameters can therefore explain the same hazy observation.

Tri-DehazeGS also addresses an optimization problem that is distinct from representation entanglement. Differentiating the observation model with respect to clean radiance yields

$$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$

When transmittance is small, the gradient entering the clean Gaussian branch is attenuated. Distant structures and regions behind dense haze consequently receive weak updates even when their clean reconstructions are inaccurate. Because transmittance reflects both propagation distance and local medium density, the paper treats it as a more direct visibility signal than depth alone.

DehazeGS also models haze through an atmospheric scattering formulation, but attaches transmission to explicit Gaussian representations and jointly learns atmospheric light and a scattering coefficient (Yu et al., 7 Jan 2025). Tri-DehazeGS instead uses an independent 3D medium field and does not introduce a separate constant atmospheric-light term.

2. Scene–medium decoupled architecture

Tri-DehazeGS contains two principal branches:

1. Clean Gaussian scene branch: an explicit set of 3D Gaussian primitives renders intrinsic scene radiance $\hat{\mathbf{J}}$.
2. Independent medium branch: a view-shared tri-plane field predicts spatial extinction and direction-dependent medium radiance, from which transmittance $\hat{T}$ and in-scattered radiance $\hat{\mathbf{S}}$ are computed.

The branches interact only during hazy observation rendering. The clean novel view is rendered from the Gaussian branch alone, whereas the hazy prediction is obtained by composing clean radiance with medium attenuation and scattering.

Clean Gaussian representation

The scene is represented by

$$\mathcal{G} = \left\{ G_i= (\boldsymbol{\mu}_i,\boldsymbol{\Sigma}_i,\alpha_i,\mathbf{c}_i) \right\}_{i=1}^{M},$$

where $\boldsymbol{\mu}_i$ is the 3D mean, $\hat{\mathbf{J}}$0 is the covariance, $\hat{\mathbf{J}}$1 is opacity, and $\hat{\mathbf{J}}$2 is view-dependent radiance parameterized using the usual 3DGS appearance representation, such as spherical harmonics.

After projection and depth sorting, Gaussian splatting renders clean radiance for pixel $\hat{\mathbf{J}}$3 as

$\hat{\mathbf{J}}$4

with accumulated Gaussian visibility

$\hat{\mathbf{J}}$5

The corresponding depth is obtained using the same compositing weights with Gaussian depths. Unlike a haze-bound Gaussian representation, this branch is interpreted as the clean scene rather than the hazy observation.

Independent tri-plane medium field

For a 3D position $\hat{\mathbf{J}}$6, the medium field samples three feature planes:

$\hat{\mathbf{J}}$7

where

$\hat{\mathbf{J}}$8

Here, $\hat{\mathbf{J}}$9 is a learnable 2D feature plane and $\hat{T}$0 projects the 3D coordinate onto the corresponding plane. Because the field is view-shared, all cameras query the same medium coordinates for the same 3D region. Because it is independent of the Gaussian parameter set, the medium is discouraged from being encoded in Gaussian appearance or geometry.

The extinction head predicts a nonnegative coefficient:

$\hat{T}$1

where $\hat{T}$2 is a learnable global extinction scale. The direction-aware medium-radiance head is

$\hat{T}$3

The sigmoid constrains RGB values, while spherical harmonics provide view dependence for in-scattered illumination.

3. Physical haze rendering

For ray samples $\hat{T}$4, let $\hat{T}$5, $\hat{T}$6, and $\hat{T}$7 be the interval length associated with sample $\hat{T}$8. Total medium transmittance is

$\hat{T}$9

The transmittance before sample $\hat{\mathbf{S}}$0 is

$\hat{\mathbf{S}}$1

and the scattering opacity of interval $\hat{\mathbf{S}}$2 is

$\hat{\mathbf{S}}$3

The accumulated in-scattered radiance is

$\hat{\mathbf{S}}$4

The final hazy prediction is therefore

$\hat{\mathbf{S}}$5

This decomposition distinguishes three physical quantities: clean scene radiance, medium attenuation, and medium in-scattering. The medium radiance is predicted spatially and directionally; the supplied description does not introduce a separate constant atmospheric-light term.

The clean output used for dehazing and novel-view evaluation is $\hat{\mathbf{S}}$6 rendered from the Gaussian branch alone. Hazy reconstruction instead uses the composed prediction $\hat{\mathbf{S}}$7. This allows the same scene representation to support both clean-view restoration and reconstruction of the original hazy observations.

4. Medium-Decoupled Transmittance Gradient Compensation

MD-TGC modifies optimization rather than forward rendering. Since the clean-radiance gradient is multiplied by $\hat{\mathbf{S}}$8, low-transmittance regions receive disproportionately weak supervision. Tri-DehazeGS compensates this attenuation by rescaling the gradient entering the clean Gaussian branch:

$\hat{\mathbf{S}}$9

where $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$0 prevents division by a value close to zero.

MD-TGC modifies only the gradient of the clean Gaussian rendering branch. It does not change Gaussian forward rendering, medium forward rendering, the hazy image-composition equation, or predicted transmittance and scattering values. Thus, the forward physical model remains unchanged while the clean-scene optimization receives a more balanced signal.

The compensation is activated only after the medium field has stabilized and has been frozen. If the medium remained jointly trainable, it could alter transmittance to manipulate gradient magnitude rather than accurately explain haze. Freezing the medium makes $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$1 a fixed visibility signal during clean-scene refinement and prevents the compensation mechanism from influencing medium estimation.

Applying inverse-transmittance compensation throughout training improves perceptual quality in some cases but reduces PSNR and SSIM because the medium estimate is unstable during early optimization. This motivates the “medium-decoupled” schedule: medium estimation precedes gradient compensation.

5. Two-stage optimization and implementation

Stage I: joint scene–medium decomposition

During the first stage, Gaussian scene parameters and tri-plane medium parameters are optimized jointly to reproduce hazy training images. The reconstruction loss combines $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$2 error and SSIM:

$$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$3

A monocular pseudo-depth regularizer is included after per-view scale- and shift-invariant normalization:

$$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$4

where $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$5 is Gaussian-rendered depth, $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$6 is monocular pseudo-depth, $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$7 is Pearson correlation after normalization, and $$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$8 is an edge-aware smoothness regularizer.

A dark-channel-prior transmittance term is used only during this stage:

$$\frac{\partial \mathcal{L}} {\partial \hat{\mathbf{J}}(\mathbf{p})} = \hat{T}(\mathbf{p}) \frac{\partial \mathcal{L}} {\partial \hat{\mathbf{I}}(\mathbf{p})}.$$9

The first-stage objective is

$\hat{\mathbf{J}}$0

MD-TGC is disabled because the estimated transmittance is not yet sufficiently reliable for gradient compensation.

Stage II: medium freezing and clean-scene refinement

After the medium stabilizes, its parameters are frozen. The DCP term is removed, giving

$\hat{\mathbf{J}}$1

MD-TGC is then activated for the clean Gaussian branch. The forward model remains

$\hat{\mathbf{J}}$2

while the backward gradient entering $\hat{\mathbf{J}}$3 is compensated using frozen transmittance.

The reported implementation uses NVIDIA RTX 3080 GPUs, 15,000 optimization iterations per scene, three $\hat{\mathbf{J}}$4 tri-planes, eight feature channels per plane, two-layer MLP heads, spherical-harmonic order 1 for medium light, and 16 ray samples for the medium field. The medium branch is frozen after 3,000 iterations, after which MD-TGC is activated. The supplied description does not provide numerical values for all loss weights or for $\hat{\mathbf{J}}$5.

6. Evaluation, ablations, and limitations

Tri-DehazeGS is evaluated on RealX3D, four foggy scenes from Mip-NeRF 360—counter, kitchen, bicycle, and garden—and Fog-NeRF. RealX3D contains eight real-world multi-view captures with scattering degradation; hazy views are used for training and paired clean images for evaluation. Mip-NeRF 360 foggy scenes use haze synthesized with an atmospheric-scattering model. Fog-NeRF provides paired foggy and clean multi-view images with predefined splits.

Baselines include vanilla 3DGS; restoration-assisted Gaussian pipelines Diff-GS, IPC-GS, and BiLaLoRA-GS; and scattering-aware methods Fog-NeRF, $\hat{\mathbf{J}}$6-NeRF, SeaSplat, WaterSplatting, Plenodium, MarineSTD-GS, and 3D-UIR. The principal restoration protocol renders novel views from the recovered clean Gaussian point cloud and compares them with haze-free ground truth using PSNR, SSIM, and LPIPS. A reconstruction protocol composites the learned medium onto Gaussian rendering and compares the result with hazy input images for methods with explicit 3D medium or scene representations.

Dataset	PSNR	SSIM	LPIPS
RealX3D	17.338	0.703	0.392
Mip-NeRF 360 foggy	22.311	0.802	0.162
Fog-NeRF	17.576	0.679	0.315

According to the supplied results, Tri-DehazeGS is best on all three benchmarks. It improves over 3D-UIR on RealX3D by 3.35 dB PSNR and 0.056 SSIM, over BiLaLoRA-GS on Mip-NeRF 360 foggy scenes by 2.28 dB PSNR, and over MarineSTD-GS on Fog-NeRF by 0.93 dB PSNR.

Representation and field ablations

Medium representation	Decoupled?	PSNR	SSIM	LPIPS
Constant medium	No	13.692	0.658	0.429
Gaussian-bound	No	15.534	0.672	0.444
Tri-plane RGB	Yes	16.425	0.697	0.403
Tri-plane + SH light	Yes	17.338	0.703	0.392

The results support the claims that a constant medium cannot model spatially varying haze, Gaussian-bound medium variables remain inferior to explicit decoupling, and direction-aware medium illumination improves over a tri-plane that predicts only RGB. The ablation does not establish that the recovered scene–medium decomposition is mathematically unique.

Among independent view-shared fields, the reported results are 15.457 PSNR for a coordinate MLP, 14.975 for a Fourier MLP, 17.113 for a voxel feature field, and 17.338 for the tri-plane field. The paper interprets these results as evidence that the gain is not attributable merely to adding an arbitrary 3D field, but also to the compactness and expressiveness of the tri-plane parameterization.

MD-TGC and auxiliary-loss ablations

Strategy	PSNR	SSIM	LPIPS
No TGC	17.205	0.702	0.444
TGC throughout training	16.168	0.678	0.405
Proposed MD-TGC	17.338	0.703	0.392

The improvement in LPIPS increases as visibility decreases, using high visibility $\hat{\mathbf{J}}$7, medium visibility $\hat{\mathbf{J}}$8, and low visibility $\hat{\mathbf{J}}$9. This is consistent with the intended role of MD-TGC in restoring optimization strength where haze most strongly attenuates gradients.

Removing depth correlation produces PSNR 12.767, SSIM 0.644, and LPIPS 0.451; removing depth smoothness produces 17.023, 0.702, and 0.405; removing DCP produces 16.894, 0.702, and 0.397; and the full method produces 17.338, 0.703, and 0.392. These results identify monocular depth alignment as particularly important for stabilizing scene–medium decomposition, while smoothness and DCP function as auxiliary stabilizers. Depth priors alone are insufficient: the reported gains require both independent medium representation and MD-TGC.

The principal stated limitation is dependence on monocular pseudo-depth. Inaccurate or over-smoothed depth around thin structures, weakly textured regions, and ambiguous object boundaries can cause blurred boundaries and loss of fine detail. The decomposition is not guaranteed to be physically unique from hazy images alone. Inverse-transmittance scaling can also be numerically sensitive when $\hat{T}$0 is very small, although clamping is used. The medium field uses 16 ray samples and spherical-harmonic order 1, which may limit representation of highly complex scattering or rapidly varying illumination. The additional tri-plane and MLP computations introduce memory and evaluation costs beyond vanilla 3DGS, and training remains a two-stage process with 15,000 iterations per scene. Effects outside the extinction-and-in-scattering model, including severe non-Lambertian weather artifacts, dynamic particles, and view-inconsistent degradations, may not be captured.