Hydro-OpticNet: Underwater Image Restoration

• Hydro-OpticNet is a physics-guided restoration component that integrates VeilNet and AttenNet to model underwater image degradation through additive backscatter and depth-dependent attenuation.
• It employs unsupervised losses based on physical priors, using exponential models to accurately estimate and correct for radiometric distortions without paired data.
• Quantitative results show significant improvements in UCIQE, UIQM, and PSNR, demonstrating robust adaptation across varied aquatic conditions and water types.

Hydro-OpticNet is the final, physics-guided restoration component in the DIVER (Domain-Invariant Visual Enhancement and Restoration) pipeline for underwater image enhancement. It is specifically designed to compensate for underwater degradations caused by additive backscatter and multiplicative, depth-dependent attenuation, operating without paired training data via unsupervised, physically meaningful constraints. Hydro-OpticNet processes the achromatic, contrast-enhanced output of the Adaptive Optical Correction Module (AOCM), utilizing a monocular depth estimate to produce an estimated scene radiance that approximates true underwater color and structure, free from haze and wavelength-dependent color distortions (Makam et al., 30 Jan 2026).

1. Physical Motivation and Image Formation Model

Hydro-OpticNet is motivated by the necessity to explicitly model the two dominant physical processes in underwater image degradation: additive backscatter (formation of a haze veil from scattered light) and wavelength-dependent, depth-sensitive attenuation of scene radiance. Purely data-driven approaches tend to overfit to a specific degradation distribution and struggle to generalize across variable water types, turbidities, and illumination regimes. Hydro-OpticNet counters this by embedding parameterized exponential models within its architecture and constraining learning through unsupervised, physically derived losses.

The revised DIVER image formation model is expressed as

$U(x) = U_J(x)\,U_A(x) + U_B(x)$

where $U(x) \equiv U_H(x)$ is the post-AOCM image, $U_J(x)$ is the true scene radiance, $U_A(x) = f_A(z(x))$ represents depth-dependent attenuation, and $U_B(x) = f_B(z(x))$ models backscatter. This model generalizes the classical atmospheric dehazing formula, supporting spatially varying, nonlinear, and domain-adaptive degradation formulations essential for underwater domains.

2. Architectural Components: VeilNet and AttenNet

Hydro-OpticNet comprises two specialized submodules tailored to estimate and compensate for backscatter and attenuation:

VeilNet estimates the additive backscatter component $U_B(x)$ as a function of monocular depth $z(x)$:

$f_B(z) = B_1\,(1-e^{-b_1 z})+B_2\,e^{-b_2 z}$

The learned parameters $\{B_1, B_2, b_1, b_2\}$ capture backscatter characteristics across water types. The module outputs

$$\hat{U}_B(x) = \tanh\left[B_1 \mathcal{S}_C^+(-b_1 z(x)) + B_2 \mathcal{S}^+(-b_2 z(x))\right]$$

where $\mathcal{S}^+(u)=\ln(1+e^u)$ (softplus activation) and $\mathcal{S}_C^+(u)=1-\mathcal{S}^+(u)$. The direct transmission component is then

$\hat{U}_D(x) = U_H(x) - \hat{U}_B(x)$

AttenNet handles attenuation compensation via an implicitly learned inverse mapping. Instead of analytically inverting $f_A(z)=\sum_{p=1}^P A_p e^{-a_p z}$, it directly parameterizes

$$\alpha_A(z) = \mathcal{S}^+\left(\sum_{p=1}^P \alpha'_p\,\mathcal{S}^+(\alpha_p\,z)\right)$$

to compute the compensation factor for each pixel, producing the restored scene radiance:

$\hat{U}_J(x) = \hat{U}_D(x)\,\alpha_A(z(x))$

This sequential separation of physical processes enables flexible and joint domain-invariant restoration across a spectrum of aquatic environments.

3. Composite Loss Functions and Physics-Guided Training

Hydro-OpticNet utilizes a composite, unsupervised loss to jointly optimize VeilNet and AttenNet in line with physical priors:

• VeilNet: Adaptive Huber loss on the predicted backscatter $\hat{U}_B$:

$$\mathcal{L}_H(\hat{U}_B) = \begin{cases} \hat{U}_B^2, & |\hat{U}_B|\le \delta \ \eta\,\delta(|\hat{U}_B|-\delta/2), & |\hat{U}_B|>\delta \end{cases}$$

• AttenNet: Combined loss $$\mathcal{L}_A = \mathcal{L}_L + \mathcal{L}_C + \mathcal{L}_S$$ includes:
  • Luminance fidelity ($\mathcal{L}_L$): Channel-wise MSE to a mid-level reference.
  • Local color consistency ($\mathcal{L}_C$): Mean inter-channel deviation penalty.
  • Sobel edge preservation ($\mathcal{L}_S$): Structural consistency by $\ell_1$ difference of Sobel edge responses between the direct and restored images.

Overall optimization is driven by:

$$\mathcal{L}_{\mathrm{HON}} = \mathcal{L}_H + \lambda_A\,\mathcal{L}_A$$

with $\lambda_A = 1$ experimentally.

4. Data, Optimization, and Training Procedure

Hydro-OpticNet is trained employing unpaired underwater images from eight public datasets spanning varied water types and illumination (SeaThru, OceanDark, USOD10K, FISHTRAC, U45, UIEB, UFO-120, LSUI, EUVP), with no reliance on clean targets. Per-pixel depth values $z(x)$ are estimated via a pre-trained transformer-based DepthAnythingV2 model. Training utilizes Adam (learning rate $10^{-3}$), batch sizes 10 (Hydro-OpticNet), 8 (IlluminateNet), and 50/150 iterations for Hydro-OpticNet/IlluminateNet, respectively. Early stopping is governed by a patience of 20 epochs. Compute resources are NVIDIA RTX 4090 GPUs; average training times are ≈20 minutes for Hydro-OpticNet and inference is ≈0.01 seconds per image.

5. Quantitative and Qualitative Performance

Hydro-OpticNet yields significant improvement on both reference-based and reference-free evaluation benchmarks. In ablation studies on the SeaThru dataset, adding Hydro-OpticNet after AOCM leads to a UCIQE increase from 0.5783 to 0.8470 (+46%) and UIQM from 2.5879 to 2.8685 (+11%). On UFO-120, PSNR improves from 21.70 dB to 23.69 dB (+9%), and UCIQE from 0.7430 to 0.9620 (+30%).

On full unpaired benchmarks, DIVER’s Hydro-OpticNet achieves top UCIQE scores across SeaThru (1.654 vs. best prior at 1.503), OceanDark, USOD10K, FISHTRAC, and U45. In the low-light SeaThru evaluation, the pipeline reduces the geometric mean per-angle error (GPMAE) by 4.9–98% relative to existing classical and learning-based baselines, indicating high color recovery fidelity. Qualitative assessments reveal only Hydro-OpticNet successfully removes haze, restores natural red hues, and preserves fine structural details in shallow, deep, and highly turbid conditions, outperforming IBLA, DCP, UDCP, ULAP, WaterNet, UDNet, P2CNet, Phaseformer, and U-Shape Transformer.

Ablation Results for SeaThru and UFO-120

Configuration	UCIQE (SeaThru)	UIQM (SeaThru)	PSNR (UFO-120)	UCIQE (UFO-120)
After IlluminateNet + AOCM	0.5783	2.5879	—	—
+ Hydro-OpticNet	0.8470	2.8685	23.69	0.9620
SEF + AOCM (UFO-120)	—	—	21.70	0.7430

6. Domain Invariance, Adaptivity, and Robustness

Hydro-OpticNet’s explicit modeling of backscatter (via learned $(B_1, B_2, b_1, b_2)$) and wavelength-dependent attenuation (via learned $(\alpha'_p, \alpha_p)$) confers robust adaptation to diverse water types and spectral absorption profiles. The use of per-pixel depth enables accurate restoration across depth ranges, from near-field (high backscatter) to far-field (strong attenuation), without need for scene-specific retraining. Unsupervised, physics-driven learning ensures that restored images are radiometrically plausible even in absence of paired ground truth.

This approach ultimately closes the DIVER enhancement loop, transforming an overexposed, green-shifted, haze-dominated AOCM output into a radiometrically stabilized result with consistent color and contrast, irrespective of water body, depth, or external illumination.

7. Significance within Underwater Visual Enhancement

Hydro-OpticNet represents a principal advance in domain-invariant underwater image restoration by integrating physical modeling and unsupervised learning. Its separation of backscatter and attenuation correction, depth-aware adjustment, and composite physics-informed losses enable generalization over a variety of underwater scenarios. Empirically, it consistently outperforms prior state-of-the-art both in quantitative indices (UCIQE, PSNR, UIQM) and in visual and structural consistency for human and machine perception tasks. This methodological innovation establishes Hydro-OpticNet as a benchmark for robust, pipeline-integrated underwater image enhancement (Makam et al., 30 Jan 2026).