Polarization-Based Underwater 3D Imaging

• The paper presents a two-stage method combining polarimetric descattering (using transformer-based DehazeFormer) with shape-from-polarization for accurate 3D reconstruction.
• Polarization-based imaging is defined by extracting DoLP and AoP to differentiate highly polarized object reflections from scattered background signals, enhancing surface normal estimation.
• The MuS-Polar3D dataset offers a comprehensive benchmark with 42 objects, controlled scattering levels, and precise ground truth, supporting rigorous evaluation of underwater imaging algorithms.

Polarization-based underwater 3D imaging is a computational imaging modality that leverages the polarization state of light to suppress background scattering and enable robust 3D shape recovery in turbid aquatic environments. By extracting polarization cues such as the degree of linear polarization (DoLP) and the angle of polarization (AoP), it exploits the statistical differences between the object signal and the multiply-scattered background, facilitating effective descattering and detailed surface normal estimation. Recent advances incorporate data-driven approaches and benchmark datasets that support rigorous evaluation across diverse scattering and viewing conditions (Wang et al., 25 Dec 2025).

1. Imaging Physics and Polarization Signal Formation

The underwater polarimetric signal formation model accounts for two dominant mechanisms: attenuation of the direct signal from the object and additive backscatter from suspended particles. Formally, the observed Stokes vector $S_{\mathrm{total}}(\theta_p)$ at analyzer angle %%%%1%%%% is:

$$S_{\mathrm{total}}(\theta_p) = T(\lambda, \tau) \cdot S_{\mathrm{obj}}(\theta_p) + B(\lambda, \tau) \cdot S_{\mathrm{scat}}(\theta_p)$$

where $T(\lambda, \tau) = e^{-c(\lambda)d}$ is the total transmission at wavelength $\lambda$ and turbidity $\tau$ over distance $d$, $c$ is the attenuation coefficient, and $B(\lambda, \tau)$ models integrated backscattering. The Stokes vectors $$S_{\mathrm{obj}} = [I_{\mathrm{obj}}, Q_{\mathrm{obj}}, U_{\mathrm{obj}}]^T$$ and $$S_{\mathrm{scat}} = [I_{\mathrm{scat}}, Q_{\mathrm{scat}}, U_{\mathrm{scat}}]^T$$ represent the object and scattered light, respectively.

The four canonical polarimetric images $I_{0^\circ}$, $I_{45^\circ}$, $I_{90^\circ}$, and $I_{135^\circ}$ yield the Stokes parameters:

• $S_0 = I_{0^\circ} + I_{90^\circ}$
• $S_1 = I_{0^\circ} - I_{90^\circ}$
• $S_2 = I_{45^\circ} - I_{135^\circ}$

Key polarization observables are computed as:

• Degree of Linear Polarization (DoLP): $\mathrm{DoLP} = \sqrt{S_1^2 + S_2^2} / S_0$
• Angle of Polarization (AoP): $\mathrm{AoP} = \frac{1}{2} \arctan(S_2/S_1)$

These polarization cues are instrumental in differentiating highly polarized object reflections from the partially polarized (random AoP, low DoLP) background scattering, directly supporting both descattering and reliable surface normal inference (Wang et al., 25 Dec 2025).

2. Computational Pipeline: Descattering and 3D Reconstruction

The dominant pipeline for polarization-based underwater 3D imaging is decomposed into two sequential stages: polarimetric descattering followed by 3D reconstruction:

• Stage 1 — Polarimetric Descattering: The objective is to estimate and subtract $B \cdot S_{\mathrm{scat}}(\theta_p)$, isolating $T \cdot S_{\mathrm{obj}}$. Data-driven baselines include transformer-based architectures such as DehazeFormer, which processes the four polarization channels simultaneously and predicts a clear-water polarization image. The total training loss comprises weighted $\ell_1$, SSIM, and total-variation regularizers:

$$L_{\mathrm{total}} = 10 L_1 + L_{\mathrm{SSIM}} + 10 L_{\mathrm{TV}}$$

with $L_1 = \|I_{\mathrm{pred}} - I_{\mathrm{gt}}\|_1$, $$L_{\mathrm{SSIM}} = 1 - \mathrm{SSIM}(I_{\mathrm{pred}}, I_{\mathrm{gt}})$$, and $L_{\mathrm{TV}}$ the total variation of the prediction, aiming to suppress artifacts.

• Stage 2 — 3D Reconstruction: Descattered (and optionally, raw) polarization images are input to shape-from-polarization (SfP) networks, which utilize DoLP and AoP to estimate the surface normal $\mathbf{n}=(n_x,n_y,n_z)$. The physical inversion involves mappings:

$$n_x = \cos\theta \cos\phi,\quad n_y = \cos\theta \sin\phi,\quad n_z = \sin\theta$$

with $\phi \approx$ AoP (ambiguous for mixed reflection types), and $\theta$ derived by inverting a diffuse polarization model.

Multi-view fusion is identified as a promising avenue, with reconstruction framed as minimization over reprojection error plus geometric regularization:

$$X^* = \arg\min_X \sum_i \|\mathrm{Proj}_i(X) - I_i\|^2 + \lambda \cdot \mathrm{Regularizer}(X)$$

This suggests future advances in integrating geometric constraints and polarization cues for more comprehensive 3D recovery (Wang et al., 25 Dec 2025).

3. MuS-Polar3D Benchmark Dataset

MuS-Polar3D provides a systematic framework for quantitative evaluation of polarization-based underwater 3D imaging algorithms. The dataset includes:

• 42 objects (ceramic and resin) comprising diffuse, specular, and mixed reflectance
• Seven controlled scattering (turbidity) levels, produced by calibrated emulsion volumes (0–60 ml, step 10 ml)
• Five distinct viewpoints: front, back, left, right, top
• Four polarization channels collected simultaneously at $0^\circ$, $45^\circ$, $90^\circ$, $135^\circ$

High-precision ground truth is supplied by 3D meshes (accuracy $\pm 0.05$ mm from structured-light scanning), per-view normal maps (via Mitsuba rendering), and foreground masks. The acquisition setup features a motorized turntable inside a water tank, a polarization camera external to the tank, constant indoor illumination, and repeatable scattering generation (Wang et al., 25 Dec 2025).

This dataset enables direct benchmarking for tasks such as normal estimation, object segmentation, descattering, and full 3D reconstruction under well-controlled, varied scattering and observation configurations.

Dataset Component	Description	Precision/Notes
Objects	42, ceramics & resin, varied BRDF	Diffuse/specular/mixed
Scattering Levels	7, 0–60 ml emulsion	Calibrated turbidity
Viewpoints	5	Orthogonal/top views
Polarization Channels	4 (simultaneous)	$0^\circ,\ 45^\circ,\ 90^\circ,\ 135^\circ$
Ground Truth Mesh	Structured-light scanner	$\pm 0.05$ mm

4. Algorithmic Baselines and Quantitative Evaluation

MuS-Polar3D establishes standardized quantitative evaluation protocols for both descattering and 3D reconstruction:

Descattering Baselines: Retinex, Dark Channel Prior, U-Net, AttentionU²Net, PUIE, and DehazeFormer. Evaluated using PSNR, SSIM, LPIPS, and NIQE metrics over 726 samples at turbidity $>$0.

• Best descattering performance: DehazeFormer (PSNR = 31.51 dB, SSIM = 0.9375, LPIPS = 0.3669, NIQE = 9.27).
• Qualitative inspection (feature-matching via ORB) verifies preservation of geometric detail at high turbidity (Wang et al., 25 Dec 2025).

3D Reconstruction Baselines: DenseDepth (adapted), DSINE, DeepSfP, SfPW, and AttentionU²Net. The loss is a cosine distance on predicted normals. Experiments consider two input configurations: with and without descattered inputs.

• Best mean angular error (MAE): 15.49$^\circ$, achieved by AttentionU²Net with DehazeFormer descattering (improved from 15.72$^\circ$ with non-descattered input).
• Error heatmaps demonstrate reduction of high-error zones around object edges and textures with descattering; stability of normal maps is observed across increasing scattering levels (Wang et al., 25 Dec 2025).

5. Significance, Challenges, and Future Directions

Polarization-based underwater 3D imaging, particularly with the advent of the MuS-Polar3D dataset, provides a unified benchmark for quantitative algorithm evaluation across both single-view SfP and prospective multi-view approaches (e.g., SDF, MVS, SfM) under controlled, systematically varied turbidity.

The two-stage paradigm—explicit scattering modeling (descattering) followed by 3D estimation—demonstrably increases robustness to multiple scattering and enhances accuracy in surface normal prediction. A plausible implication is the extensibility of this modular approach to settings with non-negligible random-walk scattering and mixed-reflection boundary conditions (Wang et al., 25 Dec 2025).

Outstanding challenges include:

• Disambiguating mixed diffuse/specular reflection cases where traditional specular-polarization inversions are unreliable.
• Retaining high-frequency surface detail under heavy multiple scattering where information loss is severe.
• Integrating multi-view geometric fusion (such as neural SDF pipelines) with polarization-based priors for dense, artifact-free 3D reconstruction.

Ongoing and future research directions include augmenting the dataset and methodologies to cover novel-view synthesis, automated material property estimation, end-to-end neural polarimetric SDF reconstruction, and applications to real-time underwater robotics.

6. Related Research Context and Broader Implications

The MuS-Polar3D dataset and associated computational frameworks promote fair comparison of polarization-imaging-based methods with traditional geometric (SfM, MVS) and learning-based 3D reconstruction paradigms in turbid aquatic regimes. The modularization of the imaging chain into decoupled descattering and shape recovery stages underlines the effectiveness of polarization cues as a foundation for robust downstream processing, suggesting a general principle for optical imaging in scattering-dominated media (Wang et al., 25 Dec 2025).

By making both the dataset and code publicly accessible, MuS-Polar3D supports reproducible experimentation and spurs development of novel algorithms in a realistic, challenging setting. This approach enables rigorous, consistent benchmarks and paves the way for research efforts targeting fully-integrated, real-world applicable underwater vision systems.