Underwater optical imaging is severely hindered by scattering, but polarization imaging offers the unique dual advantages of descattering and shape-from-polarization (SfP) 3D reconstruction. To exploit these advantages, this paper proposes UD-SfPNet, an underwater descattering shape-from-polarization network that leverages polarization cues for improved 3D surface normal prediction. The framework jointly models polarization-based image descattering and SfP normal estimation in a unified pipeline, avoiding error accumulation from sequential processing and enabling global optimization across both tasks. UD-SfPNet further incorporates a novel color embedding module to enhance geometric consistency by exploiting the relationship between color encodings and surface orientation. A detail enhancement convolution module is also included to better preserve high-frequency geometric details that are lost under scattering. Experiments on the MuS-Polar3D dataset show that the proposed method significantly improves reconstruction accuracy, achieving a mean surface normal angular error of 15.12∘ (the lowest among compared methods). These results confirm the efficacy of combining descattering with polarization-based shape inference, and highlight the practical significance and potential applications of UD-SfPNet for optical 3D imaging in challenging underwater environments. The code is available at https://github.com/WangPuyun/UD-SfPNet.
Figures & tables
Figure 2: Underwater polarization imaging model.
Figure 3: Schematic of the minimal element in the surface microfacet model.
Figure 4: Physical model of polarization-based 3D reconstruction: (a) global view; (b) camera view.
Figure 5: Relation between the degree of polarization ρ and the zenith angle θ for a given refractive index η : (a) specular reflection; (b) diffuse reflection.
Figure 6: Relation between the intensity I and the polarizer rotation angle φ .
Figure 7: Overview of the structured learning framework UD-SfPNet for underwater polarization-based 3D reconstruction.
Figure 8: Color encoding mechanism of baked normal maps.
Figure 9: Color embedding module adapted from DCC [ 31 ] : the pyramid color embedding (PCE) composed of multi-level color embedding modules (left), and the detailed implementation of the color embedding (CE) module (right).
Figure 10: Comparison of error heatmaps across different samples.
Figure 11: Schematic illustration of the DEConv module.
Figure 12: Descattering evaluation using the false match rate of ORB-based registration. Green circles indicate detected keypoints, and red lines indicate incorrect matches.
Metric
PSNR ↑
SSIM ↑
LPIPS ↓
Raw data
30.80
0.9569
0.3830
Descattering result
36.87
0.9745
0.0356
Table 1: Quantitative comparison before and after descattering. Masks are applied to both the ground truth and the evaluated samples to focus on the target region.
Metric
DeepSfP
SfP-wild
TransSfP
Attention U2-Net
DSINE
Proposed
MAE ↓
19.64 ∘
21.64 ∘
20.54 ∘
15.72 ∘
16.94 ∘
15.12 ∘
Table 2: Performance comparison of different baselines on the MuS-Polar3D test set. The metric is mean angular error (MAE, ∘ ); lower is better.
Figure 13: Comparison of different baseline methods on a representative sample (Dragon2). The red numbers in the upper-right corner of each subfigure denote the MAE (°), where lower values indicate better performance.
Figure 14: Comparison of different normal estimation methods on multiple samples under the same turbidity condition (10 ml emulsion). For each group, the results are presented in the order of predicted normal maps, enlarged local details, and angular error heatmaps. The red numbers indicate the MAE (°) of the corresponding method on each sample.
Figure 15: 3D shape integration results from predicted normal maps using a normal integration method. (a) Integrated shapes of different baselines under 10 ml emulsions. (b) Integrated shapes of the proposed method under different scattering conditions.
Model
w/o PPN
w/o DN
w/o PPN & DN
w/o CE
w/o DEConv
Proposed
Mean
16.72 ∘
15.37 ∘
15.56 ∘
15.46 ∘
23.03 ∘
15.12 ∘
Median
15.94 ∘
15.38 ∘
16.09 ∘
15.73 ∘
22.48 ∘
15.21 ∘
Table 3: Ablation results of key sub-networks/modules. The metrics are mean/median normal angular error ( ∘ ); lower is better.
Underwater 3D reconstruction recovers scene geometry and appearance from camera, sonar, and robot-sensor data despite refraction, scattering, and motion.
Department of Computer Science & Engineering and the Minnesota Robotics Institute (MnRI), University of Minnesota–Twin Cities, Minneapolis, MN 55455 USA