Structure-Aware Consistency Priors for Shape from Polarization in Complex Media

Huayang He; Kaimin Yu; Puyun Wang; Xianyu Wu

arxiv: 2606.00509 · v1 · pith:46WI5IFAnew · submitted 2026-05-30 · 💻 cs.CV

Structure-Aware Consistency Priors for Shape from Polarization in Complex Media

Kaimin Yu , Puyun Wang , Huayang He , Xianyu Wu This is my paper

Pith reviewed 2026-06-28 18:55 UTC · model grok-4.3

classification 💻 cs.CV

keywords shape from polarizationsurface normal estimationcomplex mediaicepolarization priorautocorrelationdual-branch network

0 comments

The pith

A structure-aware prior from autocorrelation of polarization angles allows a dual-branch network to recover surface normals in ice more accurately than prior methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Recovering surface normals from single-view polarization images is difficult in complex media like ice because light-matter interactions produce a nonlinear mapping from observations to geometry. The paper introduces a prior that uses autocorrelation functions of the angle of linear polarization to enforce local spatial consistency across the image. This prior is fed into a dual-branch network called IceSfP that combines raw polarization features with the consistency cues through cross-modal attention and multi-scale fusion. The authors also release the first real-world ice polarization dataset and report that their method beats existing approaches on every metric. A reader would care because the approach supplies a concrete way to obtain reliable 3D shape from polarization when the usual direct mapping breaks down.

Core claim

The structure-aware polarization prior based on autocorrelation functions of AoLP captures local spatial consistency of polarization angles and thereby mitigates the nonlinear mapping between polarization observations and surface normals in ice. When this prior is integrated with raw polarization features inside the IceSfP dual-branch network through cross-modal attention and multi-scale feature fusion, the network produces accurate surface normal estimates, as shown by its performance on the newly constructed real-world ice SfP dataset.

What carries the argument

The structure-aware polarization prior derived from autocorrelation functions of the angle of linear polarization (AoLP), which supplies spatial consistency cues that are fused into the IceSfP network via cross-modal attention.

If this is right

The method achieves a mean angular error of 16.01 degrees, 2.74 degrees lower than the second-best approach on ice data.
The first real-world ice SfP dataset enables quantitative evaluation of polarization-based shape recovery in complex media.
The dual-branch fusion strategy generalizes to other complex media where direct polarization-to-normal mapping is unreliable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The autocorrelation prior could be adapted to other scattering media such as water or fog by recomputing the same consistency measure on their polarization images.
Single-view normal maps from this pipeline could support real-time 3D reconstruction for robots operating on ice or in turbid environments.
Removing the prior from the network and measuring the resulting error increase on the released dataset would isolate how much the spatial consistency term contributes.

Load-bearing premise

Autocorrelation functions of AoLP angles can capture the local spatial consistency needed to compensate for the nonlinear polarization-to-normal mapping in ice without additional unstated modeling of light scattering.

What would settle it

An independent ground-truth measurement of surface normals on the same ice scenes (for example via laser scanning) that shows the network error rises above the reported 16.01 deg MAE when the autocorrelation prior is ablated.

Figures

Figures reproduced from arXiv: 2606.00509 by Huayang He, Kaimin Yu, Puyun Wang, Xianyu Wu.

**Figure 1.** Figure 1: Light behavior in ice and single-view surface normal estimation. Unpolarized incident light undergoes multiple internal scattering events within ice, leading to severe perturbations of polarization states and producing emergent light dominated by mixed surface and volumetric components. Original polarization image, structure-aware polarization consistency prior, and estimated surface normals are shown. n… view at source ↗

**Figure 2.** Figure 2: Schematic of light propagation in ice. Surface reflections and internal birefringence, internal reflections, and volume scattering collectively lead to multi-path emergent light. 2. Related Work 2.1. Ice Shape Recognition Existing research on 3D shape perception of ice objects has primarily focused on thin ice layers or geometrically simple scenarios. Due to the high transmissivity and volumetric scatteri… view at source ↗

**Figure 3.** Figure 3: Overall architecture of the proposed method. The network adopts a dual-branch design to process raw polarization images and physics-based priors separately. Features from the two branches are fused and forwarded to the decoder via skip connections to preserve multi-scale information. Additionally, the raw polarization images are fed into the SPADE module in the decoder for spatially-adaptive feature modula… view at source ↗

**Figure 4.** Figure 4: Schematic illustration of the structure-aware polarization consistency prior: (a) original image of the ice object, (b) corresponding AoLP map, and (c) consistency map; (d) original image of the ceramic object, (e) corresponding AoLP map, and (f) consistency map. tion response is normalized within each local window to reduce amplitude variations across different neighborhoods. To summarize directional co… view at source ↗

**Figure 5.** Figure 5: Overview of the IceSfP network. (a) Multi-branch design with a raw polarization branch and a physics prior branch guided by a structure-aware consistency prior. (b) CRA module applies cross-attention to weight physics priors and combines them with raw polarization features. (c) Multi-scale Fusion merges features at intermediate resolutions and delivers them to the decoder via skip connections. 4. Experimen… view at source ↗

**Figure 6.** Figure 6: Sensitivity analysis of the weighting parameter α in the consistency prior. 4.3. Comparisons Experiment [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: Qualitative comparison of different methods on five object models, with average MAE metrics for each model’s test set [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: Qualitative comparison of ablation variants on the Rabbit model, with the corresponding average MAE reported. erage MAE of 16.01◦ . Removing the structure-aware polarization consistency prior increases the MAE to 17.84◦ , indicating that this prior guides the network to distinguish between reliable and unstable polarization regions by modeling the structural stability of AoLP, and adaptively modulates t… view at source ↗

**Figure 9.** Figure 9: Experimental setup and data acquisition pipeline for the IceSfP dataset. (a) Illustration of the ice object models included in the IceSfP dataset. (b) Illustration of the acquisition of highprecision reference geometry of the target objects. (c) Setup for the polarization image capture under low-temperature conditions. This appendix describes the construction process and data acquisition setup of the IceS… view at source ↗

**Figure 10.** Figure 10: Structure of the network modules. (a) Encoder Module and (b) Decoder Module. construction in ice media, we construct the IceSfP dataset, which is the first real-world dataset specifically designed for ice surface SfP. The dataset contains a diverse set of ice object geometries and provides high-precision groundtruth (GT) surface normals together with synchronously captured polarization observations. The … view at source ↗

read the original abstract

Recovering surface normals from single view polarization images in complex media remains challenging. This paper focuses on ice as a representative complex medium, where intricate light matter interactions lead to a nonlinear mapping between polarization observations and surface normals. To address this, a structure-aware polarization prior based on autocorrelation functions is proposed to capture the local spatial consistency of AoLP. Building on this, a dual-branch network (IceSfP) is designed to integrate raw polarization features with priors via cross modal attention and multi-scale feature fusion, enabling accurate surface normal estimation under complex media conditions. To evaluate the method, the first real-world ice SfP dataset is constructed. Experimental results show that the method outperforms existing approaches across all metrics, achieving a MAE of 16.01 deg, which is 2.74 deg lower than the second-best method. The framework provides a generalizable solution for high-precision geometric perception in complex media.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds an autocorrelation-based prior on AoLP plus a dual-branch IceSfP network and the first real ice SfP dataset, but the abstract gives too little on baselines and validation to judge the 2.74 deg MAE gain.

read the letter

The main things to know are that the authors define a structure-aware prior using autocorrelation of the angle of linear polarization to capture local consistency, feed it into a dual-branch network with cross-modal attention and multi-scale fusion, and release a new real-world ice dataset. They claim this beats existing methods with a mean angular error of 16.01 degrees.

What is actually new is the choice of autocorrelation as the prior for this domain, the specific IceSfP architecture that mixes raw polarization features with the prior, and the dataset itself. Prior SfP work rarely targets ice or similar scattering media, so the application and the data release stand out.

The paper does a decent job identifying the nonlinear mapping problem in complex media and offering a concrete empirical fix. The idea that spatial consistency in AoLP can regularize normal estimation is reasonable on its face, and moving to real data rather than simulation is a step in the right direction.

The soft spots are the missing details. The abstract does not show how the autocorrelation is computed or why it fits ice specifically, does not name the baselines or report ablations, and gives no information on dataset capture, labeling, or split. Without those, the reported improvement is hard to interpret. The central assumption that the prior mitigates the nonlinear effects needs more support than the abstract supplies.

This is for computer vision researchers working on polarization or media-specific reconstruction. A reader in that narrow area could use the architecture or the data. It has enough new pieces and a clear empirical claim that it deserves a serious referee to check the methods and experiments.

I would send it to peer review and ask the authors for the prior derivation, full baseline list, and dataset protocol.

Referee Report

2 major / 0 minor

Summary. The paper claims to address surface normal recovery from single-view polarization images in complex media (ice as exemplar) by introducing a structure-aware prior based on autocorrelation functions of the angle of linear polarization (AoLP) to encode local spatial consistency. It proposes the IceSfP dual-branch network that fuses raw polarization features with these priors through cross-modal attention and multi-scale fusion. A new real-world ice SfP dataset is constructed, and experiments report that the method achieves MAE of 16.01 deg, outperforming prior approaches by 2.74 deg and providing a generalizable framework for high-precision geometric perception.

Significance. If the empirical gains and dataset are robustly validated, the work would supply a practical prior and network architecture for SfP under nonlinear light-matter interactions, potentially extending to other complex media. Construction of the first real-world ice dataset is a concrete contribution that could support future benchmarking.

major comments (2)

[Abstract] Abstract: the central claim of outperformance (MAE 16.01 deg, 2.74 deg better than second-best) is presented without any description of the baselines, dataset size/composition, train/test split, error analysis, or validation protocol, rendering it impossible to verify support for the claim.
[Abstract] Abstract: the structure-aware prior is asserted to capture local spatial consistency and mitigate the nonlinear mapping without additional modeling assumptions, but no derivation, explicit functional form of the autocorrelation, or ablation isolating its contribution is referenced, leaving the weakest assumption untested in the provided description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments. We address each major comment below, noting that the abstract is a high-level summary while the full manuscript contains the requested details. We propose targeted revisions to the abstract for improved clarity.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim of outperformance (MAE 16.01 deg, 2.74 deg better than second-best) is presented without any description of the baselines, dataset size/composition, train/test split, error analysis, or validation protocol, rendering it impossible to verify support for the claim.

Authors: We agree that the abstract, constrained by length, omits these specifics. The full manuscript describes the baselines, the composition of the new real-world ice SfP dataset, train/test splits, error analysis (including MAE), and validation protocol in Section 4. To improve verifiability at the abstract level, we will revise the abstract to briefly reference the real-world dataset and standard evaluation protocol used. revision: yes
Referee: [Abstract] Abstract: the structure-aware prior is asserted to capture local spatial consistency and mitigate the nonlinear mapping without additional modeling assumptions, but no derivation, explicit functional form of the autocorrelation, or ablation isolating its contribution is referenced, leaving the weakest assumption untested in the provided description.

Authors: The abstract provides a concise summary. The derivation of the structure-aware prior, including the explicit functional form of the autocorrelation of AoLP, appears in Section 3.1, with justification that it encodes local spatial consistency without further assumptions. Ablation studies isolating the prior's contribution are in Section 4. We will revise the abstract to include a reference to Section 3.1 for the prior details. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical network with new dataset and explicit prior

full rationale

The paper introduces an autocorrelation-based structure-aware prior on AoLP, integrates it into a dual-branch IceSfP network via cross-modal attention, constructs a new real-world ice SfP dataset, and reports empirical MAE improvements. No derivation, uniqueness theorem, fitted parameter renamed as prediction, or self-citation chain is described that would reduce any claimed result to its own inputs by construction. The approach is self-contained as standard supervised learning on held-out data with an independently motivated prior.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, axioms, or invented entities are identifiable. The network weights are standard learned parameters in deep learning and not counted as paper-specific free parameters. The autocorrelation prior is presented as derived from domain knowledge rather than fitted ad hoc.

pith-pipeline@v0.9.1-grok · 5690 in / 1242 out tokens · 30084 ms · 2026-06-28T18:55:59.701365+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 11 canonical work pages

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ISSN 10009361. doi: 10.1016/j.cja.2024.04.014. Zhu, J., Peng, L., Du, H., Liu, Z., Cai, Y ., Pan, C., Li, X., and Shao, X. High-quality polarization 3D reconstruc- tion of weakly textured objects by fusing multi-view im- ages. Optics Express , 33(18):38749, September 2025. ISSN 1094-4087. doi: 10.1364/OE.570825. Ziyu, L., Kang, G., Junfeng, G., and Lin, Y...

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de- ﬁnes a non-injective mapping between ρs and θs. Conse- quently, a single ρs may correspond to two valid zenith angle solutions, leading to two ambiguous surface normal estimates: Ns, 1 =   cos φ s sin θs, 1 sin φ s sin θs, 1 cos θs, 1   , Ns, 2 =   cos φ s sin θs, 2 sin φ s sin θs, 2 cos θs, 2   , φ s = ϕ + π 2 . (18) 12 Structure-Aware Consis...
[14]

+ (I v 45 − I v 135) (I r 0 − I r
[15]

(22) The volumetric scattering terms, (I v 45− I v

+ (I v 0 − I v 90) ) . (22) The volumetric scattering terms, (I v 45− I v
[16]

As a result, these perturbations introduce abrupt and disordered variations in Eq

and (I v 0 − I v 90), exhibit spatially irregular or rapidly varying behavior du e to complex internal light transport mechanisms, including subsurface scattering, birefringence, and multipath prop a- gation. As a result, these perturbations introduce abrupt and disordered variations in Eq
[17]

In contrast, the surface reﬂection terms, (I r 45 − I r

Moreover, the non- linear nature of the arctangent operation further ampli- ﬁes small ﬂuctuations in the differential polarization ter ms, thereby inducing sudden variations in the AoLP . In contrast, the surface reﬂection terms, (I r 45 − I r
[18]

Consequently, these terms vary smoothly across neighboring pixels, and the corresponding AoLP preserves strong geometric consistency in the spatial domain

and (I r 0 − I r 90), are primarily governed by the Fresnel reﬂection mechanism, whose polarization state is determined by the local surface geometry. Consequently, these terms vary smoothly across neighboring pixels, and the corresponding AoLP preserves strong geometric consistency in the spatial domain. Based on these physical characteristics, when the ...

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Chen, L.-C., Zhu, Y ., Papandreou, G., Schroff, F., and Adam, H

doi: 10.1364/OE.505074. Chen, L.-C., Zhu, Y ., Papandreou, G., Schroff, F., and Adam, H. Encoder-Decoder with Atrous Separable Con- volution for Semantic Image Segmentation. In Fer- rari, V ., Hebert, M., Sminchisescu, C., and Weiss, Y . (eds.), Computer Vision – ECCV 2018 , volume 11211, pp. 833–851. Springer International Publishing, Cham,

work page doi:10.1364/oe.505074 2018

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ISBN 978-3-030-01233-5 978-3-030-01234-2. doi: 10.1007/978-3-030-01234-2 49. Chen, Y ., Zhu, P ., Yin, Y ., Wu, M., Y u, K., Feng, L., and Chen, W . Objective assessment of IPM denoising qual- ity of ϕ -OTDR signal. Measurement, 214:112775, June

work page doi:10.1007/978-3-030-01234-2

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doi: 10.1016/j.measurement

ISSN 02632241. doi: 10.1016/j.measurement. 2023.112775. Chen, Y ., Wu, J., Lin, D., Y an, P ., Ji, Z., Zhao, J., and Cheng, J. Improving water/ice/snow depth accuracy on runway pavement with ultrasonic echo signal analysis. Cold Regions Science and T echnology, 235:104492, July

work page doi:10.1016/j.measurement 2023

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doi: 10.1016/j.coldregions.2025

ISSN 0165232X. doi: 10.1016/j.coldregions.2025. 104492. Feng, C., Wang, C., Zhang, L., Gong, W ., Liu, L., Peng, B., and Feng, C. Underwater 3D measurement using sheet of light system with multi-layer refractive inter- face. Measurement, 244:116514, February 2025. ISSN 02632241. doi: 10.1016/j.measurement.2024.116514. Gou, Y ., Li, Q., Y ao, R., Chen, J.,...

work page doi:10.1016/j.coldregions.2025 2025

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ISBN 978-3-031-72854-9 978-3-031-72855-6

Springer Nature Switzerland, Cham, 2025a. ISBN 978-3-031-72854-9 978-3-031-72855-6. doi: 10.1007/ 978-3-031-72855-6 4. Li, K., Liang, J., Wan, Z., and Liu, Y . SfP-underwater: Attention-based shape from polarization for underwater scattering environments. Optics & Laser T echnology , 192:113545, December 2025b. ISSN 00303992. doi: 10.1016/j.optlastec.2025...

work page doi:10.1016/j.optlastec.2025.113545 2025

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doi: 10.1146/ annurev-vision-102122-094213

ISSN 2374-4642, 2374-4650. doi: 10.1146/ annurev-vision-102122-094213. M¨ uller, F., B¨ ohm, A., Herrnring, H., V on Bock Und Po- lach, F., and Ehlers, S. Inﬂuence of the ice shape on ice-structure impact loads. Cold Regions Science and T echnology, 221:104175, May 2024. ISSN 0165232X. doi: 10.1016/j.coldregions.2024.104175. Peng, Y ., Liu, R., Zhang, Z.,...

work page doi:10.1016/j.coldregions.2024.104175 2024

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Shao, M., Xia, C., Y ang, Z., Huang, J., and Wang, X

doi: 10.1007/s11432-024-4212-2. Shao, M., Xia, C., Y ang, Z., Huang, J., and Wang, X. Transparent shape from a single view polarization im- age. In 2023 IEEE/CVF International Conference on Computer Vision (ICCV) , pp. 9243–9252, 2023. doi: 10.1109/ICCV51070.2023.00851. Shin, B. G., Park, J.-H., Kong, J., and Jung, S. J. Characterizing critical behavior a...

work page doi:10.1007/s11432-024-4212-2 2023

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Wang, B., Zhou, C., Meng, Y ., and Huang, J

doi: 10.1109/TP AMI.2025.3552408. Wang, B., Zhou, C., Meng, Y ., and Huang, J. Shape from polarization via a physical prior-based deep fusion network with ambiguous surface normals. Optics Ex- press, 33(14):29255, July 2025a. ISSN 1094-4087. doi: 10.1364/OE.562136. Wang, H., Wang, Z., Long, X., Lin, C., Hancke, G., and Lau, R. W . MAGE : Single Image to M...

work page doi:10.1109/tp 2025

[9] [9]

Probabilistic shaping for nonlinearity tolerance

ISSN 0733-8724, 1558-2213. doi: 10.1109/JLT. 2022.3186830. Wu, X., Chen, J., Li, P ., Wang, X., Wu, J., and Huang, F. Deep learning-based polarization 3D imaging method for underwater targets. Optics Express, 33(2):2068, Jan- uary 2025. ISSN 1094-4087. doi: 10.1364/OE.541298. Xu, G., Waitz, F., Wagner, S., Nehlert, F., Schnaiter, M., and J¨ arvinen, E. To...

work page doi:10.1109/jlt 2022

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Y ang, Y ., Long, X.-X., Dou, Z., Lin, C., Liu, Y ., Y an, Q., Ma, Y ., Wang, H., Wu, Z., and Yin, W

doi: 10.1029/2022JD037604. Y ang, Y ., Long, X.-X., Dou, Z., Lin, C., Liu, Y ., Y an, Q., Ma, Y ., Wang, H., Wu, Z., and Yin, W . Won- der3D++: Cross-Domain Diffusion for High-Fidelity 3D Generation From a Single Image. IEEE Transactions on Pattern Analysis and Machine Intelligence , 48(2):1674– 1688, February 2026. ISSN 0162-8828, 2160-9292, 1939-3539. d...

work page doi:10.1029/2022jd037604 2026

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ISBN 978-3-031-26312-5 978-3-031-26313-2

Springer Nature Switzerland, Cham, 2023. ISBN 978-3-031-26312-5 978-3-031-26313-2. doi: 10.1007/ 978-3-031-26313-2 33. Zhang, S., Y ang, Y ., Sun, Y ., Liu, N., Sun, F., and Fang, B. Artiﬁcial Skin Based on Visuo-Tactile Sensing for 3D Shape Reconstruction: Material, Method, and Eval- uation. Advanced Functional Materials , 35(1):2411686, January 2025. IS...

2023

[12] [12]

doi: 10.1016/j.cja.2024.04.014

ISSN 10009361. doi: 10.1016/j.cja.2024.04.014. Zhu, J., Peng, L., Du, H., Liu, Z., Cai, Y ., Pan, C., Li, X., and Shao, X. High-quality polarization 3D reconstruc- tion of weakly textured objects by fusing multi-view im- ages. Optics Express , 33(18):38749, September 2025. ISSN 1094-4087. doi: 10.1364/OE.570825. Ziyu, L., Kang, G., Junfeng, G., and Lin, Y...

work page doi:10.1016/j.cja.2024.04.014 2024

[13] [13]

de- ﬁnes a non-injective mapping between ρs and θs. Conse- quently, a single ρs may correspond to two valid zenith angle solutions, leading to two ambiguous surface normal estimates: Ns, 1 =   cos φ s sin θs, 1 sin φ s sin θs, 1 cos θs, 1   , Ns, 2 =   cos φ s sin θs, 2 sin φ s sin θs, 2 cos θs, 2   , φ s = ϕ + π 2 . (18) 12 Structure-Aware Consis...

[14] [14]

+ (I v 45 − I v 135) (I r 0 − I r

[15] [15]

(22) The volumetric scattering terms, (I v 45− I v

+ (I v 0 − I v 90) ) . (22) The volumetric scattering terms, (I v 45− I v

[16] [16]

As a result, these perturbations introduce abrupt and disordered variations in Eq

and (I v 0 − I v 90), exhibit spatially irregular or rapidly varying behavior du e to complex internal light transport mechanisms, including subsurface scattering, birefringence, and multipath prop a- gation. As a result, these perturbations introduce abrupt and disordered variations in Eq

[17] [17]

In contrast, the surface reﬂection terms, (I r 45 − I r

Moreover, the non- linear nature of the arctangent operation further ampli- ﬁes small ﬂuctuations in the differential polarization ter ms, thereby inducing sudden variations in the AoLP . In contrast, the surface reﬂection terms, (I r 45 − I r

[18] [18]

Consequently, these terms vary smoothly across neighboring pixels, and the corresponding AoLP preserves strong geometric consistency in the spatial domain

and (I r 0 − I r 90), are primarily governed by the Fresnel reﬂection mechanism, whose polarization state is determined by the local surface geometry. Consequently, these terms vary smoothly across neighboring pixels, and the corresponding AoLP preserves strong geometric consistency in the spatial domain. Based on these physical characteristics, when the ...