<figure><img src="image_21.png" /><figcaption>**Figure 18.** Illustration of the “Shape from Polarization” basis with the two types of reflection: specular and diffuse. The direction of polarization is indicated in green.</figcaption></figure>

<table><caption>**Table 2.** Evolution of Shape from Polarization in the literature.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Material Reflection</th><th rowspan="2">Lighting Invariance</th><th colspan="2">Ambiguity Solving</th><th>Unknown</th></tr><tr><th>Dielectric</th><th>Metallic Specular</th><th>Diffuse</th><th>Azimuth</th><th>Zenith</th><th>Refractive Index</th></tr></thead><tbody><tr><td>Rahmann 2001 [304]</td><td>✓</td><td>✓</td><td></td><td></td><td>quadric object, 2 views</td><td>-</td><td>✓</td></tr><tr><td>Miyazaki 2002 [308]</td><td>✓</td><td>✓</td><td></td><td></td><td>convex shape</td><td>visible and IR</td><td></td></tr><tr><td>Miyazaki 2004 [278]</td><td>✓</td><td>✓</td><td></td><td></td><td>convex shape</td><td>2 views</td><td></td></tr><tr><td>Atkinson 2006 [306]</td><td>✓</td><td></td><td>✓</td><td></td><td>convex shape</td><td>no ambiguity in diffuse mode</td><td></td></tr><tr><td>Morel 2006 [279]</td><td></td><td>✓</td><td></td><td></td><td>active lighting</td><td>smooth surfaces</td><td></td></tr><tr><td>Huynh 2010 [309]</td><td>✓</td><td></td><td>✓</td><td></td><td>spectral variation of the phase of polarization</td><td>convex surface</td><td>✓</td></tr><tr><td>Mahmoud 2012 [311]</td><td>✓</td><td></td><td>✓</td><td></td><td>shape from shading</td><td></td><td></td></tr><tr><td>Ngo 2015 [312]</td><td>✓</td><td></td><td>✓</td><td></td><td>shape from shading and controlled lighting</td><td></td><td>✓</td></tr><tr><td>Smith 2016 [313]</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>shape from shading</td><td></td><td></td></tr><tr><td>Smith 2018 [316]</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>shape from shading</td><td></td><td></td></tr><tr><td>Ba 2020 [317]</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>shape from shading and deep learning</td><td></td><td></td></tr><tr><td>Yang 2023 [318]</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>deep learning</td><td></td><td>✓</td></tr><tr><td>Cai 2023 [320]</td><td>✓</td><td></td><td>✓</td><td></td><td>Prior feature information of facial polarization images</td><td></td><td></td></tr></tbody></table>

### 4.4. Three-Dimensional Depth with Polarization Cues

Thanks to its ability to estimate the normals, polarization imaging is increasingly involved in 3D depth estimation. To improve the 3D reconstruction of objects, Kadambi et al. [321] combine polarization imaging with an aligned depth map obtained from a Kinect. Disambiguation is initiated by the depth map and the integration process starts with depth map estimation and is then improved by including the estimation of normals.

#### 4.4.1. Stereo-Vision Systems

Also, in some stereo-vision systems, polarization imaging can solve the reconstruction of specular or transparent surfaces: Berger et al. [288] used a pair of polarimetric cameras to estimate the depth of a scene including the presence of water areas. Instead of using the polarization parameters to simplify the matching process, Fukao et al. [322] integrated
all the measured parameters in a cost volume construction and the surface normals are then estimated. In a study carried out by Zhu and Smith [323], the pair comprises one RGB camera and one camera equipped with a linear polarizer (that could be replaced by a polarimetric camera). Even if restricted to controlled lighting, high-quality 3D reconstruction can be obtained combining polarization imaging and binocular stereo vision system thanks to the fusion scheme proposed by Tian et al. [324]. Cui et al. [325] proposed a multi-view acquisition system using polarization imaging that enables dense 3D reconstruction adapted for texture-less regions and non-Lambertian objects.

### 4.4.2. Pose Estimation and SLAM

Pose estimation and SLAM (Simultaneous Localization and Mapping) are also of major importance in the field of robotics particularly for navigation tasks and scene analysis. Yang et al. [170] were the first authors to propose a polarimetric dense monocular that can reconstruct 3D in real time and provide improved results compared to conventional techniques when some regions are specular or texture-less.

Cui et al. [326] developed a relative pose estimation algorithm from polarimetric images which reduced the point correspondence to two points but limited the analysis of diffuse reflection. High reflections and transparency objects are handled in Ref. [327]. They developed a network called PPP-net (Pose Polarimetric Prediction Network) that uses a two step framework. The fusion of polarization information and physical cues provides after learning the object mask, normal map and NOCS (Normalized Object Coordinate Space) required to a final regression network for monocular 6D object pose estimation [328]. Additionally, a learning-based algorithm that focuses on human pose and shape estimation was recently developed by Zou et al. [329].

## 4.5. Summary and Future Directions in Polarized Vision for Scene Understanding

Polarization imaging is becoming an indispensable modality for robotics both as a means of providing additional clues regarding the nature of objects and as a major contributor to 3D object recognition. Nevertheless, as presented in this section, polarization imaging could not be a standalone system providing all necessary information. Ambiguities remain regarding the azimuth and zenith angles, or the priors of the refractive index or shapes, are sometimes unavoidable in robotics. Methods based on deep learning seem to overcome most of these limitations. Huang et al. [330] used a combination of stereo-vision and a polarization system to recover normals and disparity through a deep learning-based algorithm. Assuming only diffuse reflection, ambiguities were solved, and in addition, the authors succeeded in overcoming the restriction of using orthographic cameras. Consequently, standard stereo-vision systems can be advantageously replaced by a pair of color-polarized cameras.

Improved perception of the real world through polarization extends applications to more advanced systems such as event cameras [331,332] or iTOF (indirect Time Of Flight) cameras [333]. One solution to the major challenges in scene understanding and 3D estimation could be to fuse polarization cues through various wavelengths additionally to 3D sensor to provide robust reconstruction in the presence of specular or translucent objects that can be found indoors or outdoors. Extending the fusion of polarization imaging and multispectral imaging for the detection task appears to be relevant for scene understanding.

## 5. Conclusions

The principles of polarization that we use today have been known since the 19th century, but due to the lack of experimental imaging systems able to operate in real time, few applications were reported until the late 1990s, whatever the field. Availability of digital cameras and liquid crystal modulators made it possible to implement systems and a variety of applications such as skylight navigation was considered. Commercial systems emerged in the early 2010s due to a major increase in the availability of high-definition low-noise commercial cameras able to sense linear polarization at 50–100 fps.
all the measured parameters in a cost volume construction and the surface normals are then estimated. In a study carried out by Zhu and Smith [323], the pair comprises one RGB camera and one camera equipped with a linear polarizer (that could be replaced by a polarimetric camera). Even if restricted to controlled lighting, high-quality 3D reconstruction can be obtained combining polarization imaging and binocular stereo vision system thanks to the fusion scheme proposed by Tian et al. [324]. Cui et al. [325] proposed a multi-view acquisition system using polarization imaging that enables dense 3D reconstruction adapted for texture-less regions and non-Lambertian objects.

### 4.4.2. Pose Estimation and SLAM

Pose estimation and SLAM (Simultaneous Localization and Mapping) are also of major importance in the field of robotics particularly for navigation tasks and scene analysis. Yang et al. [170] were the first authors to propose a polarimetric dense monocular that can reconstruct 3D in real time and provide improved results compared to conventional techniques when some regions are specular or texture-less.

Cui et al. [326] developed a relative pose estimation algorithm from polarimetric images which reduced the point correspondence to two points but limited the analysis of diffuse reflection. High reflections and transparency objects are handled in Ref. [327]. They developed a network called PPP-net (Pose Polarimetric Prediction Network) that uses a two step framework. The fusion of polarization information and physical cues provides after learning the object mask, normal map and NOCS (Normalized Object Coordinate Space) required to a final regression network for monocular 6D object pose estimation [328]. Additionally, a learning-based algorithm that focuses on human pose and shape estimation was recently developed by Zou et al. [329].

## 4.5. Summary and Future Directions in Polarized Vision for Scene Understanding

Polarization imaging is becoming an indispensable modality for robotics both as a means of providing additional clues regarding the nature of objects and as a major contributor to 3D object recognition. Nevertheless, as presented in this section, polarization imaging could not be a standalone system providing all necessary information. Ambiguities remain regarding the azimuth and zenith angles, or the priors of the refractive index or shapes, are sometimes unavoidable in robotics. Methods based on deep learning seem to overcome most of these limitations. Huang et al. [330] used a combination of stereo-vision and a polarization system to recover normals and disparity through a deep learning-based algorithm. Assuming only diffuse reflection, ambiguities were solved, and in addition, the authors succeeded in overcoming the restriction of using orthographic cameras. Consequently, standard stereo-vision systems can be advantageously replaced by a pair of color-polarized cameras.

Improved perception of the real world through polarization extends applications to more advanced systems such as event cameras [331,332] or iTOF (indirect Time Of Flight) cameras [333]. One solution to the major challenges in scene understanding and 3D estimation could be to fuse polarization cues through various wavelengths additionally to 3D sensor to provide robust reconstruction in the presence of specular or translucent objects that can be found indoors or outdoors. Extending the fusion of polarization imaging and multispectral imaging for the detection task appears to be relevant for scene understanding.

## 5. Conclusions

The principles of polarization that we use today have been known since the 19th century, but due to the lack of experimental imaging systems able to operate in real time, few applications were reported until the late 1990s, whatever the field. Availability of digital cameras and liquid crystal modulators made it possible to implement systems and a variety of applications such as skylight navigation was considered. Commercial systems emerged in the early 2010s due to a major increase in the availability of high-definition low-noise commercial cameras able to sense linear polarization at 50–100 fps.
The Division-of-Focal Plane (DoFP) camera for linear polarization image capture is one of these cameras and appears to be the best-suited solution to robotic applications. Like the color filter arrays, this technology seems to have reached significant maturity in terms of performance and repeatability of the measurement, such that its use could be generalized in the future. A variation of this technology also makes it possible to make a joint acquisition of color and polarization images. In our opinion, an effort toward standardization and the definition of dedicated preprocessing pipelines remains to be made, possibly with open-source software toolkits.

There are several advantages to using sky polarization for robotics navigation: this technology is undetectable, it has immunity to GNSS signal spoofing or jamming, the celestial heading detection estimate is driftless, and it could work at night by moonlight, making it exploitable in urban environments for civilian applications such as automated last-mile delivery service. An autonomous vehicle such as that proposed by the French company TwinswHeel (Figure 19) could use polarization for guidance as early as 2030.

<figure><img src="image_22.png" /><figcaption>**Figure 19.** Logistics droid ciTHy L from TwinswHeel (payload up to 300 kg). This delivery droid is currently equipped with an Integrated Navigation System (INS) based on a triple redundancy of locations: 1st 3D Lidar, 2nd Stereo Camera, and 3rd GNSS + IMU + 4 wheels with encoders. The optical path integrator + polarized geolocation will be the 4th redundancy of location to make the robot geolocation more robust in all weather conditions and complex environments. The ciTHy L picture is courtesy of Vincent and Benjamin Talon, Co-founders of TwinswHeel (https://www.twinswheel.fr/, accessed on 17 May 2024).</figcaption></figure>

The polarimetric systems described in this manuscript can estimate geolocation with a sufficient precision using only skylight, and these systems are so lightweight and inexpensive that they could be embedded into terrestrial, aerial, or underwater autonomous vehicles. Improvements of the technology will enable such vehicles to operate using, for instance, the detection of the multispectral polarization patterns. But UV usage, detection of surrounding light in panoramic view and operation in complex weather conditions remain challenges.

Moreover, current popular polarimetric sensors are megapixel cameras, which are too bulky and expensive for applications in automotive or service robotics. An alternative could take its inspiration from nature: some animals detect the celestial heading with a visual system corresponding to the equivalent of very low-definition sensors, which was corroborated by simulations with neural networks using low-definition images. Therefore, an artificial retina, consisting of one thousand pixels (instead of one million pixels for a
The Division-of-Focal Plane (DoFP) camera for linear polarization image capture is one of these cameras and appears to be the best-suited solution to robotic applications. Like the color filter arrays, this technology seems to have reached significant maturity in terms of performance and repeatability of the measurement, such that its use could be generalized in the future. A variation of this technology also makes it possible to make a joint acquisition of color and polarization images. In our opinion, an effort toward standardization and the definition of dedicated preprocessing pipelines remains to be made, possibly with open-source software toolkits.

There are several advantages to using sky polarization for robotics navigation: this technology is undetectable, it has immunity to GNSS signal spoofing or jamming, the celestial heading detection estimate is driftless, and it could work at night by moonlight, making it exploitable in urban environments for civilian applications such as automated last-mile delivery service. An autonomous vehicle such as that proposed by the French company TwinswHeel (Figure 19) could use polarization for guidance as early as 2030.

<figure><img src="image_22.png" /><figcaption>**Figure 19.** Logistics droid ciTHy L from TwinswHeel (payload up to 300 kg). This delivery droid is currently equipped with an Integrated Navigation System (INS) based on a triple redundancy of locations: 1st 3D Lidar, 2nd Stereo Camera, and 3rd GNSS + IMU + 4 wheels with encoders. The optical path integrator + polarized geolocation will be the 4th redundancy of location to make the robot geolocation more robust in all weather conditions and complex environments. The ciTHy L picture is courtesy of Vincent and Benjamin Talon, Co-founders of TwinswHeel (https://www.twinswheel.fr/, accessed on 17 May 2024).</figcaption></figure>

The polarimetric systems described in this manuscript can estimate geolocation with a sufficient precision using only skylight, and these systems are so lightweight and inexpensive that they could be embedded into terrestrial, aerial, or underwater autonomous vehicles. Improvements of the technology will enable such vehicles to operate using, for instance, the detection of the multispectral polarization patterns. But UV usage, detection of surrounding light in panoramic view and operation in complex weather conditions remain challenges.

Moreover, current popular polarimetric sensors are megapixel cameras, which are too bulky and expensive for applications in automotive or service robotics. An alternative could take its inspiration from nature: some animals detect the celestial heading with a visual system corresponding to the equivalent of very low-definition sensors, which was corroborated by simulations with neural networks using low-definition images. Therefore, an artificial retina, consisting of one thousand pixels (instead of one million pixels for a
classical camera) and a dedicated trained processing unit could be the first step toward a
low-cost polarimetric device aimed at autonomous navigation.

In this review, we also presented the benefits of polarimetric imaging for robots to help them better understand the world in which they will operate. The detection of transparent or potentially dangerous surfaces can be facilitated by analyzing the polarization of light reflected from surfaces. In an even more advanced way, we have seen how the 3D shape of objects can be estimated from the measurement of polarization parameters. Algorithms based on neural networks can now overcome the constraints associated with shape-from-polarization techniques, making it possible to generalize the reconstruction of objects outdoors under a variety of lighting conditions.

Autonomous robots working in urban environments, e.g., for last-mile delivery ser-
vices, will have to locate and position themselves with a spatial accuracy of better than 5 cm
and 0.2 degree by 2030. Concurrently, in public areas, they must meet the most stringent
safety requirements. Using and fusing the polarized sensors' outputs with an INS could be
a supplemental perceptive modality of localization techniques to reach the requested level
of performances in order to complement and reinforce conventional localization techniques
(3D LiDAR-based SLAM, GNSS, and visual-inertial odometry, see Figure 19).

**Author Contributions:** All authors wrote Section 1—"Introduction" and Section 5—"Conclusions". P.-J.L. and L.B. wrote Section 2—"Embedded polarization sensing". J.R.S., S.V., T.K.-M. and A.M. wrote Section 3—"Polarized vision for robotics navigation". O.M. wrote Section 4—"Polarized vision for scene understanding". All authors wrote the first draft of the paper, prepared, and then revised the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** J.R.S. has received funding from the Excellence Initiative of Aix-Marseille Université - A*Midex, a French "Investissements d'Avenir" programme **AMX-21-ERC-02** and **AMX-20-TRA-043** helping him to succeed in this project. This research work was also supported by the SUD Provence-Alpes-Côte d'Azur Region (PACA) (Grant #2021/08135). A.M. was supported by a CIFRE doctoral fellowship from the ANRT and Safran Electronics and Defense (agreement #2021/0056). T.K.M. was supported by an inter-doctoral school fellowship from Aix Marseille University. This work was also supported by the ANR JCJC SPIASI project, grant **ANR-18-CE10-0005** of the French Agence Nationale de la Recherche.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Léo Poughon from both the STELLANTIS group and the Institute of Movement Sciences and Étienne-Jules Marey (CNRS/Aix Marseille University, ISM UMR7287), for their fruitful discussions concerning inputs of the PILONE PbC device. We also thank Laura Eshelman from Polaris Sensor Technologies Inc. (Huntsville, AL, USA) for providing us with a picture of SkyPASS. The authors would like to thank David Wood for revising the English of the manuscript. We also thank the three anonymous referees for their valuable comments.

**Conflicts of Interest:** The authors declare no conflicts of interest.

**Abbreviations**

The following abbreviations are used in this manuscript:

AoLP Angle of Linear Polarization (sometimes referred to as *Angle of Polarization*)

APMR Accuracy of Polarization Measurement Redundancy

BM3D Block-Matching and 3D filtering

DoA Division-of-Aperture

DoFP Division-of-Focal Plane

DoLP Degree of Linear Polarization

DoP Degree of Polarization

DoT Division-Of-Time

DRA Dorsal Rim Area
classical camera) and a dedicated trained processing unit could be the first step toward a
low-cost polarimetric device aimed at autonomous navigation.

In this review, we also presented the benefits of polarimetric imaging for robots to help them better understand the world in which they will operate. The detection of transparent or potentially dangerous surfaces can be facilitated by analyzing the polarization of light reflected from surfaces. In an even more advanced way, we have seen how the 3D shape of objects can be estimated from the measurement of polarization parameters. Algorithms based on neural networks can now overcome the constraints associated with shape-from-polarization techniques, making it possible to generalize the reconstruction of objects outdoors under a variety of lighting conditions.

Autonomous robots working in urban environments, e.g., for last-mile delivery ser-
vices, will have to locate and position themselves with a spatial accuracy of better than 5 cm
and 0.2 degree by 2030. Concurrently, in public areas, they must meet the most stringent
safety requirements. Using and fusing the polarized sensors' outputs with an INS could be
a supplemental perceptive modality of localization techniques to reach the requested level
of performances in order to complement and reinforce conventional localization techniques
(3D LiDAR-based SLAM, GNSS, and visual-inertial odometry, see Figure 19).

**Author Contributions:** All authors wrote Section 1—"Introduction" and Section 5—"Conclusions". P.-J.L. and L.B. wrote Section 2—"Embedded polarization sensing". J.R.S., S.V., T.K.-M. and A.M. wrote Section 3—"Polarized vision for robotics navigation". O.M. wrote Section 4—"Polarized vision for scene understanding". All authors wrote the first draft of the paper, prepared, and then revised the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** J.R.S. has received funding from the Excellence Initiative of Aix-Marseille Université - A*Midex, a French "Investissements d'Avenir" programme **AMX-21-ERC-02** and **AMX-20-TRA-043** helping him to succeed in this project. This research work was also supported by the SUD Provence-Alpes-Côte d'Azur Region (PACA) (Grant #2021/08135). A.M. was supported by a CIFRE doctoral fellowship from the ANRT and Safran Electronics and Defense (agreement #2021/0056). T.K.M. was supported by an inter-doctoral school fellowship from Aix Marseille University. This work was also supported by the ANR JCJC SPIASI project, grant **ANR-18-CE10-0005** of the French Agence Nationale de la Recherche.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Léo Poughon from both the STELLANTIS group and the Institute of Movement Sciences and Étienne-Jules Marey (CNRS/Aix Marseille University, ISM UMR7287), for their fruitful discussions concerning inputs of the PILONE PbC device. We also thank Laura Eshelman from Polaris Sensor Technologies Inc. (Huntsville, AL, USA) for providing us with a picture of SkyPASS. The authors would like to thank David Wood for revising the English of the manuscript. We also thank the three anonymous referees for their valuable comments.

**Conflicts of Interest:** The authors declare no conflicts of interest.

**Abbreviations**

The following abbreviations are used in this manuscript:

AoLP Angle of Linear Polarization (sometimes referred to as *Angle of Polarization*)

APMR Accuracy of Polarization Measurement Redundancy

BM3D Block-Matching and 3D filtering

DoA Division-of-Aperture

DoFP Division-of-Focal Plane

DoLP Degree of Linear Polarization

DoP Degree of Polarization

DoT Division-Of-Time

DRA Dorsal Rim Area
<table><tr><td>ENU</td><td>East North Up</td></tr><tr><td>fps</td><td>frames per second</td></tr><tr><td>GNSS</td><td>Global Navigation Satellite System</td></tr><tr><td>GPS</td><td>Global Positioning System</td></tr><tr><td>IFoV</td><td>Instantaneous Field of View</td></tr><tr><td>INS</td><td>Inertial Navigation System</td></tr><tr><td>ISO</td><td>International Organization for Standardization</td></tr><tr><td>NCP</td><td>North Celestial Pole</td></tr><tr><td>PbC</td><td>Polarization-based Compass</td></tr><tr><td>PFA</td><td>Polarimetric Filter Array</td></tr><tr><td>PG</td><td>Polarization Gratings</td></tr><tr><td>PSA</td><td>Polarization State Analyzer</td></tr><tr><td>RGB</td><td>Red Green Blue</td></tr><tr><td>RMSE</td><td>Root Mean Squared Error</td></tr><tr><td>SLAM</td><td>Simultaneous Localization And Mapping</td></tr><tr><td>SNR</td><td>Signal-to-Noise Ratio</td></tr><tr><td>UAV</td><td>Unmanned Aerial Vehicle</td></tr><tr><td>UV</td><td>Ultra Violet</td></tr></table>

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<table><tr><td>ENU</td><td>East North Up</td></tr><tr><td>fps</td><td>frames per second</td></tr><tr><td>GNSS</td><td>Global Navigation Satellite System</td></tr><tr><td>GPS</td><td>Global Positioning System</td></tr><tr><td>IFoV</td><td>Instantaneous Field of View</td></tr><tr><td>INS</td><td>Inertial Navigation System</td></tr><tr><td>ISO</td><td>International Organization for Standardization</td></tr><tr><td>NCP</td><td>North Celestial Pole</td></tr><tr><td>PbC</td><td>Polarization-based Compass</td></tr><tr><td>PFA</td><td>Polarimetric Filter Array</td></tr><tr><td>PG</td><td>Polarization Gratings</td></tr><tr><td>PSA</td><td>Polarization State Analyzer</td></tr><tr><td>RGB</td><td>Red Green Blue</td></tr><tr><td>RMSE</td><td>Root Mean Squared Error</td></tr><tr><td>SLAM</td><td>Simultaneous Localization And Mapping</td></tr><tr><td>SNR</td><td>Signal-to-Noise Ratio</td></tr><tr><td>UAV</td><td>Unmanned Aerial Vehicle</td></tr><tr><td>UV</td><td>Ultra Violet</td></tr></table>

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261. Lerner, A.; Sabbah, S.; Erlick, C.; Shashar, N. Navigation by light polarization in clear and turbid waters. *Philos. Trans. R. Soc. B Biol. Sci.* **2011**, *366*, 671–679. https://doi.org/10.1098/rstb.2010.0189.

262. Horváth, G.; Varjú, D. Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell's window of the flat water surface. *Vis. Res.* **1995**, *35*, 1651–1666. https://doi.org/10.1016/0042-6989(94)00254-J.

263. Cronin, T.W.; Marshall, J. Patterns and properties of polarized light in air and water. *Philos. Trans. R. Soc. B Biol. Sci.* **2011**, *366*, 619–626. https://doi.org/10.1098/rstb.2010.0201.

264. Zhou, G.; Wang, J.; Xu, W.; Zhang, K.; Ma, Z. Polarization patterns of transmitted celestial light under wavy water surfaces. *Remote Sens.* **2017**, *9*, 324. https://doi.org/10.3390/rs9040324.

265. Bai, X.; Liang, Z.; Zhu, Z.; Schwing, A.; Forsyth, D.; Gruev, V. Polarization-based underwater geolocalization with deep learning. *eLight* **2023**, *3*, 15. https://doi.org/10.1186/s43593-023-00050-6.

266. Cheng, H.; Chen, Q.; Zeng, X.; Yuan, H.; Zhang, L. The polarized light field enables underwater unmanned vehicle bionic autonomous navigation and automatic control. *J. Mar. Sci. Eng.* **2023**, *11*, 1603. https://doi.org/10.3390/jmse11081603.

267. Zhang, T.; Yang, J.; Zhao, Q.; Liu, X.; Hu, P.; Yu, X.; Guo, L. Bio-Inspired Antagonistic Differential Polarization Algorithm for Heading Determination in Underwater Low-Light Environments. *IEEE Trans. Ind. Inform.* **2024**, *20*, 6542–6551 https://doi.org/10.1109/TII.2023.3345455.

268. Moutenet, A.; Serres, J.R.; Viollet, S. Ultraviolet vs. Visible Skylight Polarization Measurements. In Proceedings of the 2023 IEEE SENSORS, Vienna, Austria, 29 October–1 November 2023; IEEE: Vienna, Austria, 2023; pp. 1–4. https://doi.org/10.1109/SENSORS56945.2023.10325144.

269. Labhart, T. The electrophysiology of photoreceptors in different eye regions of the desert ant, Cataglyphis bicolor. *J. Comp. Physiol. A* **1986**, *158*, 1–7. https://doi.org/10.1007/BF00614514.

270. Liang, H.; Bai, H.; Hu, K.; Lv, X. Bioinspired Polarized Skylight Orientation Determination Artificial Neural Network. *J. Bionic Eng.* **2023**, *20*, 1141–1152. https://doi.org/10.1007/s42235-022-00310-0.

271. Poughon, L.; Aubry, V.; Monnoyer, J.; Viollet, S.; Serres, J.R. A 2 month-long annotated skylight polarization images database. Recherche Data Gouv, V1, 2024. https://doi.org/10.57745/9L2YUB.

272. Freas, C.A.; Narendra, A.; Murray, T.; Cheng, K. Moonlight Polarisation Pattern Guides Nocturnal Bull Ants Home. *bioRxiv* **2023**, bioRxiv:2023-12.28.573574.

273. Zhang, Y.; Guo, L.; Yu, W.; Chen, T.; Fang, S. Heading determination of bionic polarization sensor based on night composite light field. *IEEE Sens. J.* **2023**, *24*, 909–919. https://doi.org/10.1109/JSEN.2023.3333968.

274. Chen, T.; Zhang, X.; Chi, X.; Hu, P.; Yu, X.; Wu, H.N.; Guo, L. An Autonomous Positioning Method Utilizing Feature Extraction from Polarized Moonlight. *IEEE Sens. J.* **2023**, Early Access. https://doi.org/10.1109/JSEN.2023.3344728.

275. Wehner, R. Polarization vision—A uniform sensory capacity? *J. Exp. Biol.* **2001**, *204*, 2589–2596. https://doi.org/10.1242/jeb.204.14.2589.

276. Schwind, R. Spectral regions in which aquatic insects see reflected polarized light. *J. Comp. Physiol. A* **1995**, *177*, 439–448. https://doi.org/10.1007/BF00187480.

277. Wolff, L.B.; Boult, T.E. Polarization/radiometric based material classification. In Proceedings of the 1989 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA, 4–8 June 1989; pp. 387–388. https://doi.ieeecomputersociety.org/10.1109/CVPR.1989.37876.

278. Miyazaki, D.; Kagesawa, M.; Ikeuchi, K. Transparent Surface Modeling from a Pair of Polarization Images. *IEEE Trans. Pattern Anal. Mach. Intell.* **2004**, *26*, 73–82. https://doi.org/10.1109/TPAMI.2004.1261080.

279. Morel, O.; Stolz, C.; Meriaudeau, F.; Gorria, P. Active lighting applied to 3D reconstruction of specular metallic surfaces by polarization imaging. *Appl. Opt.* **2006**, *45*, 4062–4068. https://doi.org/10.1364/AO.45.004062.

280. Wolff, L.B. Polarization-based material classification from specular reflection. *IEEE Trans. Pattern Anal. Mach. Intell.* **1990**, *12*, 1059–1071. https://doi.org/10.1109/34.61705.

281. Schechner, Y.; Shamir, J.; Kiryati, N. Polarization-based Decorrelation of Transparent Layers: The Inclination Angle of an Invisible Surface. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), Los Alamitos, CA, USA, 1999; pp. 814–819. https://doi.org/10.1109/ICCV.1999.790305.

282. Kalra, A.; Taamazyan, V.; Rao, S.K.; Venkataraman, K.; Raskar, R.; Kadambi, A. Deep Polarization Cues for Transparent Object Segmentation. In Proceedings of the 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 13–19 June 2020; pp. 8599–8608. https://doi.org/10.1109/cvpr42600.2020.00863.

283. Yu, R.; Ren, W.; Zhao, M.; Wang, J.; Wu, D.; Xie, Y. Transparent objects segmentation based on polarization imaging and deep learning. *Opt. Commun.* **2024**, *555*, 130246. https://doi.org/10.1016/j.optcom.2023.130246.
257. Waterman, T.H. Polarization patterns in submarine illumination. *Science* **1954**, *120*, 927-932. https://doi.org/10.1126/science.120.3127.927.

258. Waterman, T.H. Reviving a neglected celestial underwater polarization compass for aquatic animals. *Biol. Rev.* **2006**, *81*, 111–115. https://doi.org/10.1017/S1464793105006883.

259. HU, P.; YANG, J.; GUO, L.; YU, X.; LI, W. Solar-tracking methodology based on refraction-polarization in Snell's window for underwater navigation. *Chin. J. Aeronaut.* **2022**, *35*, 380–389. https://doi.org/10.1016/j.cja.2021.02.011.

260. Cheng, H.; Zhang, Q.; Wan, Z.; Zhang, Z.; Qin, J. Study on the polarization pattern induced by wavy water surfaces. *Remote Sens.* **2023**, *15*, 4565. https://doi.org/10.3390/rs15184565.

261. Lerner, A.; Sabbah, S.; Erlick, C.; Shashar, N. Navigation by light polarization in clear and turbid waters. *Philos. Trans. R. Soc. B Biol. Sci.* **2011**, *366*, 671–679. https://doi.org/10.1098/rstb.2010.0189.

262. Horváth, G.; Varjú, D. Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell's window of the flat water surface. *Vis. Res.* **1995**, *35*, 1651–1666. https://doi.org/10.1016/0042-6989(94)00254-J.

263. Cronin, T.W.; Marshall, J. Patterns and properties of polarized light in air and water. *Philos. Trans. R. Soc. B Biol. Sci.* **2011**, *366*, 619–626. https://doi.org/10.1098/rstb.2010.0201.

264. Zhou, G.; Wang, J.; Xu, W.; Zhang, K.; Ma, Z. Polarization patterns of transmitted celestial light under wavy water surfaces. *Remote Sens.* **2017**, *9*, 324. https://doi.org/10.3390/rs9040324.

265. Bai, X.; Liang, Z.; Zhu, Z.; Schwing, A.; Forsyth, D.; Gruev, V. Polarization-based underwater geolocalization with deep learning. *eLight* **2023**, *3*, 15. https://doi.org/10.1186/s43593-023-00050-6.

266. Cheng, H.; Chen, Q.; Zeng, X.; Yuan, H.; Zhang, L. The polarized light field enables underwater unmanned vehicle bionic autonomous navigation and automatic control. *J. Mar. Sci. Eng.* **2023**, *11*, 1603. https://doi.org/10.3390/jmse11081603.

267. Zhang, T.; Yang, J.; Zhao, Q.; Liu, X.; Hu, P.; Yu, X.; Guo, L. Bio-Inspired Antagonistic Differential Polarization Algorithm for Heading Determination in Underwater Low-Light Environments. *IEEE Trans. Ind. Inform.* **2024**, *20*, 6542–6551 https://doi.org/10.1109/TII.2023.3345455.

268. Moutenet, A.; Serres, J.R.; Viollet, S. Ultraviolet vs. Visible Skylight Polarization Measurements. In Proceedings of the 2023 IEEE SENSORS, Vienna, Austria, 29 October–1 November 2023; IEEE: Vienna, Austria, 2023; pp. 1–4. https://doi.org/10.1109/SENSORS56945.2023.10325144.

269. Labhart, T. The electrophysiology of photoreceptors in different eye regions of the desert ant, Cataglyphis bicolor. *J. Comp. Physiol. A* **1986**, *158*, 1–7. https://doi.org/10.1007/BF00614514.

270. Liang, H.; Bai, H.; Hu, K.; Lv, X. Bioinspired Polarized Skylight Orientation Determination Artificial Neural Network. *J. Bionic Eng.* **2023**, *20*, 1141–1152. https://doi.org/10.1007/s42235-022-00310-0.

271. Poughon, L.; Aubry, V.; Monnoyer, J.; Viollet, S.; Serres, J.R. A 2 month-long annotated skylight polarization images database. Recherche Data Gouv, V1, 2024. https://doi.org/10.57745/9L2YUB.

272. Freas, C.A.; Narendra, A.; Murray, T.; Cheng, K. Moonlight Polarisation Pattern Guides Nocturnal Bull Ants Home. *bioRxiv* **2023**, bioRxiv:2023-12.28.573574.

273. Zhang, Y.; Guo, L.; Yu, W.; Chen, T.; Fang, S. Heading determination of bionic polarization sensor based on night composite light field. *IEEE Sens. J.* **2023**, *24*, 909–919. https://doi.org/10.1109/JSEN.2023.3333968.

274. Chen, T.; Zhang, X.; Chi, X.; Hu, P.; Yu, X.; Wu, H.N.; Guo, L. An Autonomous Positioning Method Utilizing Feature Extraction from Polarized Moonlight. *IEEE Sens. J.* **2023**, Early Access. https://doi.org/10.1109/JSEN.2023.3344728.

275. Wehner, R. Polarization vision—A uniform sensory capacity? *J. Exp. Biol.* **2001**, *204*, 2589–2596. https://doi.org/10.1242/jeb.204.14.2589.

276. Schwind, R. Spectral regions in which aquatic insects see reflected polarized light. *J. Comp. Physiol. A* **1995**, *177*, 439–448. https://doi.org/10.1007/BF00187480.

277. Wolff, L.B.; Boult, T.E. Polarization/radiometric based material classification. In Proceedings of the 1989 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA, 4–8 June 1989; pp. 387–388. https://doi.ieeecomputersociety.org/10.1109/CVPR.1989.37876.

278. Miyazaki, D.; Kagesawa, M.; Ikeuchi, K. Transparent Surface Modeling from a Pair of Polarization Images. *IEEE Trans. Pattern Anal. Mach. Intell.* **2004**, *26*, 73–82. https://doi.org/10.1109/TPAMI.2004.1261080.

279. Morel, O.; Stolz, C.; Meriaudeau, F.; Gorria, P. Active lighting applied to 3D reconstruction of specular metallic surfaces by polarization imaging. *Appl. Opt.* **2006**, *45*, 4062–4068. https://doi.org/10.1364/AO.45.004062.

280. Wolff, L.B. Polarization-based material classification from specular reflection. *IEEE Trans. Pattern Anal. Mach. Intell.* **1990**, *12*, 1059–1071. https://doi.org/10.1109/34.61705.

281. Schechner, Y.; Shamir, J.; Kiryati, N. Polarization-based Decorrelation of Transparent Layers: The Inclination Angle of an Invisible Surface. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), Los Alamitos, CA, USA, 1999; pp. 814–819. https://doi.org/10.1109/ICCV.1999.790305.

282. Kalra, A.; Taamazyan, V.; Rao, S.K.; Venkataraman, K.; Raskar, R.; Kadambi, A. Deep Polarization Cues for Transparent Object Segmentation. In Proceedings of the 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 13–19 June 2020; pp. 8599–8608. https://doi.org/10.1109/cvpr42600.2020.00863.

283. Yu, R.; Ren, W.; Zhao, M.; Wang, J.; Wu, D.; Xie, Y. Transparent objects segmentation based on polarization imaging and deep learning. *Opt. Commun.* **2024**, *555*, 130246. https://doi.org/10.1016/j.optcom.2023.130246.
284. Schwind, R. Evidence for true polarization vision based on a two-channel analyzer system in the eye of the water bug, Notonecta glauca. *J. Comp. Physiol. A* **1984**, *154*, 53–57. https://doi.org/10.1007/BF00605390.

285. Rankin, A.L.; Matthies, L.H. Passive sensor evaluation for unmanned ground vehicle mud detection. *J. Field Robotics* **2010**, *27*, 473–490. https://doi.org/10.1002/rob.20341.

286. Rankin, A.L.; Matthies, L.H.; Bellutta, P. Daytime water detection based on sky reflections. In Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, 9–13 May 2011; pp. 5329–5336. https://doi.org/10.1109/ICRA.2011.5980525.

287. Nguyen, C.V.; Milford, M.; Mahony, R. 3D tracking of water hazards with polarized stereo cameras. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation, Singapore, 29 May–3 June 2017; pp. 5251–5257. https://doi.org/10.1109/ICRA.2017.7989616.

288. Berger, K.; Voorhies, R.; Matthies, L.H. Depth from stereo polarization in specular scenes for urban robotics. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation, Singapore, 29 May–3 June 2017; pp. 1966–1973. https://doi.org/10.1109/ICRA.2017.7989227.

289. Blanchon, M.; Sidibé, D.; Morel, O.; Seulin, R.; Braun D.; Meriaudeau, F. P2D: A self-supervised method for depth estimation from polarimetry. In Proceedings of 25th International Conference on Pattern Recognition (ICPR), Milan, Italy, 10–15 January 2021; pp. 7357–7364. https://doi.org/10.1109/ICPR48806.2021.9412441.

290. Mei, H.; Dong, B.; Dong, W.; Yang, J.; Baek, S.H.; Heide, F.; Peers, P.; Wei, X.; Yang, X. Glass segmentation using intensity and spectral polarization cues. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA, 18–24 June 2022; pp. 12612–12621. https://doi.org/10.1109/CVPR52688.2022.01229.

291. Olsen, R.C.; Eyler, M.; Puetz, A.; Esterline, C. Initial results and field applications of a polarization imaging camera. In *Polarization Science and Remote Sensing IV; SPIE Optical Engineering + Applications*; SPIE: San Diego, CA, USA, 2009; Volume 7461. https://doi.org/10.1117/12.825405.

292. Piccardi, A.; Colace, L. Optical Detection of Dangerous Road Conditions. *Sensors* **2019**, *19*, 1360. https://doi.org/10.3390/s19061360.

293. Li, N.; Zhao, Y.; Wu, R.; Pan, Q. Polarization-guided road detection network for LWIR division-of-focal-plane camera. *Opt. Lett.* **2021**, *46*, 5679. https://doi.org/10.1364/ol.441817.

294. Xiang, K.; Yang, K.; Wang, K. Polarization-driven semantic segmentation via efficient attention-bridged fusion. *Opt. Express* **2021**, *29*, 4802. https://doi.org/10.1364/oe.416130.

295. El-Saba, A.; Bezuayehu, T. Higher probability of detection of subsurface land mines with a single sensor using multiple polarized and unpolarized image fusion. In *Polarization: Measurement, Analysis, and Remote Sensing VIII; SPIE Defense and Security Symposium*; SPIE: Orlando, FL, USA, 2008; Volume 6972. https://doi.org/10.1117/12.777965.

296. Zhao, Y.; Zhang, L.; Zhang, D.; Pan, Q. Object separation by polarimetric and spectral imagery fusion. *Comput. Vis. Image Underst.* **2009**, *113*, 855–866. https://doi.org/10.1016/j.cviu.2009.03.002.

297. Belskaya, I.; Cellino, A.; Gil-Hutton, R.; Muinonen, K.; Shkuratov, Y., Asteroid Polarimetry. In *Asteroids iv*; Book Section 8; Michel, P., Demeo, F.E., Bottke, W.F., Eds.; The University of Arizona Press: Tucson, AZ, USA, 2015. https://doi.org/10.2458/azu_uapress_9780816532131-ch008.

298. Ito, T.; Ishiguro, M.; Arai, T.; Imai, M.; Sekiguchi, T.; Bach, Y.P.; Kwon, Y.G.; Kobayashi, M.; Ishimaru, R.; Naito, H.; et al. Extremely strong polarization of an active asteroid (3200) Phaethon. *Nat. Commun.* **2018**, *9*, 2486. https://doi.org/10.1038/s41467-018-04727-2.

299. Beamer, D.; Abeywickrema, U.; Banerjee, P. Statistical analysis of polarization vectors for target identification. *Opt. Eng.* **2018**, *57*, 054110. https://doi.org/10.1117/1.OE.57.5.054110.

300. Miller, M.; Blumer, R.; Howe, J. Active and passive SWIR imaging polarimetry. In *Polarization Analysis and Measurement IV; International Symposium on Optical Science and Technology, San Diego, CA, USA, 29 July–3 August 2001*; SPIE: San Diego, CA, USA, Volume 4481. https://doi.org/10.1117/12.452877.

301. Liang, Y.; Wakaki, R.; Nobuhara, S.; Nishino, K. Multimodal material segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA, 18–24 June 2022; pp. 19800–19808. https://doi.org/10.1109/CVPR52688.2022.01918.

302. Lei, C.; Qi, C.; Xie, J.; Fan, N.; Koltun, V.; Chen, Q. Shape from polarization for complex scenes in the wild. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA, 18–24 June 2022; pp. 12632–12641. https://doi.org/10.1109/CVPR52688.2022.01230.

303. Wolff, L.B.; Boult, T.E. Constraining Object Features Using a Polarization Reflectance Model. *IEEE Trans. Pattern Anal. Mach. Intell.* **1991**, *13*, 635–657. https://doi.org/10.1109/10.1109/34.85655.

304. Rahmann, S.; Canterakis, N. Reconstruction of Specular Surfaces Using Polarization Imaging. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), Kauai, HI, USA, 8–14 December 2001; Volume 1, pp. 149–155. https://doi.org/10.1109/CVPR.2001.990468.

305. Miyazaki, D.; Kagesawa, M.; Ikeuchi, K. Polarization-based transparent surface modeling from two views. In Proceedings Ninth IEEE International Conference on Computer Vision, Nice, France, 13–16 October 2003; pp. 1381–1386. https://doi.org/10.1109/ICCV.2003.1238651.
284. Schwind, R. Evidence for true polarization vision based on a two-channel analyzer system in the eye of the water bug, Notonecta glauca. *J. Comp. Physiol. A* **1984**, *154*, 53–57. https://doi.org/10.1007/BF00605390.

285. Rankin, A.L.; Matthies, L.H. Passive sensor evaluation for unmanned ground vehicle mud detection. *J. Field Robotics* **2010**, *27*, 473–490. https://doi.org/10.1002/rob.20341.

286. Rankin, A.L.; Matthies, L.H.; Bellutta, P. Daytime water detection based on sky reflections. In Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, 9–13 May 2011; pp. 5329–5336. https://doi.org/10.1109/ICRA.2011.5980525.

287. Nguyen, C.V.; Milford, M.; Mahony, R. 3D tracking of water hazards with polarized stereo cameras. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation, Singapore, 29 May–3 June 2017; pp. 5251–5257. https://doi.org/10.1109/ICRA.2017.7989616.

288. Berger, K.; Voorhies, R.; Matthies, L.H. Depth from stereo polarization in specular scenes for urban robotics. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation, Singapore, 29 May–3 June 2017; pp. 1966–1973. https://doi.org/10.1109/ICRA.2017.7989227.

289. Blanchon, M.; Sidibé, D.; Morel, O.; Seulin, R.; Braun D.; Meriaudeau, F. P2D: A self-supervised method for depth estimation from polarimetry. In Proceedings of 25th International Conference on Pattern Recognition (ICPR), Milan, Italy, 10–15 January 2021; pp. 7357–7364. https://doi.org/10.1109/ICPR48806.2021.9412441.

290. Mei, H.; Dong, B.; Dong, W.; Yang, J.; Baek, S.H.; Heide, F.; Peers, P.; Wei, X.; Yang, X. Glass segmentation using intensity and spectral polarization cues. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA, 18–24 June 2022; pp. 12612–12621. https://doi.org/10.1109/CVPR52688.2022.01229.

291. Olsen, R.C.; Eyler, M.; Puetz, A.; Esterline, C. Initial results and field applications of a polarization imaging camera. In *Polarization Science and Remote Sensing IV; SPIE Optical Engineering + Applications*; SPIE: San Diego, CA, USA, 2009; Volume 7461. https://doi.org/10.1117/12.825405.

292. Piccardi, A.; Colace, L. Optical Detection of Dangerous Road Conditions. *Sensors* **2019**, *19*, 1360. https://doi.org/10.3390/s19061360.

293. Li, N.; Zhao, Y.; Wu, R.; Pan, Q. Polarization-guided road detection network for LWIR division-of-focal-plane camera. *Opt. Lett.* **2021**, *46*, 5679. https://doi.org/10.1364/ol.441817.

294. Xiang, K.; Yang, K.; Wang, K. Polarization-driven semantic segmentation via efficient attention-bridged fusion. *Opt. Express* **2021**, *29*, 4802. https://doi.org/10.1364/oe.416130.

295. El-Saba, A.; Bezuayehu, T. Higher probability of detection of subsurface land mines with a single sensor using multiple polarized and unpolarized image fusion. In *Polarization: Measurement, Analysis, and Remote Sensing VIII; SPIE Defense and Security Symposium*; SPIE: Orlando, FL, USA, 2008; Volume 6972. https://doi.org/10.1117/12.777965.

296. Zhao, Y.; Zhang, L.; Zhang, D.; Pan, Q. Object separation by polarimetric and spectral imagery fusion. *Comput. Vis. Image Underst.* **2009**, *113*, 855–866. https://doi.org/10.1016/j.cviu.2009.03.002.

297. Belskaya, I.; Cellino, A.; Gil-Hutton, R.; Muinonen, K.; Shkuratov, Y., Asteroid Polarimetry. In *Asteroids iv*; Book Section 8; Michel, P., Demeo, F.E., Bottke, W.F., Eds.; The University of Arizona Press: Tucson, AZ, USA, 2015. https://doi.org/10.2458/azu_uapress_9780816532131-ch008.

298. Ito, T.; Ishiguro, M.; Arai, T.; Imai, M.; Sekiguchi, T.; Bach, Y.P.; Kwon, Y.G.; Kobayashi, M.; Ishimaru, R.; Naito, H.; et al. Extremely strong polarization of an active asteroid (3200) Phaethon. *Nat. Commun.* **2018**, *9*, 2486. https://doi.org/10.1038/s41467-018-04727-2.

299. Beamer, D.; Abeywickrema, U.; Banerjee, P. Statistical analysis of polarization vectors for target identification. *Opt. Eng.* **2018**, *57*, 054110. https://doi.org/10.1117/1.OE.57.5.054110.

300. Miller, M.; Blumer, R.; Howe, J. Active and passive SWIR imaging polarimetry. In *Polarization Analysis and Measurement IV; International Symposium on Optical Science and Technology, San Diego, CA, USA, 29 July–3 August 2001*; SPIE: San Diego, CA, USA, Volume 4481. https://doi.org/10.1117/12.452877.

301. Liang, Y.; Wakaki, R.; Nobuhara, S.; Nishino, K. Multimodal material segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA, 18–24 June 2022; pp. 19800–19808. https://doi.org/10.1109/CVPR52688.2022.01918.

302. Lei, C.; Qi, C.; Xie, J.; Fan, N.; Koltun, V.; Chen, Q. Shape from polarization for complex scenes in the wild. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA, 18–24 June 2022; pp. 12632–12641. https://doi.org/10.1109/CVPR52688.2022.01230.

303. Wolff, L.B.; Boult, T.E. Constraining Object Features Using a Polarization Reflectance Model. *IEEE Trans. Pattern Anal. Mach. Intell.* **1991**, *13*, 635–657. https://doi.org/10.1109/10.1109/34.85655.

304. Rahmann, S.; Canterakis, N. Reconstruction of Specular Surfaces Using Polarization Imaging. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), Kauai, HI, USA, 8–14 December 2001; Volume 1, pp. 149–155. https://doi.org/10.1109/CVPR.2001.990468.

305. Miyazaki, D.; Kagesawa, M.; Ikeuchi, K. Polarization-based transparent surface modeling from two views. In Proceedings Ninth IEEE International Conference on Computer Vision, Nice, France, 13–16 October 2003; pp. 1381–1386. https://doi.org/10.1109/ICCV.2003.1238651.
306. Atkinson, G.A.; Hancock, E.R. Recovery of surface orientation from diffuse polarization. *IEEE Trans. Image Process.* **2006**, *15*, 1653-1664. https://doi.org/10.1109/TIP.2006.871114.

307. Tozza, S.; Smith, W.A.; Zhu, D.; Ramamoorthi, R.; Hancock, E.R. Linear differential constraints for photo-polarimetric height estimation. In Proceedings of the IEEE International Conference on Computer Vision, Venice, Italy, 22-29 October 2017; pp. 2279-2287. https://doi.org/10.1109/ICCV.2017.250.

308. Miyazaki, D.; Saito, M.; Sato, Y.; Ikeuchi, K. Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths. *J. Opt. Soc. Am. A* **2002**, *19*, 687-694. https://doi.org/10.1109/10.1364/JOSAA.19.000687.

309. Huynh, C.P.; Robles-Kelly, A.; Hancock, E. Shape and refractive index recovery from single-view polarisation images. In Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA, 13-18 June 2010; pp. 1229-1236. https://doi.org/10.1109/CVPR.2010.5539828.

310. Huynh, C.P.; Robles-Kelly, A.; Hancock, E.R. Shape and refractive index from single-view spectro-polarimetric images. *Int. J. Comput. Vis.* **2013**, *101*, 64-94. https://doi.org/10.1007/s11263-012-0546-3.

311. Mahmoud, A.H.; El-Melegy, M.T.; Farag, A.A. Direct method for shape recovery from polarization and shading. In Proceedings of the 2012 19th IEEE International Conference on Image Processing, Orlando, FL, USA, 30 September-3 October 2012; pp. 1769-1772. https://doi.org/10.1109/ICIP.2012.6467223.

312. Ngo Thanh, T.; Nagahara, H.; Taniguchi, R.i. Shape and light directions from shading and polarization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA, 7-12 June 2015; pp. 2310-2318. https://doi.org/10.1109/CVPR.2015.7298844.

313. Smith, W.A.P.; Ramamoorthi, R.; Tozza, S. Linear depth estimation from an uncalibrated, monocular polarisation image. In Proceedings of the Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, 11-14 October 2016; Proceedings, Part VIII 14; Springer: Berlin/Heidelberg, Germany, 2016; pp. 109-125. https://doi.org/10.1007/978-3-319-46484-8_7.

314. Baek, S.H.; Jeon, D.S.; Tong, X.; Kim, M.H. Simultaneous acquisition of polarimetric SVBRDF and normals. *ACM Trans. Graph.* **2018**, *37*, 1-15. https://doi.org/10.1145/3272127.3275018.

315. Deschaintre, V.; Lin, Y.; Ghosh, A. Deep polarization imaging for 3D shape and SVBRDF acquisition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 20-25 June 2021; pp. 15567-15576. https://doi.org/10.1109/CVPR46437.2021.01531.

316. Smith, W.A.; Ramamoorthi, R.; Tozza, S. Height-from-polarisation with unknown lighting or albedo. *IEEE Trans. Pattern Anal. Mach. Intell.* **2018**, *41*, 2875-2888. https://doi.org/10.1109/TPAMI.2018.2868065.

317. Ba, Y.; Gilbert, A.; Wang, F.; Yang, J.; Chen, R.; Wang, Y.; Yan, L.; Shi, B.; Kadambi, A. Deep Shape from Polarization. In Proceedings of the Computer Vision-ECCV, Glasgow, UK, 23-28 August 2020; Vedaldi, A., Bischof, H., Brox, T., Frahm, J.M., Eds.; Springer: Cham, Switzerland, 2020; pp. 554-571. https://doi.org/10.1007/978-3-030-58586-0_33.

318. Yang, X.; Cheng, C.; Duan, J.; Hao, Y.F.; Zhu, Y.; Zhang, H. Polarized Object Surface Reconstruction Algorithm Based on RU-GAN Network. *Sensors* **2023**, *23*, 3638. https://doi.org/10.3390/s23073638.

319. Ichikawa, T.; Purri, M.; Kawahara, R.; Nobuhara, S.; Dana, K.; Nishino, K. Shape from sky: Polarimetric normal recovery under the sky. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 20-25 June 2021; pp. 14832-14841. https://doi.org/10.1109/CVPR46437.2021.01459.

320. Cai, Y.; Li, X.; Liu, F.; Liu, J.; Liu, K.; Liu, Z.; Shao, X. Enhancing polarization 3D facial imaging: Overcoming azimuth ambiguity without extra depth devices. *Opt. Express* **2023**, *31*, 43891-43907. https://doi.org/10.1364/OE.505074.

321. Kadambi, A.; Taamazyan, V.; Shi, B.; Raskar, R. Polarized 3d: High-quality depth sensing with polarization cues. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), Santiago, Chile, 7-13 December 2015; pp. 3370-3378. https://doi.org/10.1109/ICCV.2015.385.

322. Fukao, Y.; Kawahara, R.; Nobuhara, S.; Nishino, K. Polarimetric normal stereo. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 20-25 June 2021; pp. 682-690. https://doi.org/10.1109/CVPR46437.2021.00074.

323. Zhu, D.; Smith, W.A.P. Depth From a Polarisation + RGB Stereo Pair. In Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA, 15-20 June 2019; pp. 7578-7587. https://doi.org/10.1109/CVPR.2019.00777.

324. Tian, X.; Liu, R.; Wang, Z.; Ma, J. High quality 3D reconstruction based on fusion of polarization imaging and binocular stereo vision. *Inf. Fusion* **2022**, *77*, 19-28. https://doi.org/10.1016/j.inffus.2021.07.002.

325. Cui, Z.; Gu, J.; Shi, B.; Tan, P.; Kautz, J. Polarimetric multi-view stereo. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA, 21-26 July 2017; pp. 1558-1567. https://doi.org/10.1109/CVPR.2017.47.

326. Cui, Z.; Larsson, V.; Pollefeys, M. Polarimetric relative pose estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (CVPR), Seoul, Republic of Korea, 27 October-2 November 2019; pp. 2671-2680. https://doi.org/10.1109/ICCV.2019.00276.

327. Gao, D.; Li, Y.; Ruhkamp, P.; Skobleva, I.; Wysocki, M.; Jung, H.; Wang, P.; Guridi, A.; Busam, B. Polarimetric Pose Prediction. In Proceedings of the Computer Vision-ECCV, Tel Aviv, Israel, 23-27 October 2022; Avidan, S., Brostow, G., Cissé, M., Farinella, G.M., Hassner, T., Eds.; Springer: Cham, Switzerland, 2022; pp. 735-752. https://doi.org/10.1007/978-3-031-20077-9_43.
306. Atkinson, G.A.; Hancock, E.R. Recovery of surface orientation from diffuse polarization. *IEEE Trans. Image Process.* **2006**, *15*, 1653-1664. https://doi.org/10.1109/TIP.2006.871114.

307. Tozza, S.; Smith, W.A.; Zhu, D.; Ramamoorthi, R.; Hancock, E.R. Linear differential constraints for photo-polarimetric height estimation. In Proceedings of the IEEE International Conference on Computer Vision, Venice, Italy, 22-29 October 2017; pp. 2279-2287. https://doi.org/10.1109/ICCV.2017.250.

308. Miyazaki, D.; Saito, M.; Sato, Y.; Ikeuchi, K. Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths. *J. Opt. Soc. Am. A* **2002**, *19*, 687-694. https://doi.org/10.1109/10.1364/JOSAA.19.000687.

309. Huynh, C.P.; Robles-Kelly, A.; Hancock, E. Shape and refractive index recovery from single-view polarisation images. In Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA, 13-18 June 2010; pp. 1229-1236. https://doi.org/10.1109/CVPR.2010.5539828.

310. Huynh, C.P.; Robles-Kelly, A.; Hancock, E.R. Shape and refractive index from single-view spectro-polarimetric images. *Int. J. Comput. Vis.* **2013**, *101*, 64-94. https://doi.org/10.1007/s11263-012-0546-3.

311. Mahmoud, A.H.; El-Melegy, M.T.; Farag, A.A. Direct method for shape recovery from polarization and shading. In Proceedings of the 2012 19th IEEE International Conference on Image Processing, Orlando, FL, USA, 30 September-3 October 2012; pp. 1769-1772. https://doi.org/10.1109/ICIP.2012.6467223.

312. Ngo Thanh, T.; Nagahara, H.; Taniguchi, R.i. Shape and light directions from shading and polarization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA, 7-12 June 2015; pp. 2310-2318. https://doi.org/10.1109/CVPR.2015.7298844.

313. Smith, W.A.P.; Ramamoorthi, R.; Tozza, S. Linear depth estimation from an uncalibrated, monocular polarisation image. In Proceedings of the Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, 11-14 October 2016; Proceedings, Part VIII 14; Springer: Berlin/Heidelberg, Germany, 2016; pp. 109-125. https://doi.org/10.1007/978-3-319-46484-8_7.

314. Baek, S.H.; Jeon, D.S.; Tong, X.; Kim, M.H. Simultaneous acquisition of polarimetric SVBRDF and normals. *ACM Trans. Graph.* **2018**, *37*, 1-15. https://doi.org/10.1145/3272127.3275018.

315. Deschaintre, V.; Lin, Y.; Ghosh, A. Deep polarization imaging for 3D shape and SVBRDF acquisition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 20-25 June 2021; pp. 15567-15576. https://doi.org/10.1109/CVPR46437.2021.01531.

316. Smith, W.A.; Ramamoorthi, R.; Tozza, S. Height-from-polarisation with unknown lighting or albedo. *IEEE Trans. Pattern Anal. Mach. Intell.* **2018**, *41*, 2875-2888. https://doi.org/10.1109/TPAMI.2018.2868065.

317. Ba, Y.; Gilbert, A.; Wang, F.; Yang, J.; Chen, R.; Wang, Y.; Yan, L.; Shi, B.; Kadambi, A. Deep Shape from Polarization. In Proceedings of the Computer Vision-ECCV, Glasgow, UK, 23-28 August 2020; Vedaldi, A., Bischof, H., Brox, T., Frahm, J.M., Eds.; Springer: Cham, Switzerland, 2020; pp. 554-571. https://doi.org/10.1007/978-3-030-58586-0_33.

318. Yang, X.; Cheng, C.; Duan, J.; Hao, Y.F.; Zhu, Y.; Zhang, H. Polarized Object Surface Reconstruction Algorithm Based on RU-GAN Network. *Sensors* **2023**, *23*, 3638. https://doi.org/10.3390/s23073638.

319. Ichikawa, T.; Purri, M.; Kawahara, R.; Nobuhara, S.; Dana, K.; Nishino, K. Shape from sky: Polarimetric normal recovery under the sky. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 20-25 June 2021; pp. 14832-14841. https://doi.org/10.1109/CVPR46437.2021.01459.

320. Cai, Y.; Li, X.; Liu, F.; Liu, J.; Liu, K.; Liu, Z.; Shao, X. Enhancing polarization 3D facial imaging: Overcoming azimuth ambiguity without extra depth devices. *Opt. Express* **2023**, *31*, 43891-43907. https://doi.org/10.1364/OE.505074.

321. Kadambi, A.; Taamazyan, V.; Shi, B.; Raskar, R. Polarized 3d: High-quality depth sensing with polarization cues. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), Santiago, Chile, 7-13 December 2015; pp. 3370-3378. https://doi.org/10.1109/ICCV.2015.385.

322. Fukao, Y.; Kawahara, R.; Nobuhara, S.; Nishino, K. Polarimetric normal stereo. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA, 20-25 June 2021; pp. 682-690. https://doi.org/10.1109/CVPR46437.2021.00074.

323. Zhu, D.; Smith, W.A.P. Depth From a Polarisation + RGB Stereo Pair. In Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA, 15-20 June 2019; pp. 7578-7587. https://doi.org/10.1109/CVPR.2019.00777.

324. Tian, X.; Liu, R.; Wang, Z.; Ma, J. High quality 3D reconstruction based on fusion of polarization imaging and binocular stereo vision. *Inf. Fusion* **2022**, *77*, 19-28. https://doi.org/10.1016/j.inffus.2021.07.002.

325. Cui, Z.; Gu, J.; Shi, B.; Tan, P.; Kautz, J. Polarimetric multi-view stereo. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA, 21-26 July 2017; pp. 1558-1567. https://doi.org/10.1109/CVPR.2017.47.

326. Cui, Z.; Larsson, V.; Pollefeys, M. Polarimetric relative pose estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (CVPR), Seoul, Republic of Korea, 27 October-2 November 2019; pp. 2671-2680. https://doi.org/10.1109/ICCV.2019.00276.

327. Gao, D.; Li, Y.; Ruhkamp, P.; Skobleva, I.; Wysocki, M.; Jung, H.; Wang, P.; Guridi, A.; Busam, B. Polarimetric Pose Prediction. In Proceedings of the Computer Vision-ECCV, Tel Aviv, Israel, 23-27 October 2022; Avidan, S., Brostow, G., Cissé, M., Farinella, G.M., Hassner, T., Eds.; Springer: Cham, Switzerland, 2022; pp. 735-752. https://doi.org/10.1007/978-3-031-20077-9_43.
328. Wang, G.; Manhardt, F.; Tombari, F.; Ji, X. Gdr-net: Geometry-guided direct regression network for monocular 6D object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA, 20-25 June 2021; pp. 16611-16621. https://doi.org/10.1109/CVPR46437.2021.01634.

329. Zou, S.; Zuo, X.; Wang, S.; Qian, Y.; Guo, C.; Cheng, L. Human Pose and Shape Estimation from Single Polarization Images. *IEEE Trans. Multimed.* **2022**, *25*, 3560-3572. https://doi.org/10.1109/tmm.2022.3162469.

330. Huang, T.; Li, H.; He, K.; Sui, C.; Li, B.; Liu, Y.H. Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023; pp. 17287-17296. https://doi.org/10.1109/CVPR52729.2023.01658.

331. Muglikar, M.; Bauersfeld, L.; Moeys, D.P.; Scaramuzza, D. Event-based shape from polarization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023; pp. 1547-1556. https://doi.org/10.1109/CVPR52729.2023.00155.

332. Mei, H.; Wang, Z.; Yang, X.; Wei, X.; Delbruck, TobiMei, H.; Wang, Z.; Yang, X.; Wei, X.; Delbruck, T. Deep Polarization Reconstruction With PDAVIS Events. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern RecognitionProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023. https://doi.org/10.1109/CVPR52729.2023.02121.

333. Jeon, D.S.; Meuleman, A.; Baek, S.H.; Kim, M.H. Polarimetric iToF: Measuring High-Fidelity Depth through Scattering Media. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023; pp. 12353-12362. https://doi.org/10.1109/CVPR52729.2023.01189.

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
328. Wang, G.; Manhardt, F.; Tombari, F.; Ji, X. Gdr-net: Geometry-guided direct regression network for monocular 6D object pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA, 20-25 June 2021; pp. 16611-16621. https://doi.org/10.1109/CVPR46437.2021.01634.

329. Zou, S.; Zuo, X.; Wang, S.; Qian, Y.; Guo, C.; Cheng, L. Human Pose and Shape Estimation from Single Polarization Images. *IEEE Trans. Multimed.* **2022**, *25*, 3560-3572. https://doi.org/10.1109/tmm.2022.3162469.

330. Huang, T.; Li, H.; He, K.; Sui, C.; Li, B.; Liu, Y.H. Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023; pp. 17287-17296. https://doi.org/10.1109/CVPR52729.2023.01658.

331. Muglikar, M.; Bauersfeld, L.; Moeys, D.P.; Scaramuzza, D. Event-based shape from polarization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023; pp. 1547-1556. https://doi.org/10.1109/CVPR52729.2023.00155.

332. Mei, H.; Wang, Z.; Yang, X.; Wei, X.; Delbruck, TobiMei, H.; Wang, Z.; Yang, X.; Wei, X.; Delbruck, T. Deep Polarization Reconstruction With PDAVIS Events. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern RecognitionProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023. https://doi.org/10.1109/CVPR52729.2023.02121.

333. Jeon, D.S.; Meuleman, A.; Baek, S.H.; Kim, M.H. Polarimetric iToF: Measuring High-Fidelity Depth through Scattering Media. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Vancouver, BC, Canada, 17-24 June 2023; pp. 12353-12362. https://doi.org/10.1109/CVPR52729.2023.01189.

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.