Learning to dehaze with polarization
Year: 2022

Abstract:
Haze, a common kind of bad weather caused by atmospheric scattering, decreases the visibility of scenes and degenerates the performance of computer vision algorithms. Single-image dehazing methods have shown their effectiveness in a large variety of scenes, however, they are based on handcrafted priors or learned features, which do not generalize well to real-world images. Polarization information can be used to relieve its ill-posedness, however, real-world images are still challenging since existing polarization-based methods usually assume that the transmitted light is not significantly polarized, and they require specific clues to estimate necessary physical parameters. In this paper, we propose a generalized physical formation model of hazy images and a robust polarization-based dehazing pipeline without the above assumption or requirement, along with a neural network tailored to the pipeline. Experimental results show that our approach achieves state-of-the-art performance on both synthetic data and real-world hazy images.

heading: 1 Introduction
text: When taking photos in hazy environments, the visibility and color fidelity of recorded scenes are usually contaminated, because the captured images often contain a superposition of two unknown components: the transmitted light (an attenuated fraction of original scene radiance), and the airlight (ambient light scattered towards the viewer). It is highly ill-posed to separate them in a single hazy image as it requires estimating multiple unknowns from a single observation. Handcrafted priors from natural image statistics [21, 15, 1] have been wildly used to solve this problem. With the development of deep neural networks, learning-based methods (e.g., CNN-based [24, 65, 7, 82] and GAN-based [79, 5]) have also been adopted to recover the haze-free images by extracting image features from a large amount of training data. However, these methods do not generalize well to real-world images, because they depend strongly on the image features extracted from training data and do not explicitly consider useful constraints from physical image formation models.
For better generalization, multi-image dehazing methods have been proposed. They capture multiple images from different viewpoints [38, 52, 84, 63], weather conditions [58, 55, 56, 57], or polarization angles [77, 78, 53, 81, 76, 25, 54]. Although all of these multi-image dehazing methods can relieve the ill-posedness, polarization-based ones have their unique advantages, since they directly utilize the physical image formation model with less dependency on image features extracted from training data. Nowadays, multiple polarized images can be conveniently captured in a single shot using a
∗Corresponding author.
35th Conference on Neural Information Processing Systems (NeurIPS 2021).
polarization camera such as Lucid Vision Phoenix polarization camera2. However, these polarizationbased methods are not robust due to several issues:
(1). They are largely based on a strong assumption that the transmitted light is not significantly polarized, while it is not the case for real-world images since both transmitted light and airlight contribute to the polarization [13, 29].
(2). They usually require specific clues (e.g., sky regions [13, 77, 53], similar objects [54, 50], known depth [54]) to estimate the infinite airlight and the degree of polarization (DoP), which significantly reduces their applicability since these requirements are not always met.
(3). They are optimization-based methods which do not make full use of semantic and contextual information in image features to handle the spatially-variant real-world scattering.
In this paper, to enable the polarization-based dehazing methods to handle images captured in the wild more robustly, we propose a generalized physical formation model of hazy images, without assuming that the transmitted light is not significantly polarized, while considering the spatiallyvariant real-world scattering. Based on the physical model, we propose a robust polarization-based dehazing pipeline to extend their applicability by adopting deep learning to estimate the infinite airlight and the DoP of both transmitted light and airlight without the requirement of specific clues like sky regions, similar objects, etc. According to our dehazing pipeline, we design a neural network to perform the dehazing process: It first estimates the DoP of both transmitted light and airlight to solve the transmitted light, then predicts the infinite airlight to reconstruct the original scene radiance. Thanks to our learning-based pipeline, our method extracts image features from training data and use semantic and contextual information to refine the results, which is suitable for handling the spatially-variant real-world scattering.
To summarize, this paper makes contributions by demonstrating:
(1). A generalized physical formation model of hazy images, taking into account the polarization effects of both transmitted light and airlight, along with the spatially-variant real-world scattering.
(2). A robust polarization-based dehazing pipeline without the requirement of specific clues, by adopting deep learning to estimate necessary physical parameters (infinite airlight, DoP of both transmitted light and airlight).
(3). A neural network making full use of semantic and contextual information to handle the spatially-variant real-world scattering to improve the clarity of original scene radiance recovery.
Experimental results show that our approach achieves state-of-the-art performance on both synthetic data and real-world hazy images.

heading: 2 Related work
text: Single-image dehazing. Single-image dehazing is a highly ill-posed problem because it requires estimating multiple unknowns (the transmitted light and airlight) from a single observation. Park et al. [64] estimated haze from the difference among the RGB channels. Some methods adopted an adaptive contrast enhancement strategy to maximize the local contrast of restored images [87, 17, 47]. Some works proposed several assumptions (e.g., the surface shading and transmission are locally uncorrelated [14], the scene albedo and depth are independent [59], both the scene albedo and transmission are constant inside each patch [86]) or image priors (e.g., dark channel prior [21, 89, 49, 37], color attenuation prior [98], non-local prior [1, 43], ellipsoid prior [19], color-lines [15]) to handle this problem. Recently, with the development of deep neural networks, learning-based methods have also been adopted to recover haze-free images by extracting image features from a large amount of training data. These learning-based methods could be divided into two groups: direct methods, which dehaze in an end-to-end manner using convolutional neural networks (CNN) [2, 68, 30, 31, 62, 6, 18, 45, 95, 44, 36, 24, 65, 7, 8, 70, 94, 51, 4, 48, 3] or generative adversarial networks (GAN) [93, 69, 35, 92, 66, 33, 34, 79, 5, 9, 12, 85, 10, 82], and indirect methods, which
2https://thinklucid.com/product/phoenix-5-0-mp-polarized-model/
estimate image priors or their variants [88, 74, 91, 46, 20] first and then use them to dehaze. Although these methods have shown their effectiveness in a large variety of scenes, their generalization ability is still limited, since image priors are not always observed in the input and the image features extracted from synthetic training data often have a large domain gap with real-world ones.
Multi-image dehazing. For better generalization and less ill-posedness, multi-image dehazing methods have been proposed. They use computational photography techniques to capture multiple images with conventional or unconventional cameras for acquiring extra information. Some methods used separately measured range data [60] and georeferenced digital terrain with urban models [28] to facilitate dehazing. Some works captured multiple images under different unknown weather conditions to recover scene depth maps for dehazing [58, 55, 56, 57]. Some approaches take advantage of stereo vision to remove the effects of haze [38, 52, 84, 63] by taking multiple photos from different viewpoints. Some methods fuse RGB images with NIR (near-infrared) ones to help dehaze [75, 16, 42, 11, 83], because the scattering is significantly smaller in NIR than in visible light since NIR wavelengths are longer. Although these methods have better generalization ability, capturing such data is not easy since they require multiple shots and/or complicated imaging systems.
Polarization-based dehazing. Recently, polarization-based methods have been proposed to solve the dehazing problem by capturing multiple polarized images at the same view with different polarization angles. These methods have their unique advantages: they directly utilize the physical image formation model without dependence on image features extracted from training data, and multiple polarized images can be captured in a single shot using a polarization camera. However, most of them are based on a strong assumption that the transmitted light is not significantly polarized [77, 78, 53, 81, 76, 25, 54, 50, 41, 40, 39, 67, 80], while it is not the case for real-world images since both transmitted light and airlight contribute to the polarization [13, 29]. Fang et al. [13] takes the polarization of transmitted light into consideration, however, it supposes that the depth of sky regions is approximately infinite and require sky regions to estimate the infinite airlight and the DoP, just like [77, 53], which significantly reduces the applicability since sky regions are not always available.

heading: 3 Method
text: In this section, we show the physical formation model of hazy images in Section 3.1, demonstrate our polarization-based dehazing pipeline in Section 3.2, and introduce our neural network in Section 3.3.

heading: 3.1 Physical image formation model
text: As shown in Figure 1 (top row), when taking photos in hazy environments, caused by atmospheric scattering, the captured image I = {I(x, y, c)} ((x, y) is the pixel coordinate and c denotes the color channel index) is composed of two components: the transmitted light T = {T (x, y, c)} (an attenuated fraction of original scene radiance R = {R(x, y, c)}), which decreases with the scene depth z = {z(x, y)}, and the airlight A = {A(x, y, c)} (ambient light scattered towards the viewer), which increases with z. According to [77], the formation of a hazy image can be described as
I = T + A = R · e−β·z + A∞ · (1− e−β·z), (1) where β = {β(c)} is the scattering coefficient, A∞ = {A∞(c)} denotes the infinite airlight (the airlight radiance corresponding to an object at an infinite distance, e.g., the horizon), and · stands for element-wise multiplication. A synthetic example of its visualization can be found in Figure 1 (bottom left). However, real-word scattering does not always satisfy such an ideal model, which means that both β and A∞ are not only dependent on wavelength, but also on the the size of the scattering particles [27, 22] and angular scattering coefficient [78]. To encode such variations, we replace them with β = {β̄(c) +N(x, y, c)} and A∞ = {Ā∞(c) +N(x, y, c)} respectively, where ·̄ marks the mean value and N(x, y, c) denotes the spatially-variant turbulence. Assume for a moment that the illumination of any scattering particle comes from one direction, the light ray from the source to a scatterer and the line-of-sight from the camera to the scatterer define a plane of incidence (PoI) [77], as shown in Figure 1 (top row). We decompose I, T, and A into two components respectively: I‖ and I⊥, T‖ and T⊥, A‖ and A⊥, where the subscript ‖ (⊥) means the component is parallel (perpendicular) to the PoI. The degrees of polarization (DoP) of I, T, and A are defined as
P , I⊥ − I‖
I , PT ,
T⊥ − T‖
T , and PA ,
A⊥ − A‖
A , (2)
respectively, where
I = I⊥ + I‖, T = T⊥ + T‖, and A = A⊥ + A‖. (3)
Since the scattered light is partially polarized perpendicular to the PoI [77, 27, 22, 13], P, PT , and PA are not less than zero. Besides, although P is spatially-variant (i.e., P = {P (x, y, c)}), the distributions of PT and PA are not irregular: the values of PT are approximately uniform in the same semantic segment3, while PA can be regarded as spatially-uniform, i.e., PA = {PA(c)}, according to [13]. A synthetic example of their visualization can be found in Figure 1 (bottom right).
When we place a polarizer with polarization angle α in front of the camera, according to Malus’ law [22], the captured polarized image Iα can be calculated as
Iα = I · (1− P · cos(2(α− θ‖)))
2 , (4)
where θ‖ = {θ̄‖ +N(x, y, c)} denotes the orientation of the polarizer for best transmission of the component parallel to the PoI. Similarly, the two components T and A at angle alpha can be calculated as
Tα = T · (1− PT · cos(2(α− θ‖)))
2 and Aα = A · (1− PA · cos(2(α− θ‖))) 2 , (5)
which satisfy Iα = Tα + Aα. Note that both T and A contribute to the polarization, and the polarization of T should not be ignored [13, 29]. From Equation (4) and Equation (5), we can derive the following equation:
I · P = T · PT + A · PA, (6)
which reveals that the relationship among I, T, and A are determined by P, PT , and PA.
3The polarization properties of transmitted light depend on material properties of scene objects (e.g., surface texture) [29], and objects in the same semantic segment often have similar material properties.

heading: 3.2 Polarization-based dehazing pipeline
text: We aim to restore the original scene radiance R using three polarized images Iα(i)(i = 1, 2, 3) captured at the same view with different polarization angles α(i)(i = 1, 2, 3). Eliminating A from Equation (1) and Equation (6), T and R could be computed by the following two equations:
(a) T = P · I− I · PA
PT − PA and (b) R = T · A∞ A∞ − (I− T) , (7)
where PT , PA, and A∞ are required to be estimated, I and P can be directly calculated by Iα(i)(i = 1, 2, 3).
Now we first explain how to calculate I and P using Iα(i)(i = 1, 2, 3). Expanding Equation (4), we obtain (〈〉 denotes inner product)
Iα = 〈 [ 1 2 − cos(2α) 2 − sin(2α) 2 ] , [D1 D2 D3]〉, where D1 = I, D2 = I · P · cos(2θ‖) and D3 = I · P · sin(2θ‖). (8)
Since Equation (8) has three unknowns (Di(i = 1, 2, 3)), we can use Iα(i)(i = 1, 2, 3) to obtain a linear system that allows to compute them. Then, we could calculate I and P by I = D1 and
P = √ (D22+D 2 3)
D1 respectively.
Next, we only need to estimate three parameters PT , PA, and A∞ to reconstruct R. To alleviate the dependency on specific clues (such as sky regions [13, 77, 53] or similar objects [54, 50], which are required by other polarization-based methods) for estimating these parameters, we choose to design a deep neural network that comprehensively explores physics and semantic features.

heading: 3.3 Polarization-based dehazing network
text: As shown in Figure 2, our network consists of two stages: transmitted light estimation and original scene radiance reconstruction.
Transmitted light estimation. As shown in the first stage of Figure 2, it aims to estimate the DoP of both transmitted light and airlight (PT and PA) for solving the transmitted light T. So, it adopts a subnetwork g1 to estimate PT and PA, then uses Equation (7) (a) to calculate T̂ (the coarse value
of T). However, we cannot directly feed T̂ into the second stage since the numerical problem will occur when the denominator of Equation (7) (a) approaches zero, which often happens in pixels where PT ≈ PA (the DoP of transmitted light and airlight are approximately the same). Besides, the estimated PT and PA by g1 are prone to be noisy which distorts the calculated T̂, because the spatially-variant turbulence is hard to learn due to its irregularities. So, we adopt another subnetwork g2 to refine T̂ using semantic and contextual information extracted from Iα(i)(i = 1, 2, 3). In practice, we construct g1 using the U-Net architecture [71] since it works well on per-pixel estimation tasks such as semantic segmentation [71, 61]. As for g2, we choose the autoencoder architecture [23], by virtue of its excellent context generalization ability for refining image contents.
Original scene radiance reconstruction. As shown in the second stage of Figure 2, it aims to estimate the infinite airlight A∞ to reconstruct the original scene radiance R. So, it first adopts a subnetwork g3 to estimate A∞, then uses Equation (7) (b) to calculate R̂ (the coarse value of R). However, R̂ also needs to be refined, because when the haze in some pixels is very thick and leaves little information of the transmitted light (T ≈ 0), the numerator of Equation (7) (b) approaches zero, which leads to a wrong result that R ≈ 0. So, similar to the first stage, we also adopt a subnetwork g4 to refine R̂. We also choose the U-Net architecture [71] for g3 and the autoencoder architecture [23] for g4.

heading: 4 Data preparation and network training
text: In this section, we first detail our synthetic dataset generation pipeline in Section 4.1, then show our loss function and training strategy in Section 4.2.

heading: 4.1 Synthetic dataset generation pipeline
text: It is difficult to obtain pairwise hazy and clear images with three polarized observations at a large scale. Besides, getting the ground truth values of the DoP or infinite airlight is not feasible. So, we propose to generate a synthetic dataset for training our network. Since we require spatially-variant β and A∞ to simulate real-world scattering, and need the semantic segmentation map S for generating reasonable PT (see Section 3.1 for details about the properties of PT ), we cannot directly generate the polarized images from the hazy images in existing dehazing benchmarks [32, 97, 96, 73, 72]. The desired data source for generating our dataset should provide:
(1). clear image R with depth map z, from which we can calculate I using Equation (1) by generating spatially-variant β and A∞;
(2). semantic segmentation map S, from which we can generate reasonable PT using PT = f(S), where f denotes a function which randomly maps each semantic segment to a value of PT .
The Foggy Cityscapes-DBF dataset [72] meets the above two requirements4, so we use the provided z, R, and S to generate our synthetic dataset. In short, with z, R, and S available, our synthetic dataset generation pipeline could be described as5:
(1). Randomly generate β (in [0.01, 0.02]), A∞ (in [0.85, 0.95]), and PA (in [0.05, 0.4]) to calculate T, A, and I using Equation (1);
(2). generate PT from S using PT = f(S) (in [0.025, 0.2]), then calculate P using Equation (6); (3). randomly generate θ‖ (in [−45◦, 45◦]), then use Equation (4) to calculate Iα(i)(i = 1, 2, 3)
(α(i)(i = 1, 2, 3) are set to be 0◦, 45◦, and 90◦ respectively).
The visualization of above mentioned parameters can be found in the bottom row of Figure 1. Note that for β = {β̄(c) + N(x, y, c)} and A∞ = {Ā∞(c) + N(x, y, c)}, we first generate their mean values β̄(c) and Ā∞(c) for each channel, then add 5% Gaussian noise to make them spatially-variant. Besides, we also add 2% Gaussian noise to Iα(i)(i = 1, 2, 3). To conform to the real-world scattering
4Although it does not directly provide z, it offers the transmittance (e−β·z) with known spatially-uniform scattering coefficient β, so that we can can compute z by ourselves.
5The range of β is from Li et al. [32] with some adjustment (changing the sampling space from discrete to continuous), and the ranges of PA and PT are from the statistics in Fang et al. [13].
[77], we ensure that β̄(r) < β̄(g) < β̄(b) and PA(r) > PA(g) > PA(b). The images are resized and randomly cropped to 240× 240 patches during the training process, and cropped to 496× 240 patches for test6.

heading: 4.2 Loss function and training strategy
text: Loss function. The total loss function of our network is L = λ1 ·Lg1 +λ2 ·Lg2 +λ3 ·Lg3 +λ4 ·Lg4 , where Lgi(i = 1, 2, 3, 4) define the loss of our four subnetworks. Each of them could be described as
6Our training (test) images are generated from the training (test) images of the Foggy Cityscapes-DBF dataset [72].
Lgi = 2 · L1 + L2, where L1 and L2 denote the L1 and L2 loss respectively. λi(i = 1, 2, 3, 4) are empirically set to be 1.0, 1.0, 2.0, 2.0 respectively.
Training strategy. We implement our network using PyTorch on an NVIDIA 2080Ti GPU and apply a two-phase training strategy. First, to ensure a stable initialization of the training process, we train our two network stages independently for 400 epochs. ADAM optimizer [26] is used with an initial learning rate 5× 10−4 for the first 300 epochs, and a linear decay to 2.5× 10−4 in the next 100 epochs. Then, we finetune the entire network in an end-to-end manner for another 300 epochs, keeping the learning rate to 5× 10−4. Instance normalization [90] are added during training.

heading: 5 Experiments

heading: 5.1 Evaluation on synthetic data
text: We compare our results to a representative polarization-based dehazing algorithm SPCVE [54] which also takes three polarized images as the input and five state-of-the-art learning-based dehazing methods including GDN [44], BPP [82], FFA [65], HardGAN [5], and MSBDN [7] which take a single hazy image as the input7. SPCVE [54] assumes that the transmitted light is not significantly polarized (PT = 0), and uses optimization to estimate PA and A∞, while our method takes into account the polarization effects of transmitted light and adopts deep learning to estimate PT , PA, and A∞. All of these learning-based methods are re-trained on our dataset using R and Î (the calculated hazy image from Iα(i)(i = 1, 2, 3) using the linear system from Equation (8))8. Note that comparing with learning-based dehazing methods might be a bit unfair because of the difference in types of input data (ordinary image vs. polarized image), and we conduct such a comparison to show the advantage of using polarized images over image-only approaches.
Visual quality comparisons of dehazed results are shown in Figure 39. Compared to the polarizationbased dehazing algorithm SPCVE [54], our method can dehaze robustly with fewer artifacts; compared to the learning-based methods, our method performs better in recovering details. Taking the sky region (green box) in the first group of Figure 3 as an example, SPCVE [54] suffers severely from noise, and the learning-based methods yield bad pixels (shown as black streaks in the sky). This is because in our synthetic dataset we not only simulate the polarization effects of airlight but also transmitted light, and add spatially-variant turbulence to the scattering process, while SPCVE [54] ignores the polarization effects of the transmitted light and does not consider semantic and contextual information to refine the results, and the learning-based methods [44, 82, 65, 5, 7] are prone to artifacts for the pixels with large spatially-variant turbulence. To evaluate the results quantitatively, we adopt two frequently-used image quality metrics including PSNR and MS-SSIM (multi-scale SSIM). Results are shown in Table 1 (also below corresponding examples in Figure 3). Our model consistently outperforms the polarization-based and learning-based dehazing methods on all metrics.
7Note that the code of SPCVE [54] is not available and the demonstrated results are based on our own implementation. We directly provide the ground truth A∞ to our implementation as its upper bound performance, also owing to that SPCVE [54] requires similar objects or known depth to estimate A∞, which are not always available in our scenes.
8We should not use the ground truth I as the input of these learning-based methods since we could only get Î during the inferring phase of real data; and if we use I to re-train them, their results will be degenerated due to the large domain gap between I and Î (caused by the noise in Iα(i)(i = 1, 2, 3)).
9Additional synthetic results can be found in the supplementary material.

heading: 5.2 Evaluation on real data
text: We use the Lucid Vision Phoenix polarization camera (RGB) to capture real data. The polarization camera can take four images with different polarization angles (0◦, 45◦, 90◦, and 135◦) at a single shot. We use three of them (0◦, 45◦, and 90◦) as the input to our method and SPCVE [54], and calculate the hazy image Î from the polarized images Iα(i)(i = 1, 2, 3) using the linear system from Equation (8) as the input to learning-based methods (GDN [44], BPP [82], FFA [65], HardGAN [5], and MSBDN [7]). Visual quality comparisons of dehazed results are shown in Figure 410. Our method is able to generate clearer and brighter images than those by the state-of-the-art polarization-based and learning-based methods. For example, the color of the buildings (red box) in the first group of Figure 4, is correctly recovered by our method, while other methods suffer from color distortion
10Additional real results can be found in the supplementary material.
artifacts which dim the results. For better visualization, we also show the polarized images side by side with the estimated PA and PT in Figure 5. We can see that the distributions of PA and PT satisfy the ones mentioned in Section 3.1, which demonstrates the rationality of our motivation.

heading: 5.3 Ablation study
text: To verify the validity of each model design choice, we conduct a series of ablation studies and show comparisons in Table 2. We first show the effectiveness of our physical image formation model by comparing with a model that ignores the polarization effects of the transmitted light (by taking PT as zero) and a model that neglects the spatially-variant real-world scattering (by taking PT , PA, and A∞ as spatially-uniform parameters). From the results we can see that our model is more generalized and reasonable. We further verify the contribution of our dehazing pipeline which estimates three parameters (PT , PA, and A∞) to solve T and R by comparing with a model that directly estimates T and R. We find that our dehazing pipeline is better than directly estimating T and R since these parameters are easier to learn than T and R. Then, we demonstrate the necessity of the refinement subnetworks (g2 and g4) by removing g2, g4, and both of them. We could tell that without the refinement subnetworks11, the performance degenerates rapidly, while it still outperforms the existing polarization-based (also optimization-based) dehazing algorithm SPCVE [54] (see Table 1 for the performance of SPCVE [54]) thanks to our generalized physical image formation model.

heading: 6 Conclusion
text: We presented a learning-based solution which leverages the properties of polarized light for image dehazing. To handle the images captured in the wild, we proposed a generalized physical formation model of hazy images, introduced a robust polarization-based dehazing pipeline, and designed a neural network tailored to the pipeline, showing state-of-the-art performance. Our solution extended the applicability of polarization-based dehazing methods by adopting deep learning to estimate the infinite airlight and the DoP of both transmitted light and airlight without the requirement of specific clues (e.g., sky regions, similar objects), while considering the spatially-variant real-world scattering.
Limitations. Since our method is based on the physical image formation model of hazy images, it may fail in situations which does not conform to the model, such as fog or mist. As shown in Figure 6, our method shows degenerate performance on those images, because fog and mist are caused by a suspension of water droplets, while haze is a suspension of extremely small particles (other than water droplets) in the air. As future work, we plan to extend our model to support other situations.
11Synthetic results without refinement can be found in the supplementary material.
Acknowledgments and Disclosure of Funding
This work is supported by National Key R&D Program of China (2020AAA0105200), and National Natural Science Foundation of China under Grant No. 62136001, 62088102, 61872012, 61876007.

Review summaries:
This paper proposes a method for image dehazing by polarization-based learning pipeline. It is based on a physical formation model which is considering the spatially variant real-world scattering and taking into account the polarization effects of both transmitted light and airlight. Experiments demonstrate that the proposed method can dehaze robustly with fewer artifacts, and performs better in recovering details. 

This paper proposes a neural network for image dehazing where the input is expected to contain polarization information (e.g. multiple polarized images of the exact same scene). The total irradiance and total degree of polarization can be obtained directly from the polarized input frames. The paper then follows the image formation model of [77] (and others) to identify key quantities to estimate: the infinite airlight color, and the degree of polarization of the ambient and scene light. Multiple neural networks are designed to estimate these components; they are coupled using closed-formed expressions derived from the image formation model to produce the final dehazed image. The networks are trained independently, then finetuned jointly on a synthetic dataset. 

This paper presents dehazing algorithm using characteristics of polarized images. It first introduces generalized physical formation model of polarized hazy images, regarding spatially-variant real-world scattering. Taking three differently polarized hazy images as input, the proposed algorithm estimates and refines degrees of polarization (DoP) of the transmitted light T and airlight A, and utilizes these predictions to finally obtain original scene radiance R. By doing so, this paper was able to show outstanding performances, especially on real-world images due to its consideration on spatially-variant DoP and global airlight.

The paper presents a method for polarization-based dehazing of images. Using a camera with a polarization filter array, multiple polarization images can be captured in a single snapshot. These images are used to estimate an unpolarized image $I$ and a degree-of-polarization image $P$. A series of neural networks are trained on synthetic data to estimate the polarization and radiance of the ambient and transmitted scene light conditioned on $I$ and $P$. The results of the dehazed estimated scene radiance are compared with other methods for dehazing using polarization images or a single unpolarized image. Quantitatively, the approach appears to offer roughly 1-2 dB in improvement over previous methods in terms of PSNR. Qualitatively, the method appears to generate improved results on captured data as well.