Fast outdoor hazy image dehazing based on saturation and brightness

IET Image ProcessingEarly View ORIGINAL RESEARCH PAPEROpen Access Fast outdoor hazy image dehazing based on saturation and brightness Daosong Hu, Daosong Hu orcid.org/0000-0002-5118-7202 School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, ChinaSearch for more papers by this authorYang Yang, Yang Yang School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, ChinaSearch for more papers by this authorBo Li, Corresponding Author Bo Li Li_bo@cug.edu.cn School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, China Correspondence Bo Li, School of Mechanical Engineering and Electronic Information, China university of Geosciences, Wuhan, No.388 Lumo Road, Wuhan, China. Email: Li_bo@cug.edu.cn Huiming Tang, Faculty of Engineering, China university of Geosciences, No.388 Lumo Road, Wuhan, China. Email: tanghm@cug.edu.cnSearch for more papers by this authorHuiming Tang, Corresponding Author Huiming Tang tanghm@cug.edu.cn Faculty of Engineering, China University of Geosciences, Wuhan, China Correspondence Bo Li, School of Mechanical Engineering and Electronic Information, China university of Geosciences, Wuhan, No.388 Lumo Road, Wuhan, China. Email: Li_bo@cug.edu.cn Huiming Tang, Faculty of Engineering, China university of Geosciences, No.388 Lumo Road, Wuhan, China. Email: tanghm@cug.edu.cnSearch for more papers by this authorYu Xu, Yu Xu School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, ChinaSearch for more papers by this author Daosong Hu, Daosong Hu orcid.org/0000-0002-5118-7202 School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, ChinaSearch for more papers by this authorYang Yang, Yang Yang School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, ChinaSearch for more papers by this authorBo Li, Corresponding Author Bo Li Li_bo@cug.edu.cn School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, China Correspondence Bo Li, School of Mechanical Engineering and Electronic Information, China university of Geosciences, Wuhan, No.388 Lumo Road, Wuhan, China. Email: Li_bo@cug.edu.cn Huiming Tang, Faculty of Engineering, China university of Geosciences, No.388 Lumo Road, Wuhan, China. Email: tanghm@cug.edu.cnSearch for more papers by this authorHuiming Tang, Corresponding Author Huiming Tang tanghm@cug.edu.cn Faculty of Engineering, China University of Geosciences, Wuhan, China Correspondence Bo Li, School of Mechanical Engineering and Electronic Information, China university of Geosciences, Wuhan, No.388 Lumo Road, Wuhan, China. Email: Li_bo@cug.edu.cn Huiming Tang, Faculty of Engineering, China university of Geosciences, No.388 Lumo Road, Wuhan, China. Email: tanghm@cug.edu.cnSearch for more papers by this authorYu Xu, Yu Xu School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, ChinaSearch for more papers by this author First published: 24 December 2021 https://doi.org/10.1049/ipr2.12396AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Haze usually limits the visibility and reduces the contrast of outdoor images. The removal of haze in a single image has always been a challenging problem. Recently, many methods have been proposed to effectively remove haze in harsh conditions. However, these methods fail to balance the dehazing effect and time consumption. This paper proposes a method based on HSV colour space to restore the visibility of uniform scattering medium. It can prevent the atmospheric light and transmission from being miscalculated. This method uses the brightness component of haze image to estimate the global atmospheric light, which reduces the influence of luminescent objects on atmospheric light estimation. Then, this paper deduces the estimation model of the saturation of scene radiance based on the atmospheric scattering model. In the meantime, according to the advantages and problems of the model, the fast estimation of the transmission is realized by using the stretching function. Finally, this paper solves the parameters in the model by iterative method. Since this method can estimate different media transmission for each pixel, better results can be obtained. The simulation results show that the algorithm is superior to the existing algorithms in terms of dehazing effect and time consumption. 1 INTRODUCTION When outdoor images are taken, they are easily affected by the outdoor environment, resulting in poor visibility, which is caused by the absorption and scattering of light by particles in the atmosphere. In particular, fog and haze can hinder the light and blur the captured image, which may cause errors in vision applications due to poor contrast and colour fidelity. Therefore, image dehazing has always been a hot research topic. Numerous efforts have been made in the last few years regarding the image dehazing. In these works, researchers tried to extract fog-related information from the haze image, and use complex mathematical tools or ingenious image processing methods to achieve the restoration of the haze image. Generally speaking, these methods can be further divided into three categories according to different processing procedures. The first category is multi-image-fusion-based methods. Researchers intended to obtain multiple images at the same location based on different degrees of polarization or under different conditions, and process and merge these images to obtain a better restoration effect. Literatures [1-3] obtained multiple images in the same scene based on different degrees of polarization for image dehazing. In order to eliminate haze, multiple images of the same scene were taken under different weather conditions, and the depth information is estimated by using these images [4]. [5-7] process the input image by using the traditional image enhancement techniques to get two or more images, and then merge these images to achieve the purpose of dehazing. Although the restoration quality of these methods is good, it is difficult to meet the real-time dehazing requirements because of the need to obtain multiple images at the same location. The second category is single image dehazing. Earlier dehazing method is mainly based on image enhancement, only considering the use of image processing techniques to adjust the contrast of the haze image to achieve the purpose of dehazing [8-10], but the recovery result is limited. The main reason is that these methods do not consider the physical degradation process of the image. Later, the atmospheric scattering model is proposed to describe the atomization mechanism of the image, and various dehazing algorithms based on the model are also proposed. He et al. [11] verified that the pixel value of at least one colour channel in the non-sky region of the image has low intensity, so the concept of dark channel prior (DCP) was proposed, and the dark channel prior was used to estimate the transmission of the haze image. But in the area similar to atmospheric light, the processing effect is poor. Therefore, some later algorithms improved it [12-14]. Most methods assume that the transmission and radiance are piece-wise constant, which will lead to the problem of halo artefacts. Berman et al. [15] proposed a haze-lines model, which is based on the assumption that the colour will appear repeatedly in the natural scene, and the distance from the camera is different, so the influence of haze is different. The algorithm performs well, but it has high computational cost and will fail in the case of colour distortion. He et al. [16] proposed the use of saturation and intensity for transmission estimation. On this basis, Kim et al. [17] constructed the mapping relationship between haze image and haze-free image saturation to realize the fast estimation of transfer function. However, due to the rough stretching function, the saturation map of scene radiance will be stretched incorrectly, resulting in a failure to estimate the transmission. Zhu et al. [18] proposed a colour attenuation prior (CAP), that is, the depth of field is positively correlated with the difference between the lightness component and the saturation component of the image. Therefore, a linear model of the depth of field of the haze image is established, and the model parameters are solved by supervised learning. Zhang et al. [19] proposed a novel bright channel prior model to accurately estimate the transmission of bright areas in haze image. Finally, this paper proposes a saliency analysis strategy to refine transmission. The third category is deep-learning-based methods. Cai et al. [20] proposed the DehazeNet based on convolutional neural network for single image dehazing. By inputting the haze image, the model will calculate and output the corresponding transmission map. After that, Ren et al. [21] proposed the MSCNN model, which will first generate a rough transmission graph and then refine it step by step. Li et al. [22] proposed an all-in-one dehazing network AOD-Net, which can directly generate haze-free images from the input haze image. GFN [23] obtained three images from the original image by using white balance, contrast enhancement and gamma correction, and input them into the network to finally achieve the effect of dehazing. [24] proposed a new Multi-Scale Boosted Dehazing Network based on multi-scale fusion by combining multi-scale fusion strategy with deep learning. This method is designed based on boosting and error feedback, and better dehazing effect was obtained. Zhao et al. [25] proposed a two-stage weakly supervised dehazing framework, RefineDNet. First, this method adopts the DCP to restore visibility. Then, it refines preliminary dehazing results in the first stage. Yin et al. [26] proposed a variational image dehazing method. By creating a colour-transfer image dehazing model to remove haze obscuration and acquire information regarding the coefficients of the model by using the devised convolutional neural network-based deep framework as a supervised learning strategy. [27, 28] applied the adversarial network to the task of image dehazing. These dehazing methods based on deep learning have obtained promising results; however, the results are easily affected by the dataset. This is because in the real world, it is difficult to take both haze and haze-free images simultaneously at the same location, which leads to the unsatisfactory performance of the methods based on deep learning in real world haze images. The haze image is considered to be a combination of the haze-free image and fog. However, in the sandy weather or extreme light environment, there may be a colour veil. In recent years, more and more authors have begun to consider how to remove the colour veil. [17] proposed a new white balance method to remove the colour veil. In [36], the atmospheric illuminance prior (AIP) is applied to the removal of colour veil, and this method can be used as image preprocessing. Berman et al. [31] proposed that the Gray-World assumption prior can meet the needs of colour veil removal. However, for haze images, the colour veil does not necessarily exist. Therefore, we need to judge and process the obtained images. In summary, the existing methods mostly focus on obtaining higher restoration quality, ignoring the overall processing efficiency, and are unsuitable for vision systems that require high real-time performance. Generally, The method based on saturation is considered to be one of the best dehazing methods because of its simplicity and rapidity. But it also has some problems. For example, due to incomplete estimation of the transmission in CAP, the demisting intensity is weak. In [17], the rough stretching function will lead to the unsatisfactory estimation of transmission. Therefore, it is urgent to solve these problems. To solve these problems, we propose a fast estimation method of transmission based on image saturation and brightness. The flowchart of proposed method is shown in Figure 1. Firstly, atmospheric light is estimated on the brightness component of haze image, and we judged and removed the colour veil based on the set atmospheric light colour shift coefficient. Then, the saturation map of scene radiance is derived based on the atmospheric scattering model. Next, the transmission is derived pixel by pixel. Finally, we can recover haze image by estimating atmospheric light and transmission. FIGURE 1Open in figure viewerPowerPoint The flowchart of the proposed method Our contributions can be summarized as three-folds: We propose an atmospheric light estimation method based on blocks, which can effectively reduce the interference of light-emitting objects on atmospheric light estimation. Simultaneously, we define the colour shift coefficient based on atmospheric light, which can quickly and accurately determine whether there is a colour veil in the haze image. We obtain a saturation map estimation model of scene radiation. This model reasonably establishes a relationship between haze image and dehaze image to prevent it from being overestimated. We extract the estimation function of transmission based on the above model. We considered the relationship between the regional intensity value and the haze concentration, and constructed a reasonable adjustment function to enhance the quality of the restored image. The structure of this paper is as follows. Section 2 introduces the theoretical background of this paper. Section 3 specifically discusses the proposed method of improved transmission estimation based on CAP. Section 4 provides complete experimental results for comparison with the latest methods. Section 5 is the conclusion. 2 RELATED WORK 2.1 Atmospheric scattering model In computer vision analysis, atmospheric scattering model is widely used to describe fogging mechanism as shown in Figure 2. From [29], The haze image received by the camera through scattering media can be expressed as follows I ( x ) = J ( x ) t ( x ) + ( 1 − t ( x ) ) A , (1)where I ( x ) is the haze image, J ( x ) is the haze-free image, A is the atmospheric light, t ( x ) is the transmission, whose physical meaning is the proportion of light that can reach the detection system through particles attenuation, that is t ( x ) = e − β d ( x ) , (2)where β is the scattering coefficient, which is related to the wavelength of light, and d ( x ) is the scene depth. FIGURE 2Open in figure viewerPowerPoint Atmospheric scattering model The purpose of dehazing is to solve J ( x ) through the model. For this model, t ( x ) and Aare unknowns. Therefore, the essence of the dehazing method based on atmospheric scattering model is to estimate the transmission t ( x ) and atmospheric light A. 2.2 Dark channel prior When the atmospheric light is given, according to (1), the normalized results can be obtained by dividing both sides of the atmospheric scattering model by the atmospheric light, namely I c ( x ) A c = t ( x ) J c ( x ) A c − t ( x ) + 1 , c ∈ { r , g , b } . (3) He et al. [11] found that in the non-sky region of image, there is always a certain pixel value that is very low. Based on this, he proposed the concept of dark channels as J d a r k ( x ) = min y ∈ Ω ( x ) ( min c J c ( y ) ) ≈ 0 , (4)where Ω ( x ) is a local patch centred on x, J c is the one colour channel of J, and J d a r k is known as the dark channel map. Then combining DCP and (1), the estimated function of the transmission can be obtained as t ( x ) = 1 − min y ∈ Ω ( x ) min c I c ( y ) A c . (5) 2.3 Colour attenuation prior According to experimental findings, Zhu et al. [18] found that the image depth of scene is positively correlated with the difference between brightness and saturation components, namely d ( x ) = θ 0 + θ 1 × v ( x ) + θ 2 × s ( x ) + ε ( x ) , (6)where θ 0 , θ 1 , θ 2 are linear coefficients, ε ( x ) is a random variable representing the random error of the model, d ( x ) is depth of scene, v ( x ) is brightness component of the image, s ( x ) is saturation component of the image. Due to the existence of haze, the channel values of each pixel in the image tend to be the same, that is, the saturation tends to be zero. In (6), when s ( x ) = 0 and v ( x ) ∈ ( 0 , 1 ) , we find that d ( x ) is in the range of (0,1). In (2), d ( x ) ∈ ( 0 , ∞ ) , that is, d ( x ) = 0 represents the closest distance to the camera, and d ( x ) = ∞ is the opposite. Therefore, when β = 1 , for the situation in (2), e − β d ( x ) is a complete mapping in the range of (0,1). However, in CAP, when d ( x ) ∈ ( 0 , 1 ) , e − β d ( x ) is not a complete mapping in the range of (0,1), so the effect of dehazing is not complete. 2.4 Dehazing based on saturation In the estimation of transmission of DCP, J dark ( x ) ≈ 0 . However in actual situations, the dark channel value is not zero. He et al.[16] proposed a transmission estimation method based on image saturation and intensity. Assuming that the transmission between pixels is different, take the minimum of both sides of (3) at the same time to get m I n ( x ) = m J n ( x ) t ( x ) + 1 − t ( x ) , (7)where m I n ( x ) = min c I c ( x ) A c , m J n ( x ) = min c J c ( x ) A c . From (7), it can be derived that t ( x ) = 1 − m I n ( x ) 1 − m J n ( x ) . (8) Let S K ( x ) is the saturation component of a given image K. It is defined as follows S K ( x ) = 1 − m K ( x ) I K ( x ) , (9)where m K ( x ) = min c ∈ { r , g , b } K c ( x ) , I K ( x ) is the intensity component of a given image K. By combining (8) and (9), t ( x ) is obtained as t ( x ) = I I n ( x ) ( 1 − S I n ( x ) ) I J n ( x ) ( 1 − S J n ( x ) ) , (10) where S I n ( x ) is the saturation of I ( x ) normalized by A, and S J n ( x ) is the saturation of J ( x ) normalized by A. From (3), we take the intensity component of I ( x ) A and J ( x ) A at the same time, we can get I J n ( x ) = I I n ( x ) − 1 t ( x ) − 1 . (11) Then, we substitute (11) to (10), the result of t ( x ) can be obtained as follow t ( x ) = 1 − I I n ( x ) ( 1 − S I n ( x ) S J n ( x ) ) . (12) Kim et al.[17] established a simple quadratic function based on the rough condition of S J n ( x ) ≥ S I n ( x ) , and estimated S J n ( x ) using S I n ( x ) of haze image. Finally, the fast estimation of transmission is realized by (12). However, this rough condition will cause some uncertainty. 3 PROPOSED METHOD 3.1 Atmospheric light estimation The estimation of atmospheric light is usually realized based on the scene depth estimation. Based on the observation experiment, this paper proposes a block-based atmospheric light estimation method. According to practical experience, the deeper regions in the image are usually greatly affected by fog. In other words, with the increase of scene depth, the haze contribution also increases, which will lead to the increase of pixel brightness in the distance. The brightness change of the section of haze image is shown in Figure 3. It can be found that haze contributes the most to the distant scenery. Inspired by this experimental observation, it can be said that in the deeper region, the pixel value gradually increases to the high brightness side, and the increase will be gentle in the region, as shown in the green circle in Figure 3. However, because of the high brightness objects that may exist in the image, the brightness of low-haze and medium-haze areas are also high, as shown in the blue circle in Figure 3. This situation will affect the atmospheric light estimation, so we propose a block-based atmospheric light estimation method. The steps of this method are as follows, A ∼ = min ξ ∈ Ω ( x ) I v ( ξ ) , (13)where A ∼ is the candidate atmospheric light map, v is the brightness component of haze image in the HSV colour space, I is haze image, Ω ( x ) is a 5 × 5 block in position x.Next, we need to refine candidate atmospheric light maps A ∼ . We choose the top 1 % of brightest pixels from A ∼ , that is, A ∼ m = max i = 0.01 × N A ∼ i , (14)where N is the number of nonzero pixels in A ∼ . A ∼ m is the top 1 % of brightest pixels from A ∼ . FIGURE 3Open in figure viewerPowerPoint Brightness variation of haze image with scene depth According to the above analysis, we find that there are often bright objects in the image, and when these objects are in haze image, the brightness is usually higher than that of atmospheric light. Based on this, we obtain the final step of atmospheric optical estimation method as follows, A = m e a n ( min i = 0.2 × M A ∼ m ) , (15)where M is the number of nonzero pixels in A ∼ m , Ais the atmospheric light for the haze image. The experimental results are shown in Figure 4. Our method can effectively find the atmospheric light value. FIGURE 4Open in figure viewerPowerPoint Flow chart of atmospheric light estimation 3.2 Colour veil Generally, in atmospheric light estimation, it is assumed that all atmospheric lights are similar, because fog has no colour. However, in actual situations, colour veil will appear due to the influence of yellow dust or some special light colours. Therefore, this paper uses the atmospheric light estimated by the proposed method to judge whether the image contains colour veil. We define the light colour shift coefficient Δ as follow Δ = max ( A ) − min ( A ) 255 , (16)where A is the atmospheric light of haze image. max ( · ) represents the largest channel value in the RGB space, and min ( · ) is the lowest channel value. Then we define Δ 0 as the indicator of colour distortion. In this paper, we set the bar Δ 0 = 0.15 . If Δ > Δ o , we think that the haze image has colour veil. If Δ < Δ o , there is no colour veil. The colour veil can be reduced to image dehazing, so we need to remove it. In particular, we find that the Gray-World assumption prior [31] to work well for our needs. The method is illustrated in Figure 5. The proposed method can judge whether there is a colour veil in the haze image. At the same time, the Gray-World assumption prior can correct the haze image better. FIGURE 5Open in figure viewerPowerPoint Example of a haze image with color veil and its color correction by Gray-World assumption prior. (a) Haze image, (b) the atmospheric light of veil image and (c) corrected image 3.3 Transmission map estimation In this section, in HSV colour space, we can easily find out another solution of transmission map. Due to the ease of solution, we assume that A is a global air light constant. Firstly, let S K ( x ) is the saturation component of image K, which is defined as S K ( x ) = 1 − m K ( x ) v K ( x ) , (17)where m K ( x ) is the minimum value of image K in the colour channel at position x. v K ( x ) is the brightness of the image K at position x, that is, v K ( x ) = max c ∈ { r , g , b } K c ( x ) . (18) By combining (3), (8) and (17), t ( x ) is obtained as t ( x ) = 1 − v I n ( x ) 1 − S I n ( x ) S J n ( x ) , (19)where S I n ( x ) and v I n ( x ) is the saturation and brightness of I ( x ) normalized by A. S J n ( x ) is the saturation of J ( x ) normalized by A. There are only two unknown variables S J n ( x ) and t ( x ) . Once we can obtain S J n ( x ) , t ( x ) also can be estimated. 3.4 Saturation map estimation The aim in this section is to find out the relationship between the saturation map of haze image and scene radiance. Using (2), (19) can be rewritten as e − β d ( x ) = 1 − v I n ( x ) 1 − S I n ( x ) S J n ( x ) . (20) By combining (6) and (20), S J ( x ) is obtained as S J ( x ) = S I ( x ) 1 − 1 − e − β ( θ 0 + θ 1 × v I ( x ) + θ 2 × S I ( x ) + ε ( x ) ) v I n ( x ) . (21) Equation (21) needs to be simplified in order to reduce the computational cost of S J ( x ) . Based on 4322 real haze images from RTTS dataset, the average brightness v I ( x ) and the normalized average brightness by atmospheric light v I n ( x ) are calculated, and the statistical results are shown in Figure 6. FIGURE 6Open in figure viewerPowerPoint Average brightness distribution: (a) average brightness v I ( x ) and (b) the normalized average brightness by atmospheric light v I n ( x ) Figure 6 indicated that both distributions obey the normal distribution. Through data fitting, the expected brightness is v I ( x ) ¯ = 0.579 , v I n ( x ) ¯ = 0.709 . Substituting the expectation into (19), the final estimation of S J ( x ) is obtained as S J ( x ) = S I ( x ) 1.42 e α 0 S I ( x ) − α 1 − 0.42 , (22)where α 0 , α 1 are adjustment parameters, α 0 = − β ( θ 0 + θ 1 × v I ( x ) ¯ + ε ( x ) ) , α 1 = − β θ 2 . The result of this estimation satisfies S J ( x ) ≥ S I ( x ) , which is shown in Figure 7. FIGURE 7Open in figure viewerPowerPoint Estimation model of the saturation of scene radiance (proposed: α 0 = 0.24 , α 1 = 0.24 ) The comparison results of the two methods are shown in Figure 8. We can find that due to the existence of haze, the edge details of the image become blurred. [17] uses quadratic function to estimate the saturation map of scene radiance to produce an overestimation phenomenon, owing to excessive stretching, resulting in the disappearance of skirt folds. The method in this paper reasonably quantified the estimation function, so that the edge details were retained as much as possible. At the same time, it also sacrificed a little brightness. Therefore, we will optimize the problem next section. FIGURE 8Open in figure viewerPowerPoint Analysis of saturation map estimation method (proposed: α 0 = 0.24 , α 1 = 0.24 ) 3.5 Brightness restoration In this section, we will optimize the above problems. By combining (19) and (22), inspired by He et al.[16], we introduced an adjustment factor φ. Then t ( x ) is obtained as t ( x ) = 1 − φ 1.42 v I ( x ) ( 1 − e α 0 S I ( x ) − α 1 ) A , (23)where φ is a fitting coefficient which can be used to adjust the brightness of saturation map, and affected by the haze changes. Due to the existence of fog, the pixel values in each channel of image tend to be equal, that is, the saturation approaches zero. Figure 9 gives the relationship between the scene depth and brightness, when S ( x ) < 0.02 . According to Figure 9 and Zhu et al. [18], when the value of S ( x ) is very small, S ( x ) is the constant 0 by default, so that the scene depth d ( x ) ∝ v ( x ) is obtained. Combined with (2), if d ( x ) → ∞ , then t ( x ) → 0 , and if d ( x ) → 0 , then t ( x ) → 1 . According to the properties of exponential function, we can find out 1 − t ( x ) > v I ( x ) always holds. At the same time, in (23), when S ( x ) is a constant, only φ and v I ( x ) are variables, that is, φ · v I ( x ) > v I ( x ) always holds. Therefore, we redefine the adjustment function as E ( x ) = 1 − e − k x 1 + e − k x , (24)where E ( · ) is the adjustment function and k is the adjustment coefficient, the function is shown in Figure 10, and this function helps adjust brightness. The final transmission estimation function is obtained as follows t ( x ) = 1 − 1.42 E ( v I ( x ) ) ( 1 − e α 0 S I ( x ) − α 1 ) A , (25)where E ( v I ( x ) ) = 1 − e − k v I ( x ) 1 + e − k v I ( x ) . FIGURE 9Open in figure viewerPowerPoint The relationship between the scene depth and brightness, when S ( x ) < 0.02 : (a) haze image and (b) shows the brightness change of (a) at the red line position with the change of the scene depth FIGURE 10Open in figure viewerPowerPoint Adjustment function In this way, the saturation S I ( x ) and the brightness v I ( x ) of haze image can be used to calculate transmission quickly, and the transmission is a complete mapping within the range of (0,1). Finally, the h