Single image dehazing via self-constructing image fusion

Signal Processing 167 (2020) 107284

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Signal Processing journal homepage: www.elsevier.com/locate/sigpro

Single image dehazing via self-constructing image fusion Yin Gao a, Yijing Su a, Qiming Li a, Hongyun Li b, Jun Li a,∗ a b

Quanzhou Institute of Equipment Manufacturing, CAS, Quanzhou, China Quanzhou Institute of Technology, Quanzhou, China

a r t i c l e

i n f o

Article history: Received 25 June 2019 Revised 8 September 2019 Accepted 9 September 2019 Available online 10 September 2019 Keywords: Image dehazing Self-constructing Adaptive boundary constraint Selective sift flow multi-exposure fusion

a b s t r a c t Haze usually degrades the visibility of outdoor images and decreases their visual quality. Previous techniques are not sufficient enough to deal with dehazing problem by using various hand-crafted priors or supervised training on paired manners. In this paper, we propose a self-constructing image fusion method for single image dehazing, which does not rely on the accuracy of global atmospheric light and transmission map. Hence, the proposed method can avoid some visual problems, such as undesirable brightness perception, unsatisfied halo artifacts and edge blur in sky regions or bright objects in dehazed images. To produce several self-constructing images with different exposures, a novel segmentation method is exploited to capture the range of global atmospheric light approximately, and a new adaptive boundarylimited L0 gradient optimization method is employed to optimize the transmission map. An adaptive selective SIFT flow multi-exposure fusion method is constructed by applying the two-layer visual sensory selector. Extensive experimental results on both synthetic and real-world images demonstrate that the proposed algorithm performs favorably against the state-of-the-art algorithms in terms of no-reference and full-reference image quality. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Haze often occurs when water vapours, dust or other particulates accumulate in a stable atmosphere [1]. Due to the effect of light scattering, images of distant subject acquired in haze would suffer from loss of image contrast and color cast. This would pose an additional challenge to computer vision-based systems such as outdoor surveillance, intelligent transportation and topographic survey [2]. Hence, dehazing is an important problem being actively addressed by the research community. Image dehazing is ill-posed as it involves many unknowns [3]. Dehazing based on a single image is more challenging due to limited input information [2,4–13]. Global atmospheric light and transmission map are two major factors in image dehazing based on the atmospheric scattering model [5,6,14]. The former determines the brightness perception of the dehazed image, and the latter one decides whether there are halo artifacts, edge blur or hazy remains in the dehazed image. Most of existing methods can be divided into two categories: prior-based methods and learning-based methods. The former ones use prior knowledge to estimate global atmospheric light or transmission map, such as dark channel prior method [4,15] and color prior method [8,10,16,17]. However, these ∗

Corresponding author. E-mail addresses: [email protected] (Y. Gao), [email protected] (Y. Su), [email protected] (J. Li). https://doi.org/10.1016/j.sigpro.2019.107284 0165-1684/© 2019 Elsevier B.V. All rights reserved.

priors can be easily violated in practice, especially when the scene is complex or contains irregular illumination. For instance, dark channel prior does not hold in regions with a brightness similar to the atmospheric light. This usually leads to undesirable brightness loss in dehazed image. On the other hand, when dealing with the overexposed hazy images, these color-based prior methods can’t remove the haze completely. Recently, learning-based methods, in particular, deep networks are proposed to address the dehazing problem. Most of these studies use machine learning algorithms to estimate the transmission map or global atmospheric light from input image [7,9,13,18]. These methods rely on the accurate global atmospheric light and transmission map. Moreover, big data sets are required to learn a large amount of parameter in the model, and the performance of these systems rely heavily on the quality of the dataset. However, lacking mated image pairs (haze image and the corresponding hazefree image), most of existing methods use synthetic hazy images as training data which would result in undesired haze artifacts. In this paper, we propose a novel dehazing method that does not explicitly estimate the transmission map and atmospheric light. The method is built on a fusion strategy which aims to selectively blend several self-constructed images by preserving only the high visual qualities regions. Firstly, the range of the global atmospheric light can be approximately estimated by the novel statistical experiment and histogram analysis of sky regions in hazy images. Then, the transmission maps are optimized effectively

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through the new adaptive boundary-limited L0 gradient optimization method. Finally, a satisfied dehazing image is obtained by a self-constructed image fusion method. More specifically, our contributions are: •

•

•

A novel method is proposed to estimate the range of the global atmospheric light instead of a value to construct several images with different exposures and solve the brightness distortion problem. A new adaptive boundary-limited L0 gradient optimization method is proposed to improve the accuracy of the transmission map. An adaptive selective SIFT flow multi-exposure fusion method is further constructed to improve the visual effects of image dehazing.

The rest of this paper is organized as follows: In Section 2, a brief overview of related work is provided. The proposed method is described in Section 3. Experimental results are presented and discussed in Section 4. Finally, the conclusions are given in Section 5. 2. Related work Existing dehazing methods can be divided into three categories: hand-crafted prior-based methods, learning-based methods and multi-scale image fusion methods. The hand-crafted prior-based method originates from the atmospheric scattering model [1]. Depth information of input image is required in this model, which limits the development of this model because of the high computational complexity. Afterward, different image priors have been explored for single image dehazing [19,20]. He et al. presented a dark channel prior (DCP) for outdoor images [4], which assumed that the local minimum of the dark channel of a haze-free image was close to zero. Several methods were proposed to improve the efficiency and quality of DCP algorithm [21,22]. Zhu et al. [23] proposed a linear model to represent the scene depth of hazy images based on a color attenuation prior, and learned the parameters of the model in a supervised manner. Fattal [17] discovered that pixels of image patches typically exhibit a onedimensional distribution, which could be used to recover the scene transmission map. Berman et al. [8] assumed that the colors of a haze-free image were well approximated by a few hundred distinct colors, which formed tight clusters in the RGB space. Recently, Bui et al. [10] statistically analyzed haze pixel clusters in RGB space and constructed color ellipsoid geometry color ellipsoids to calculate the transmission map. However, these methods are still based on hand-crafted features, and may perform poorly especially when the assumptions are insufficient to describe real-world images. Learning-based methods [6,7,18,24,9,13,2,25,26,27,28] can be divided into two categories: single-model optimization method and multi-model optimization method. The former optimizes only one of the major factors which affect the visual dehazing effect. To estimate transmission map, some methods [6,7,18,24,9,27] replace the guided image filtering [5] with random forest, DehazeNet, coarsescale network, deep neural network, all-in-one dehazing network, ranking convolutional neural network, respectively. However, these methods ignored the influence of global atmospheric light, which could lead to the unsatisfactory effect of dehazing images. In order to include more factors affecting the visual dehazing effect into consideration, the multi-model optimization method was proposed to model unifiedly for image dehazing. Zhang et al. [13] constructed pyramid densely connected transmission map estimation network and a global atmospheric light estimation network respectively to restore hazy images by using the DCP-based method. For the purpose of getting rid of the prior limitation of DCP model, Zhang et al. [2] proposed a perceptual pyramid deep network to directly estimate hazy free image from the original hazy images.

To solve the paired dependency problem, Engin et al. [25] presented a cycle-dehaze for single image dehazing problem. More recently, Wang et al. [28] proposed an atmospheric illumination priori network through extensive statistical experiments for haze removal. Different from these hand-crafted prior-based methods, most learning-based methods require accurate parameters of the atmospheric scattering model during the training phase, and have also relied on a prior model. Therefore, when using these arguably trained model to deal with these partial overexposure natural hazy images not in the training data set, these learning-based methods may suffer from model failure. In order to solve these undesired haze artifacts, a fusion principle has been introduced into image dehazing. Ancuti et al. [29] constructed two input images by a white balance and a contrast-enhancing procedure and then fused the two corresponding maps with a multi-scale scheme. Due to the insufficient fusion objects and the inaccurate global atmospheric light, the method suffers from an unsatisfactory visual sense. Galdran et al. [30] proposed a fusion-based Variational method via the minimization of two energy and a fusion scheme for image dehazing. However, the method only uses the enhanced variational image dehazing (EVID) iterating optimization. This results in partial removal of haze. Gao et al. [31] presented a new image dehazing method by a multi-focus fusion approach. This method avoids the interference of the global atmospheric light, but it blends all the input images which increase the time-consuming. Galdran [11] constructed multiple images with different exposure levels via artificial gamma correction, and fused these images through a multi-scale Laplacian blending scheme for image dehazing. This method can avoid interference factors affecting the visual dehazing effect, but it is insufficient to obtain multiple images with different exposure levels by adopting the artificial gamma correction method, and may appear excessive local contrast for haze removal. In summary, to our knowledge, no self-constructed fusion dehazing method with the range of the global atmospheric light has been published in the literature. While these fusion methods have been used for individual modules of a latent image dehazing, their performance has increased the computational complexity due to fuse all input images. Even the number of available fusion dehazing method is limited. In recent fusion-based dehazing literatures, these methods achieve better visual effects though neutralizing the interference visual factors to some extent. The proposed method selectively fuse these self-constructed images for decreasing the computational complexity and optimal visual effects with a minimum number of images. Although our method uses the DCP theory to obtain several initial dehazing images, we make up for the lack of global atmospheric light accuracy estimation and transformation map optimization. 3. Proposed method A framework of the proposed method is given in Fig. 1. The first step is the sky segmentation. It is a pre-processing step performed for estimating the global atmospheric light. Subsequently, to properly optimize the transmission map, a new adaptive boundary constraint smoothing method (ACS) is applied to the hazy image in the different global atmospheric light. Finally, we use a new selective image fusion method to obtain the final dehazed image after the classical atmospheric scattering model processing. 3.1. Atmospheric scattering model In the field of computer vision and graphics computing, the atmospheric scattering model [5,6] is usually represented as:

I (x ) = J (x )t (x ) + A(1 − t (x ) ),

(1)

Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284

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Fig. 1. A framework of our method.

where I(x) denotes an observed or received image from a camera. J(x) denotes image without haze. t(x) is the transmission map describing the portion of the light that is not scattered and reaches the camera. A represents the global atmospheric light. J(x)t(x) is direct decay, which describes the attenuation of the reflected light caused by the scattering in the medium. A(1 − t (x ) ) indicates the atmospheric optical shifted component. In the model, transmission map t(x) in Eq. (1) can be refined with the Guided Image Filtering [5].

⎧ ⎨t (x ) = 1 − ω · Imin (x ) ⎩Imin (x ) = c∈min {r,g,b}

min Ic (y )/A



,

(2)

y∈(x )

Ic (y) is the pixel intensity of channel c ∈ {r, g, b} in the RGB image. ω [0, 1] is an adjustment parameter that controls the residual amount of haze after dehazing and is set as 0.95. Substituting the value of t(x):

J (x ) = (I (x ) − A )/ max (t (x ), t0 ) + A,

(3)

where t0 is the lower bound of the transmission map t(x), and is set as 0.1. Then A is computed as A = max(I (x ) ) ∗ 0.1 %.

filter function. h and σ are the sizes of the filter and standard deviation, h and σ are set as 3, 0.5, respectively. mc = max( fc (x ) ). fl ( · ) represents the dichotomy method for solving the histogram of the corresponding smoothing image. The upper threshold au of the range of segmenting the sky region in a hazy image can be defined as:

au = max (ordf ilter (Ic (x ) ) ),

(5)

c [r,g,b]

where ordfilter( · ) is the minimum filter processing for a hazy image(filter window 3 × 3 pixels). After solving the lower and upper threshold of the range of segmenting the sky region in a hazy image, we can effectively segment the sky region of a hazy image. Therefore, the effective range of global atmospheric light is described as [Amin , Amax ]:

Amin =

min ({ad , au } ), Amax = max ({ad , au } ),

c [r,g,b]

(6)

c [r,g,b]

where Amin is the lower threshold of the effective range of global atmospheric light. Amax is the upper threshold of the effective range of global atmospheric light, An = Amax − Amin + 1. Fig. 2 show a few pairs of hazy image and sky segmentation results. In Fig. 2, if the sky region is set as B, then pixels of B are in [Amin , Amax ].

3.2. Estimation of the effective range of global atmospheric light In classical DCP model, the global atmospheric light is assumed to be known, and its value is set as max(I(x))∗ 0.1 %. But there are many uncertainties for the global atmospheric light artificial setting in different scenes. For example, the highly reflective regions in the dehazed image are included in the range of global atmospheric light. Misleading value can produce local overexposure or halo artifacts in the final dehazing result. To solve the problem, we estimate the effective range of global atmospheric light instead of a single value. As sky region generally has a small gradient and pixel values tending to concentrate in a certain range, we segment hazy images into the sky and non-sky region by the dichotomy method for the histogram of the hazy image. The lower threshold ad of the global atmospheric light can be solved as follows:



fc (x ) = Ic (x ) ∗ g(x )h,σ ad = argmax(x| fl ( fc (x ) ) ), c{r, g, b} ,

3.3. The transmission map optimization The classical method of getting dark channel image is mainly based on the three-channel maximum value method. However, the abrupt sawtooth effect in the edges of the dark channel image leads to halo artifacts in the dehazed image. In order to solve the problem, we use the radiance cube definition to get a relatively smooth dark channel image. We describe this dark channel image as the initial transmission map. According to radiance cube definition, a pixel in I(x) contaminated by haze will be “pushed” towards the global atmospheric light A in Eq. (1). As a result, we can reverse this process and recover the clean pixel J(x) by the linear extrapolation method from A to I(x) [10]. Therefore, we define an adaptive boundary constraint of an arbitrary haze image with initial translation as:



(4)

x [0,mc )

where ad describes the lower threshold of each channel of segmenting the sky region in a hazy image. g(x)h, σ is a Gaussian

t˜i (x ) = min

i [1,An ]



max

c [r,g,b]

Ai − Ic (x )↓n Ai − Ic (x )↓n , Ai − C0c (x ) Ai − C1c (x )



,

(7)

where t˜i (x ) is the initial transmission map estimation in each global atmospheric light A. C0c (x ) and C1c (x ) are the interval values

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Fig. 2. Sample of sky region segmentation results. Source: (a), (c), (e) The hazy images. (b), (d), (f) The corresponding segmentation results.

Fig. 3. Results of the transmission map optimization by different methods. Source: (a) The hazy image. (b)-(c) The dark channel image and the optimized transmission map by He et al. [4]. (d)-(e) The boundary constraint image, the optimized transmission map by Meng et al. [32]. (f)-(g) Our adaptive boundary constraint image and refined transmission map. (h) Our dehazing result.

that are relevant to color channel pixel. To achieve optimal stretching for low brightness and high brightness areas in a hazy image, we adopt a piecewise stretching method.

⎧ c c ⎪ ⎨D0c (x ) − 100, D0 (x ) ≥ c100 D0 (x ) − 60, 100 > D0 (x ) ≥ 60 C0c (x ) = , c 60 > Dc0 (x ) ≥ 30 ⎪ ⎩D0c (x ) − 30, c D0 (x ), D0 (x ) < 30  c D1 (x ), Dc1 (x ) ≥ 230 c c C1 (x ) = D1 (x ) + 50, 230 > Dc1 (x ) ≥ 180 , Dc1 (x ) + 70, Dc1 (x ) < 180

(8)

(9)

where Dc0 (x ) represents the minimum value of the color channel pixel, Dc0 (x ) = min (Ic (x )↓n ). Dc1 (x ) represents the maximum c [r,g,b]

value of color channel pixel, Dc1 (x ) = max (Ic (x )↓n ). ↓n is the c [r,g,b]

downsampling operator and is down-scaled by a factor of 0.5. Image scaling has a spatial smoothing effect on the image and can reduce computational complexity. To properly optimize the transmission map, the hazy image is down-scaled before smoothed with the new adaptive boundary constraint. Ai contains some values getting by Eq. (5). To suppress the light halo problem and maintain major edges for the transmission map, we introduce a new smoothing method to optimize the transmission map via L0 gradient minimization [33]. In 2D image representation, the transmission map t˜i (x ) in Eq. (7) can be refined by:





ti (x ) = L0 t˜i (x ) , i [1, An ],

(10)

where L0 ( · ) is the image smoothing method via L0 gradient minimization. ti (x) is the transmission map with the new image smoothing method in each global atmospheric light Ai . We give an example to illustrate the promotion made by our method in Fig. 3. As can be seen in Fig. 3(c) and (e), these transmission maps lost the clear edges using He et al. [4] and Meng et al. [32]. Our refined transmission map can smooth the abrupt sawtooth effect for sky regions and its dehazing result can achieve better visual effects in Fig. 3(h).

3.4. The new selective sift flow image fusion In Section 3.2, we estimate the range of the global atmospheric light. The rough estimation of the global atmospheric light has a certain deviation from the image brightness. In order to effectively solve the influence of this deviation on the image visibility, we propose a selective image fusion method based on scaleinvariant feature transform (SIFT) flow. The fusion method relies on the two-layer visual sensory selector to adaptively select these self-constructing images with different exposures. According to the first layer visual sensory selector, we choose the assessment values of these initial dehazed images Ji (x). And then, we rank these values in the descending order and optimize these unsatisfied lowranking images. Finally, we use the second layer visual sensory selector to select these optimized results Ji (x ) via the 3σ criteria and fuse these chosen dehazed images Jˆi (x ) via the characteristics of the SIFT flow to get the final dehazed image J˜i (x ). In Eq. (3), by substituting Ai and ti (x) in the equation, Ji (x) can be represented as:



Ji (x ) = (I (x ) − Ai )/ max



ti (x )↑n , t˜0

λ

+ Ai , i [1, An ],

(11)

where Ji (x) is an initial dehazing result with different Ai and ti (x), and i has a value of 1, 2, 3. λ is an adjustable parameter in the range of [0 1]. t˜0 is the lower bound of the transmission map ti (x). ↑n is the upsampling operator, which is to get the same size of the original image t(x). λ and t˜0 are set as 0.85, 0.001, respectively. To creat better visual effects, the new selective fusion method is employed to improve the image quality. The selective fusion measure is expressed as:

J˜(x ) = SF (Ji (x ) ), i [1, An ],

(12)

where J˜(x ) represents a final dehazed image obtained by our new fusion method. SF represents a new selective SIFT flow fusion method, which is described in Fig. 4. For the new selective fusion method via SIFT flow, we will describe in more detail in the following sections. Inspired by Zhu et al. [34], we design a two-layer visual sensory selector to adaptively select these self-constructing images with different

Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284

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Fig. 4. Flowchart of selective SIFT flow fusion.

exposures. First, we construct the first layer visual sensory selector to choose these initial dehazed images, which can be written as:

Vi (x ) = E (Ji (x )↓n ), i [1, An ],

(13)

where Vi (x) is the assessment values of the initial dehazing results. E(x) is the image quality assessment computing [35]. When the value of Vi (x) is larger, the visual effect of the result is better.↓n is the downsampling operator to speed up the processing, which is set as 1/4 of the initial dehazing result Ji (x). Once the first layer visual sensory selector is designed, we can rank these assessment values of the initial dehazing results. By analyzing these values, we find that half of these dehazing results have an unsatisfied visual effect. To optimize the choice values of Vi (x), these unsatisfied images need to be improved via the LIME method [36]. The optimization process can be described as:

Ji (x ) =

 r



L Ji (x ) , Jir (x ),

i [1, An /2] , i (An /2, An ]

(14)

where Jir (x ) is the unsatisfied visual dehazing result through ranking these assessment values Vi (x). L( · ) is the optimization process using the LIME method. Ji (x ) is the final optimized result. To illustrate the effect of selective fusion processing, we set an example to show this in Fig. 5. As can be seen in Fig. 5, the dehazing result has better visual effect for the actual scene via selective fusion method. To choose the final images to be fused, we design second layer visual sensory selector via the 3σ criteria. We again use the image quality assessment for these final optimized results to compute the assessment values Vi (x ), Vi (x ) = E (Ji (x )↓n ). After that, in order to ensure the promising visual effect of dehazing result J˜i (x ) remains stable between different scenes, we use the 3σ criteria to choose them as:



Wi (x ) =

1, 0,

i f Vi (x ) > μ0 + σ0 , otherwise

(15)

where μ0 is the mean value of the assessment values of the dehazing results Vi (x ). σ 0 is the variance of the assessment values of the dehazing results Vi (x ). Wi (x) describes the sifts coefficient. When

the values of Vi (x ) is within the interval [μ0 + σ0 , max(Vi (x ))], the different degrees of exposure images are completely included in these results, moreover, the visual effect of initial dehazing results gradually become better with the Vi (x ) increasing. The final selective images to be fused can be expressed as:

Jˆi (x ) = Vi (x ) · Wi (x ), i [1, Aq ],

(16)

where Jˆi (x ) is the final selective dehazing images for the image fusion. Aq is the number of final selective dehazing images to be fused, which is calculated by the Vi (x ) within the interval [μ0 + σ0 , max(Vi (x ) )]. The dense SIFT map is used to extract the local contrast information in multiple source images [37]. Due to the difference of these final dehazed images Jˆi (x ) in exposure, we can use the prominent character of the dense SIFT maps to fuse these final selective dehazed images Jˆi (x ) and obtain the final dehazing fusion result J˜(x ). The dense SIFT maps can be defined as:

DSi (x ) = DSIF T (Gi (x ) ),

(17)

DSi (x )

where is a dense SIFT map. DSIFT( · ) denotes the operator which aims to calculate the unnormalized dense SIFT map for an input image. Gi ( · ) describes the gray processing for the final selective dehazed images Jˆi (x ), Gi (x ) = Gray (Jˆi (x ) ). The grayscale information describes the exposure of pixels in the final selective dehazed images. The dense SIFT map denotes the local contrast information in multiple source images. Therefore, we propose a dual weight method which combines the local contrast weight Lci (x ) and exposure quality weight LBi (x ) to obtain the fusion weight of the dehazed image. Since all the pixels in a dense SIFT map are not negative, the activity level map of Gray (Jˆi (x ) ) can be represented as the l1 norm of DSi (x ) at each pixel. The local contrast weight is expressed as:



Lci (x ) =

1, 0,



DLi (x ) = max DLi (x ) , otherwise

(18)

where DLi (x ) denotes the l1 norm of DSi (x ), DLi (x ) = DSi (x )1 . Lci (x ) describes the local contrast weight of the DLi (x ).

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Fig. 5. Results of the fusion component and final images to be fused. Source: (a) The hazy image. (b) The histogram of image quality assessment Ji (x). (c) The histogram of image quality assessment Ji (x ). (d)–(k) The final selective images to be fused Jˆi . (l) Our result.

The exposure quality weight LBi (x ) can be described as:



LBi (x ) =

α < Gi ( x ) < 1 − α

1, 0,

otherwise

,

(19)

where LBi (x ) = 1 denotes the corresponding pixels of the image Gi (x) have a good exposure. α is the range of exposure. If the value of α is between [0,1], it denotes an acceptable exposure on the fusion image, otherwise represents overexposure or underexposure on the fusion image. α is set as 0.1. According to solving the local contrast weight Lci (x ) and exposure quality weight LBi (x ), we obtain the fusion weight of the dehazed image, which is expressed as:

WiL (x ) = Lci (x ) × LBi (x ),

(20)

WiL (x )

where is the initial fusion weight of the dehazed image. LBi (· ) denotes the corresponding normalized exposure qualLBi (x )+ε ity weight, LB (x ) = , ɛ is a small positive value (e.g., i

A q

i=1

(LBi (x )+ε )

10−20 ). After the dual weight method solving, the final fusion dehazed image J˜i (x ) can be refined by:

J˜(x ) =

Aq 

ˆ i (x ) × Jˆi (x ), W

(21)

i=1

ˆ i (x ) is final fusion weight maps. Due to the discontinuity where W of the initial fusion weight maps obtained above, the initial fusion weight maps WiL (x ) need to be refined before used for the final fusion. In this paper, we use the recursive filter [38] to refine the L (x ) = RF (W L (x ), Jˆ(x )). The refined initial fusion weight maps, W i i i weight maps are normalized to guarantee that the sum of all the ˆ i (x ) = weight maps is one at each pixel location, W

 WiL (x )+ε . Aq L (Wi (x )+ε ) i=1

4. Experiment results and analysis In order to verify the effectiveness of our method, we test it on outdoor and indoor hazy images. In [39], the global atmospheric light is given as the input parameter. In order to ensure a fair

comparison in the experimental evaluation, we use the provided method of He et al. [4] to solve the global atmospheric light. All the methods are implemented on Windows PC with a Pentium Dual-core 2.4GHZ CPU and 32.00 GB RAM using MATLAB2016a. To evaluate the dehazed performance quantitatively, no-reference focus quality assessment (NR-FQA) [40], entropy-based no-reference image quality assessment (ENIQA) [41] and structure similarity (SSIM) [42] are employed to assess the corresponding results. 4.1. Qualitative comparison of color fidelity and detail features When the outdoor monitoring equipment collects real-world images, it is inevitable that there is a sky region in the image. Since the brightness of sky regions has a great influence on the dehazing process, how to effectively reduce the impact becomes a key issue in the current research of hazy images. Therefore, to avoid these problems, we make a qualitative comparison between the distortion of the sky region and the detailed features of objects by extracting specific regions in the hazy image. Fig. 6 shows the qualitative comparison of results with six state-of-the-art dehazing methods on challenging natural environment images (named as mountain and deer) [4,32,8,39,10,15]. In the first and third line, Fig. 6(a) shows the hazy images. Fig. 6(b– g) depicts the results of He et al. [4], Meng et al. [32], Berman et al. [8], Zhang et al. [39], Bui et al. [10] and Zhu et al. [15] respectively. The results of the proposed method are given in Fig. 6(h). In the first two rows, it can be seen that all methods can remove the haze, but the color fidelity of the sky region is different. As shown in Fig. 6(b), (c), (e), (f) and (g), the results of the five methods remove most of the haze in thin haze regions, but significantly appear halo artifacts in the sky regions of the mountain image. In the results of Meng et al. [32] and Bui et al. [10], the sky regions appear serious over-enhancement and the top of mountains appear fog edge. The halo artifacts in Zhang et al. [39] are weaker than the above two in these five methods, followed by He et al. [4] which also appear brightness distortion. The results of Zhu et al. [15] are better than the other four in these four methods, but still deteriorate the quality of the hazy image visually. As we can observe in Fig. 6(d) and ours, the color fidelity of the sky regions are very natural. Nevertheless, these two methods are different in

Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284

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Fig. 6. Qualitative comparison results of color fidelity and detail features. Source: (a) The hazy images. (b) Results by He et al. [4]. (c) Results by Meng et al. [32]. (d) Results by Berman et al. [8]. (e) Results by Zhang et al. [39]. (f) Results by Bui et al. [10]. (g) Results by Zhu et al. [15]. (h) Our results.

the quality of image dehazing. The color fidelity of Berman et al. [8] is between Zhu et al. [15] and ours in sky regions which appear a little over-enhancement in Fig. 6(d). Compared with the results of using the other six methods, our method achieves the best color fidelity and generates more haze-clear results in Fig. 6(h). In image detail features, as we can see in the last two rows, all the seven methods including our can remove the hazy and obtain clear detail features. Nevertheless, these methods achieve different image visibility. He’ method [4] greatly enhances the detail and visibility in Fig. 6(b). The deer head contains deeper colors and has a higher saturation in Fig. 6(b). The results of Bui et al. [10] are close to those observed by He et al. [4] as displayed in Fig. 6(f). Zhu’s method [15] performs well but shows an obvious reduction of image brightness as shown in Fig. 6(g). The results of Meng et al. [32] appears excessively saturated color, especially in Fig. 6(c). The results of Zhang et al. [39] achieve better contrast than the above four methods in image detail features. Nevertheless, the color of the grass becomes yellow and suffer from more serious image color cast in Fig. 6(e). The results of Berman et al. [8] have the most obvious detail features among the six comparison methods, but suffer from more serious image color cast. The color of sky regions become yellow in Fig. 6(d). Compared with the results of the six methods, our results have achieved the best visual effects. The details of the deer head are visible, and the color of the grass is green in Fig. 6(h). 4.2. Quantitative evaluation of real images For subjective evaluation, we test on several hazy visible images on real image dataset. In this case, we evaluate methods in two aspects: color fidelity and image visual effect. Fig. 7(a) shows the real hazy images (named as Temple, Paddy, Pumpkin, Mountain, Farm and Building). The results of the six methods are shown in Fig. 7(b–g), respectively. The results of the proposed method are given in Fig. 7(h). The results of He et al. [4] appear serious over-enhancement and suffer from halo artifacts in the sky regions of the Temple,

Paddy, Pumpkin, Mountain and Building. After processing, the image brightness appears large loss in Fig. 7(b). In color fidelity, the results of Bui et al. [10] are close to those observed by He et al. [4] as displayed in Fig. 7(f). The color of sky regions also appear halo artifacts in the Temple, Pumpkin, Mountain, and Building, and the object regions have a serious color cast in the hazy area where the color tends to be bluish yellow in the Pumpkin as shown in Fig. 7(c) and (f). By observing the images in Fig. 7(c), we can find that the results of Meng et al. [32] have a poor visual effect. Fig. 7(c), we can find that the results of Meng et al. [32] have a poor visual effect. The sky regions of the Temple, Pumpkin, Mountain and Building appear halo artifacts in Fig. 7(c). The results of Zhang et al. [39] have similar halo problems with the results of Meng et al. [32] in sky regions. The Paddy with many rice straws remains a little hazy, the Pumpkin suffers from over-enhancement and the Building appears halo artifacts in Fig. 7(f). The results of Zhu et al. [15] achieve a better color fidelity, but still show slight over-enhancement in sky regions for the Temple, Pumpkin, Mountain and Building in Fig. 7(g). After processing by Zhu et al. [15], the images show a certain brightness loss for the six images. The results of Berman et al. [8] are the best in color fidelity among the six comparison methods. Nevertheless, the sky regions of the Temple and Building appear the slight halo artifacts and a certain brightness loss in Fig. 7(d). By the comparison Fig. 7, our results have the best balance in color fidelity and visual effects. After our method processing, the objects of the six dehazed images can be recovered clearly, and the sky regions of these dehazed images are more natural. In addition, to further evaluate the dehazing capability of different methods when compared to our method, we apply the noreference focus quality assessment (NR-FQA) [40] and entropybased no-reference image quality assessment (ENIQA) [41], which are specifically designed for assessing image sharpness and image dehazing methods. Table 1 list the quantitative results of the NRFQA and ENIQA scores. A lower NR-FQA score implies less blurriness of input image. A higher ENIQA score indicates a more

8

Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284

Fig. 7. Qualitative comparison on real images. Source: (a) The hazy images. (b) Results by He et al. [4]. (c) Results by Meng et al. [32]. (d) Results by Berman et al. [8]. (e) Results by Zhang et al. [39]. (f) Results by Bui et al. [10]. (g) Results by Zhu et al. [15]. (h) Our results.

visual effect of the dehazed image. Best and second-best results are marked in boldface. As can be seen from these results, our results produce five lower NR-FQA scores in the six images, followed by the results of Berman et al. [8] which have four lower NR-FQA scores. The results of Zhang et al. [39] producing two lower NR-FQA scores outperform the results of Bui et al. [10] None of the other methods produce higher NR-FQA scores. For the ENIQA scores, our results produce four higher ENIQA scores in the six images. As for the results of Berman et al. [8] and Zhu et al. [15], they have consistent performance in the six images, which only produce two higher ENIQA scores and rank at the second. The results of He et al. [4] are similar to the results of Bui et al. [10] and Meng et al. [32], which only produce one higher ENIQA score. It is obvious that our method has a higher image sharpness and image dehazing effects among all the seven methods on real hazy images.

4.3. Quantitative evaluation of synthetic datasets To further evaluate the proposed method, we use the part of D-HAZY dataset [43], which includes two individual environments presented as Middlebury [44] and NYU-Depth [45]. We have chosen Middlebury to make an experiment and evaluated these methods by two criteria: no-reference focus quality assessment (NR-FQA) [40] and Structure Similarity (SSIM) [42]. In this section, we compare the proposed algorithm with seven methods on the synthesized datasets. Fig. 8 shows the synthesized hazy images (named as Recliner, Classroom, Flowers, Motorcycle, Desk and Bookcase), and the corresponding dehazing results by the different methods, respectively. Table 2 lists the quantitative results of the NR-FQA and SSIM scores. By observing the images in Fig. 8, we can find that the results of Meng et al. [32] produce the worst visual effect in the six

Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284

9

Fig. 8. Qualitative comparison on indoor images. Source: (a) The hazy images. (b) Results by He et al. [4]. (c) Results by Meng et al. [32]. (d) Results by Berman et al. [8]. (e) Results by Zhang et al. [39]. (f) Results by Bui et al. [10]. (g) Results by Zhu et al. [15]. (h) Our results. (i) Ground truth image. Table 1 Quantitative results of the NR-FQA and ENIQA on real images.

N/E He et al. [4] Meng et al. [32] Berman et al. [8] Zhang et al. [39] Bui et al. [10] Zhu et al. [15] our

Temple

Paddy

Pumpkin

Mountain

Farm

Building

10.15/0.12 −20.70/0.09 −27.93/0.11 −33.05/0.11 −22.01/0.11 −24.53/0.11 −22.87/0.10 −30.24/0.12

12.97/0.01 8.90/0.04 12.30/0.03 −6.31/0.33 −11.48/0.06 11.85/0.03 10.49/0.01 −8.90/0.23

−0.73/−0.03 −4.65/0.13 −3.37/0.14 −7.67/0.04 −9.99/0.10 −4.86/0.15 −2.23/0.15 −12.23/0.09

−11.59/0.13 −10.50/0.21 −12.13/0.17 −18.34/0.15 −12.89/0.20 −13.08/0.19 −5.54/0.16 −12.17/0.11

−10.03/0.10 −16.73/0.11 −12.13/0.13 −20.71/0.21 −16.22/0.11 −16.33/0.14 −12.15/0.13 −21.18/0.27

16.55/0.08 −3.75/0.13 −6.88/0.10 −15.4/0.13 −5.68/0.10 −7.93/0.12 −0.11/0.14 −14.07/0.23

Table 2 Quantitative results of the NR-FQA and SSIM on synthetic images.

N/S He et al. [4] Meng et al. [32] Berman et al. [8] Zhang et al. [39] Bui et al. [10] Zhu et al. [15] our

Recliner

Classroom

Flowers

Motorcycle

Desk

Bookcase

−13.65/−22.03/0.76 −18.01/0.84 −24.26/0.85 −22.18/0.75 −24.52/0.74 −24.61/0.86 −30.31/0.85

−6.01/−32.20/0.92 −38.60/0.89 −40.02/0.93 −34.85/0.84 −36.88/0.91 −26.14/0.91 −25.70/0.87

−13.72/−13.48/0.85 −16.62/0.81 −24.44/0.89 −16.77/0.85 −21.05/0.84 −17.95/0.86 −25.24/0.79

−23.87/−25.33/0.67 −21.23/0.77 −26.24/0.68 −26.79/0.78 −23.43/0.70 −22.91/0.78 −22.36/0.78

0.37/−26.67/0.87 −24.95/0.85 −28.08/0.84 −23.14/0.84 −28.86/0.86 −24.27/0.89 −23.24/0.83

−19.09/−32.46/0.84 −30.13/0.85 −35.23/0.86 −27.08/0.80 −32.39/0.78 −26.04/0.89 −24.79/0.88

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Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284 Table 3 The execution time of algorithms on the different dataset(s). methods

He et al. [4]

Meng et al. [32]

Berman et al. [8]

Zhang et al. [42]

Bui et al. [10]

Zhu et al. [15]

our

Pumpkin Classroom

21.94 141.23

5.66 17.47

2.23 8.84

88.48 93.37

13.79 15.87

3.58 23.43

5.52 34.62

images, followed by Bui et al. [10]. After processing by these two methods, the brightness regions of the Recliner, Flowers, Desk, and Bookcase appear image over-enhancement and color cast so that it affects the visual effect. The results of Zhu et al. [15] achieve the best visual effect, but they remain a little hazy in these synthesized hazy images. The method of Zhang et al. [39] improves the image brightness when dehazing, but it still appears fog edge and local over-enhancement in the Recliner and Motorcycle. As for the results of He et al. [4] and Berman et al. [8], they have the similar performance in the six images, which appear image color cast and over-enhancement in the brightness regions of the Recliner, Desk, and Bookcase. To objectively evaluate these methods, we apply the no-reference focus quality assessment (NR-FQA) [40] to assess image sharpness. Table 2 list the quantitative results of the NR-FQA scores. Best and second-best results are marked in boldface. In producing lower NR-FQA scores, the results of Berman et al. [8] have four lower scores in the six images. Our results are similar to He et al. [4] in NR-FQA scores, which have two lower NR-FQA scores. The other methods only produce one lower NR-FQA scores. Compared with the ground truth image, these recovered images remove the haze to some extent but appear certain problems. As shown in Fig. 8(b), (c), (e) and (f), these images suffer from halo artifacts in the brightness regions of the Flowers. For the Motorcycle and Desk, the ground of the seven dehazed images included our method appear image color cast, but our result has the least image color cast. To further evaluate the dehazing effect on the synthetic dataset, we use the full-reference image quality assessment which is the structure similarity (SSIM) method [42]. A higher SSIM score indicates that the dehazed image is closer to the ground truth image. For the computation of a full-reference quality score, we have obtained the available hazy images with corresponding haze-free versions. Table 2 list the quantitative results of the SSIM scores. Best and second-best results are marked in boldface. As can be seen in Table 2, the results of Zhu et al. [15] have five higher SSIM scores in the six images, followed by our results which produce three higher scores. The results of Berman et al. [8] and He et al. [4] have the same number of higher scores, which produce two higher scores. The results of Zhang et al. [39] are similar to Bui et al. [10] and Meng et al. [32], which have the worst scores and do not produce higher scores. Overall, the subjective and objective comparison results in Fig. 8 and Tables 2 demonstrate that our method can keep a balance in color fidelity and visual effects in the six images. 4.4. Evaluation of the execution time One critical aspect of image dehazing methods is the execution time. As for the computation time, we measure the execution time on different image resolutions in Fig. 7 (e.g. Pumpkins, 600 × 400) and Fig. 8 (e.g. Classroom, 1500 × 960).The unit is second. All the code formats in the time-consuming comparison are the Matlab source codes from the author’s homepage. Table 3 shows the execution time in different image resolution. As can be seen in Table 3, the execution times of seven methods increase with the increase of the image resolution. The total execution times of Zhang et al. [39] are the most in seven methods, followed by He et al. [4]. Our total execution times are in third in seven methods. The total execution times of Bui et al. [10] are more than those obtained by Zhu et al. [15] and Meng et al. [32].

The method of Berman et al. has the least total execution times in seven methods. When the image resolution is 600 × 400, our execution time is the third-least in the Pumpkin. However, with the increase of the image resolution, our execution time increases dramatically mainly because the image fusion increases the computational complexity. 5. Conclusion In this work, we proposed a single image dehazing method via self-constructing SIFT flow multiple-exposure image fusion. According to the novel statistical experiment and histogram analysis of hazy images, the range of the global atmospheric light could be approximately estimated by these pixels in the brightness or sky regions of hazy images. Through the new adaptive boundarylimited L0 gradient optimization method, the transmission map was optimized effectively to avoid the unsatisfied halo artifacts and edge blur for sky regions or bright objects. After that, several initial dehazed images with different exposures are self-constructed through the two parameters obtained above. Finally, an adaptive selective SIFT flow multi-exposure fusion method was designed to blend these images to obtain a satisfying visual effect via the twolayer visual sensory selector. Compared with previous methods which rely on restrictions on scene transmission map and global atmospheric light, our method is the first that self-construct several initial dehazed images from an observed hazy image to solve the single image dehazing problem. This makes our method more efficient and robust to obtain important information from the input hazy image for improving visual effects. Experimental results showed the effectiveness of our self-constructing and selective fusion method. The method proposed in this paper also illustrated a better performance compared with some state-of-the-art methods in the aspects of image visibility, color fidelity, and overall visual effect. However, because the method in this paper blends features for every selective initial dehazed images, the execution time is currently a weakness, which needs to be improved to reduce redundant computations in the future work. Declaration of Competing Interest The authors have declared that no conflict of interest exists. Acknowledgments This work was supported by the National Key Research and Development Program of China (No. 2016YFC110 0 0502) and Scientific and Technological Project of Quanzhou (No. 2018C015). References [1] S.G. Narasimhan, S.K. Nayar, Vision and the atmosphere, Int. J. Comput. Vis. 48 (2002) 233–254, doi:10.1023/A:1016328200723. [2] H. Zhang, V. Sindagi, V.M. Patel, Multi-scale single image dehazing using perceptual pyramid deep network, in: IEEE Conf. Comput. Vis. Pattern Recognit. Work., 2018, pp. 902–911, doi:10.1109/CVPRW.2018.00135. [3] N. Hautière, J.P. Tarel, D. Aubert, Towards fog-free in-vehicle vision systems through contrast restoration, in: Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit., 2007, pp. 1–8, doi:10.1109/CVPR.2007.383259. [4] K. He, J. Sun, X. Tang, Single image haze removal using dark channel prior, IEEE Trans. Pattern Anal. Mach. Intell. 33 (2011) 2341–2353, doi:10.1109/TPAMI. 2010.168.

Y. Gao, Y. Su and Q. Li et al. / Signal Processing 167 (2020) 107284 [5] K. He, J. Sun, X. Tang, Guided image filtering, IEEE Trans. Pattern Anal. Mach. Intell. 35 (2013) 1397–1409, doi:10.1109/TPAMI.2012.213. [6] K. Tang, J. Yang, J. Wang, Investigating haze-relevant features in a learning framework for image dehazing, in: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2014, pp. 2995–30 0 0, doi:10.1109/CVPR.2014.383. [7] B. Cai, X. Xu, K. Jia, C. Qing, D. Tao, DehazeNet: an end-to-end system for single image haze removal, IEEE Trans. Image Process 25 (2016) 5187–5198, doi:10. 1109/TIP.2016.2598681. [8] D. Berman, T. Treibitz, S. Avidan, Non-local image dehazing, in: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2016, pp. 1674–1682, doi:10.1109/cvpr. 2016.185. [9] B. Li, X. Peng, Z. Wang, J. Xu, D. Feng, AOD-Net: all-in-one dehazing network, in: Proc. IEEE Int. Conf. Comput. Vis., 2017, pp. 4770–4778, doi:10.1109/ICCV. 2017.511. [10] T.M. Bui, W. Kim, Single image dehazing using color ellipsoid prior, IEEE Trans. Image Process. 27 (2018) 999–1009, doi:10.1109/TIP.2017.2771158. [11] A. Galdran, Image dehazing by artificial multiple-exposure image fusion, Signal Process. 149 (2018) 135–147, doi:10.1016/j.sigpro.2018.03.008. [12] W. Ren, L. Ma, J. Zhang, J. Pan, X. Cao, W. Liu, M.-.H. Yang, Gated fusion network for single image dehazing, in: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2018, pp. 3253–3261, doi:10.1109/CVPR.2018.00343. [13] H. Zhang, V.M. Patel, Densely connected pyramid dehazing network, in: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2018, pp. 3194–3203, doi:10.1109/ CVPR.2018.00337. [14] R. Wang, R. Li, H. Sun, Haze removal based on multiple scattering model with superpixel algorithm, Signal Process. 127 (2016) 24–36, doi:10.1016/j.sigpro. 2016.02.003. [15] M. Zhu, B. He, J. Liu, L. Zhang, Dark channel : the devil is in the details, IEEE Signal Process. Lett. 26 (2019) 981–985, doi:10.1109/LSP.2019. 2914559. [16] Q. Zhu, J. Mai, L. Shao, Single image dehazing using color attenuation prior, in: Proc. 25th Br. Mach. Vis. Conf., 2014, pp. 1–10, doi:10.5244/C.28.114. [17] R. Fattal, Dehazing using color-lines, ACM Trans. Graph. 34 (2014) 1–13, doi:10. 1145/2651362. [18] W. Ren, S. Liu, H. Zhang, J. Pan, X. Cao, M.H. Yang, Single image dehazing via multi-scale convolutional neural networks, in: Eur. Conf. Comput. Vis., 2016, pp. 154–169, doi:10.1007/978- 3- 319- 46475- 6_10. [19] R. Fattal, Single image dehazing, ACM Trans. Graph 27 (2008) 1, doi:10.1145/ 1360612.1360671. [20] R. Tan, Visibility in bad weather froma single image, in: 2008 IEEE Conf. Comput. Vis. Pattern Recognit., IEEE, Anchorage, AK, USA, 2008, pp. 1–8, doi:10. 1109/CVPR.2008.4587643. [21] K. Nishino, L. Kratz, S. Lombardi, Bayesian defogging, Int. J. Comput. Vis. 98 (2012) 263–278, doi:10.1007/s11263-011-0508-1. [22] J. Tarel, N. Hauti, Fast visibility restoration from a single color or gray level image, in: 2009 IEEE 12th Int. Conf. Comput. Vis., IEEE, Kyoto, Japan, 2009, pp. 2201–2208, doi:10.1109/ICCV.2009.5459251. [23] Q. Zhu, J. Mai, L. Shao, A fast single image haze removal algorithm using color attenuation prior, IEEE Trans. Image Process. 24 (2015) 3522–3533, doi:10.1109/TIP.2015.2446191. [24] D. Huang, K. Chen, J. Lu, W. Wang, Single image dehazing based on deep neural network, in: 2017 Int. Conf. Comput. Network, Electron. Autom., 2017, pp. 294– 299, doi:10.1109/ICCNEA.2017.107. [25] D. Engin, A. Genc, H.K. Ekenel, Cycle-dehaze: enhanced cyclegan for single image dehazing, in: Proc. IEEE Conf. Comput. Vis. Pattern Recognit. Work., 2018, pp. 825–833, doi:10.1109/CVPRW.2018.00127. [26] H. Zhu, X. Peng, V. Chandrasekhar, L. Li, J.H. Lim, DehazeGAN: when image dehazing meets differential programming, in: Int. Jt. Conf. Artif. Intell., Interna-

[27]

[28]

[29] [30]

[31]

[32]

[33] [34]

[35]

[36]

[37]

[38] [39]

[40]

[41]

[42]

[43]

[44]

[45]

11

tional Joint Conferences on Artificial Intelligence Organization, 2018, pp. 1234– 1240, doi:10.24963/ijcai.2018/172. Y. Song, J. Li, X. Wang, X. Chen, Single image dehazing using ranking convolutional neural network, IEEE Trans. Multimed. 20 (2018) 1548–1560, doi:10. 1109/TMM.2017.2771472. A. Wang, W. Wang, J. Liu, N. Gu, AIPNet: image-to-image single image dehazing with atmospheric illumination prior, IEEE Trans. Image Process. 28 (2019) 381–393, doi:10.1109/TIP.2018.2868567. C.O. Ancuti, C. Ancuti, Single image dehazing by multi-scale fusion, IEEE Trans. Image Process. 22 (2013) 3271–3282, doi:10.1109/TIP.2013.2262284. A. Galdran, J. Vazquez-Corral, D. Pardo, M. Bertalmio, Fusion-based variational image dehazing, IEEE Signal Process. Lett. 24 (2017) 151–155, doi:10.1109/LSP. 2016.2643168. Y. Gao, Y. Su, Q. Li, J. Li, Single fog image restoration with multi-focus image fusion, J. Vis. Commun. Image Represent. 55 (2018) 586–595, doi:10.1016/ j.jvcir.2018.07.004. G. Meng, Y. Wang, J. Duan, S. Xiang, C. Pan, Efficient image dehazing with boundary constraint and contextual regularization, in: Proc. IEEE Int. Conf. Comput. Vis., 2013, pp. 617–624, doi:10.1109/ICCV.2013.82. L. Xu, C. Lu, Image smoothing via L0 gradient minimization, ACM Trans. Graph. 30 (2011) 1–12, doi:10.1145/2024156.2024208. J. Zhu, T. Park, A.A. Efros, B. Ai, U.C. Berkeley, Unpaired image-to-image translation using cycle-consistent adversarial networks, in: Proc. IEEE Int. Conf. Comput. Vis., 2017, pp. 2223–2232, doi:10.1109/ICCV.2017.244. A. Mittal, R. Soundararajan, A.C. Bovik, Making a ‘Completely blind’ image quality analyzer, IEEE Signal Process. Lett. 20 (2013) 209–212, doi:10.1109/LSP.2012. 2227726. X. Guo, Y. Li, H. Ling, LIME: low-light image enhancement via illumination map estimation, IEEE Trans. Image Process 26 (2017) 982–993, doi:10.1109/TIP.2016. 2639450. C. Liu, J. Yuen, A. Torralba, J. Sivic, W.T. Freeman, SIFT flow : Dense correspondence across different scenes, in: Eur. Conf. Comput. Vis., Springer, Berlin Heidelberg, 2008, pp. 28–42, doi:10.1007/978- 3- 540- 88690- 7_3. E.S.L. Gastal, M.M. Oliveira, Domain transform for edge-aware image and video processing, ACM Trans. Graph 30 (2011) 69, doi:10.1145/2010324.1964964. S. Zhang, H. Fazhi, J. Yao, Single image dehazing using deep convolution neural networks, in: Pacific Rim Conf. Multimed., Springer International Publishing, 2017, pp. 128–137, doi:10.1007/978- 3- 319- 77380- 3_13. M.S. Hosseini, K.N. Plataniotis, Image sharpness metric based on maxpol convolution kernels, in: 2018 25th IEEE Int. Conf. Image Process., IEEE, 2018, pp. 296–300, doi:10.1109/icip.2018.8451488. X. Chen, Q. Zhang, M. Lin, G. Yang, C. He, No-Reference color image quality assessment: From entropy to perceptual quality, ArXiv Prepr. ArXiv1812.10695. (2018) 1–12. http://arxiv.org/abs/1812.10695. Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment : from error visibility to structural similarity, IEEE Trans. Image Process 13 (20 04) 60 0–612, doi:10.1109/TIP.2003.819861. C. Ancuti, C.O. Ancuti, C. De Vleeschouwer, D-HAZY: a dataset to evaluate quantitatively dehazing algorithms, in: 2016 IEEE Int. Conf. Image Process., 2016, pp. 2226–2230, doi:10.1109/ICIP.2016.7532754. D. Scharstein, H. Hirschm¨, Kitajima York, Krathwohl Greg, W. Xi, W. Porter, High-Resolution stereo datasets with subpixel-accurate ground truth daniel, in: Ger. Conf. Pattern Recognit, 2014, pp. 31–42, doi:10.1007/978- 3- 319- 11752- 2_ 3. N. Silberman, D. Hoiem, P. Kohli, R. Fergus, Indoor segmentation and support inference from RGBD images, in: 12th Eur. Conf. Comput. Vis., 2012, pp. 746– 760, doi:10.1007/978- 3- 642- 33715- 4_54.