Keywords

1 Introduction

Haze can seriously accelerate the degeneration of the optical image or video. Therefore, image dehazing research has been one of the hot-spots in both academic and industrial societies [1, 2].

Currently, the mainstream dehazing methods are almost based on atmospheric scattering model [3], or called Koschmieder model. In this model, the key process is the computation of the transmission of the air-light, and the core procedure of it is Edge Preserving Smoothing Filter/Filtering (EPF), which is the research emphasis in recent years.

He [4] proposed dark channel prior and guided image filter to compute the air-light transmission. Essentially, dark channel prior could suppress the pixel value and increase the transmission value around dark pixel. Tarel [5] used median filter as smoothing filter, but median filter was not strict edge-preserving, which resulted in serious halo effect. Berman [6] presented a haze-line dehazing algorithm, which used the WLS-filter [7] as EPF; Cai [8] built the Spatio-temporal Markov Random Field to estimate the transmission. Gibson [9] adopted a two-step method to calculate Wiener filter as EPF. Meng [10] used geometric boundary constraint to estimate the accurate transmission with regularization of optimization. Kim [11] proposed an adaptive contrast enhancement algorithm, which computed the transmission map by iterating the optimization function of contrast and information loss. Park [12] raised the optimization process of information entropy and image fidelity to obtain the transmission map, which is also performed in iterative manner.

In recent years, many novel dehazing algorithms have been proposed instead of tradition atmospheric scattering model. MSCNN [13] used a multi-scale Convolutional Neural Network (CNN) to train the dataset that remove the haze on the _target fog images. Double-DIP [14] proposed a unified framework for unsupervised layer decomposition of a single image, which based on coupled Deep-Image-Prior (DIP) networks. These novel algorithms had excellent dehazing effects for most haze images, but some images are still slightly deficient.

The above-mentioned methods based on Koschmieder model focused on EPF rather than the systematic framework. They’re not entire solutions of haze removal, Therefore, these methods usually exist some defects, e.g. the whole result becomes dark, the sky area is over-saturated, and the details are not sufficient, and so on.

Therefore, in this paper, we attempt to develop a systematic framework for Brightness-Area Suppression Mechanism Dehazing (BASMDE), which includes new brightness-area suppression mechanism and necessary post-processing operations, what’s more, it can integrate all other relevant techniques in this solution.

2 Methodology

This section describes an entire dehazing framework based on Koschmieder model. The whole flowchart is shown in Fig. 1, and the model is expressed as follows:

$$ \varvec{J}(x) = \varvec{I}(x)\varvec{t}(x) + {\mathbf{A}} ( 1- \varvec{t}(x) ) $$
(1)

where J(x) is hazy image, I(x) is haze-free image desired, other parameters are need to be evaluated: A is the intensity of atmospheric light, t(x) is transmission describing the atmospheric light how reach the camera.

Fig. 1.
figure 1

The flowchart of the proposed dehazing framework

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2.1 Sky Detection

The sky area is usually abnormity in color and occurrence of colour spots causes over-saturated after using above algorithms. Dai [15] proposed a method to detect sky region. The parameters k was obtained through the sky analysis function as:

$$ \varvec{k} = a_{0} ({\text{B}} \times \beta \times {\text{Mean}}) + 1 $$
(2)

where a0 is a constant and parameter B is a Boolean value to indicate whether there exists sky in hazy image, and parameter β is the confidence coefficient of parameter B. Parameter Mean represent the mean value of the sky area in the hazy image J(x). The parameter k is a scalar of local brightness suppression that will be adopted in Sect. 2.4 to suppress the local brightness-area.

2.2 Atmospheric Light Detection

In order to faster estimate the air light, this paper proposes a statistical method based on the gray intervals of histogram. Jmin(x) is defined as the minimum component of RGB image, which can be obtained as below:

$$ \varvec{J}_{min} (x ) = min_{{{\text{c}}{ \in }\{ {\text{r,g,b}}\} }} (\varvec{J}^{{ {\mathbf{c}}}} (x ) ) $$
(3)

where, Jc(x) is the input hazy image, c is the index of RGB channel. Then, the histogram of Jmin was computed. When the accumulative value of this histogram accounted for 98% and 99.5% of the total pixel number, the corresponding gray values are A0 and A1. Moreover, the atmospheric light values of the RGB channels are as follows:

$$ {\mathbf{A}}^{c} { = }\frac{{\sum \varvec{J}^{ c} ( {\text{x)}}}}{{\mathbf{m}}} , {\text{s}}{.}{\text{t}}{.} \{ x | {\mathbf{A}}_{ 0} \le \varvec{J}_{min} (x )\le {\mathbf{A}}_{ 1} \} $$
(4)
$$ {\mathbf{A}} = \frac{{{\mathbf{A}}^{r} { + }{\mathbf{A}}^{g} { + }{\mathbf{A}}^{b} }}{ 3} $$
(5)

where m is the total number of pixels in the interval of [A0, A1] in Jmin(x).

2.3 Edge-Preserving Filtering

The core step of the dehazing algorithm based on the model (1) is edge-preserving filtering. In the systematic framework of this paper, all kinds of EPFs could suit and be adopted in our EPF module, which is presented as a fixed module. Let the image JEPF be the result of EPF on Jmin. As shown in Fig. 2(b). the detail layer Jdetail is obtained by the basic layer JEPF after using the formula (7). The detail layer is as shown in Fig. 2(c).

$$ \varvec{J}_{EPF} (x )= {\text{EPF(}}\varvec{J}_{min} (x ) ) $$
(6)
$$ \varvec{J}_{detail} (x )= \varvec{J}_{min} (x ) - a_{ 1} \times \varvec{J}_{EPF} (x ) $$
(7)

where, a1 is the detail control parameter of the detail image, and its value is within the interval [0.8, 1.0].

Fig. 2.
figure 2

Intermediate results of brightness-area suppression

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2.4 Brightness-Area Suppression

There are sky areas and white objects in the hazy images, the white areas of hazy images will darken after dehazing, such as: sky, white cars, the zebra of road signs, etc. In theory, for the part of the brighter, the JEPF value is larger generally, which will lead to a smaller transmission and the luminance of these brightness areas will be suppressed in the restored result. In order to solve this defects, a brightness-area suppression method is proposed to decrease the brightness of JEPF.

A large-scale mean filtering was performed on Jmin to obtain the atmospheric veil Jveil, as shown in Fig. 2(d). Then, by fusing JEPF and Jveil with formula (8), the global brightness-area suppression is achieved.

$$ \varvec{J}_{global} (x )= \text{min}\left( {a_{ 2} \times \varvec{J}_{EPF} (x ) ,\;\varvec{J}_{veil} (x )} \right) $$
(8)

where a2 is the fusion coefficient, Jglobal is the image after global brightness-area suppression, as shown in Fig. 2(e). By comparing between Fig. 2(b) and (e), it can be seen that the brightness of the sky areas, roads and building are suppressed as a whole.

After performing the above operation, if Jglobal value of the sky-area is still larger, the transmission will get smaller. It would lead to the color of the sky-area be abnormal and over-saturated. Therefore, a local brightness-area suppression method is proposed to overcome this disadvantages as formula (9).

$$ \varvec{J}_{local} (x ) {\text{ = min}}\left( {\frac{{\left| {\varvec{gray} (x ) - {\mathbf{A}}} \right|}}{\varvec{k}} , 1} \right) \times \varvec{J}_{global} (x ) $$
(9)

where the gray is the grayscale of the input hazy image, k is the local brightness suppression parameter proposed in Sect. 2.1, and Jlocal is the result of local brightness-area suppression as shown in Fig. 2(f). By comparison of Fig. 2(e) and (f), the brightness of the sky region of Fig. 2(f) is significantly suppressed, which will increase the value of the sky region of the transmission map, thus obtaining a without anomalous dehazing image.

Consequently, transmission map could be deduced as formula (10).

$$ \varvec{t} (x ) = 1 - \frac{{\varvec{J}_{local} (x )}}{\varvec{A}} $$
(10)

By further deformation [16] of t via formula (11),

$$ \varvec{t} (x ) = 1 + \varvec{t}_{\varvec{0}} -\varvec{\omega}\frac{{\varvec{J}_{local} (x )}}{\varvec{A}} $$
(11)

where ω is a parameter to control the degree of haze removal, and its value is in the interval [0, 1]. t0 is a control parameter to increase the overall brightness of the restored image, and its value interval is [0.05, 0.15].

2.5 Image Restoration

According to the physical model (1), the restored result Jdehaze of the hazy image is listed as:

$$ \varvec{J}_{dehaze}^{ c} \left( x \right) = \frac{{\varvec{J}^{ c} \left( x \right) - {\mathbf{A}}^{c} }}{{\varvec{t}(x)}} { + }{\mathbf{A}}^{c} $$
(12)

where A is the atmospheric light values calculated by the Eq. (5), t(x) is the transmission map after the brightness-area suppression, J(x) is the hazy image. The result image Jdehaze is dehazing image after restore, as shown in Fig. 4(a).

2.6 Post-processing Procedures

Comparing with the Fig. 3(b), it is obvious that, in Fig. 4(a), after brightness-area suppression, the sky area is no longer distorted and the road looks more natural, however, the result image is still depressing with worse perceptive effect. In order to further improve the visual perception, a post-processing procedure is performed on the restored result Jdehaze.

Fig. 3.
figure 3

Comparisons of brightness-area suppression

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Fig. 4.
figure 4

Demonstration of post-processing

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The first step shown in the formula (13) is to enhance the details for Jdehaze.

$$ \varvec{J}_{sum}^{ c} (x ) = \varvec{J}_{dehaze}^{ c} (x) + \varvec{J}_{detail} (x) $$
(13)

The next step is to improve the luminance of Jsum, which adopts the fitting function [17] of weber’s law curve.

$$ \varvec{J}_{final}^{ c} (x) = \frac{{\varvec{J}_{sum}^{ c} (x) \times (255 + a_{3} )}}{{\varvec{J}_{sum}^{ c} (x) + a_{3} }} $$
(14)

where a3 is the controlling parameter, and the smaller the value a3 is, the greater the brightness adjustment degree will be.

The results of the post-processing operations are shown in Fig. 4(b) and (c). It can be seen that the final output of the proposed framework has better degree of naturalness, without obvious defects on the other side.

3 Experimental Results

In this section, the results of dehazing image of three comparison algorithms for Meng [10], Berman [6] and Cai [8] are listed in Fig. 5(b)–(d). Several classic EPFs such as Bilateral Filter (BF) [18], WLS Filter [7], RTV Filter [19], and Recursive Filtering (RF) [20] are selected as the optional EPF in the EPF module in framework. Dehazing images using different EPFs in BASMDE framework of this paper are shown in Fig. 5(e)–(h). Furthermore, Fig. 6 is a comparison of the other dehazing results of BASMDE framework with MSCNN [13] and Double-DIP [14].

Fig. 5.
figure 5

Result comparison of four dehazing methods and four EPFs in framework (a) Original, (b) Meng [10], (c) Berman [6], (d) Cai [8], (e) BASMDE(BF), (f) BASMDE (WLS), (g) BASMDE (RF), (h) BASMDE (RTV). (The last row is the detail enlarged of images at the 2nd row)

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Fig. 6.
figure 6

Result comparison with MSCNN and Double-DIP

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To evaluate the superiority of the proposed method, it is compared with those of Meng [10], Berman [6], Cai [8], MSCNN [13], Double-DIP [14] and the EPF module in this framework using different EPFs dehazing result. Ten classic test images were listed for subjective and objective evaluation.

In the following experiments, for all competitor algorithms and BASMDE, parameter ω = 0.9, a0= 1.1, a1= 0.95, a2= 0.95, and a3= 255 + 4 * mean(Jsum).

3.1 Subjective Evaluation

As can be seen from Fig. 5(a)–(d), all the haze-free images resulted from the Meng, Berman and Cai have a certain degree of distortion in the sky area. The detail of Cai’s result is very obscure in the first and second images. For Meng’s and Cai’s results, the road in the first and third images are lackluster and not natural. Berman’s method is over-saturated for half of test images. As one can see from Fig. 5(e)–(h), the dehazing images by using four different EPFs in BASMDE framework without obvious disadvantages, and all the results have steady and excellent effects.

In Fig. 6, one can find that the two algorithms are darkened in the bottom half of the image Aerial. In the image Mountain, the color of the MSCNN is a slight imbalance, and the Double-DIP has a good result, whereas the detail is not as good as us. In the image of Cones and Train, the dehazing of their algorithm result insufficient degree, and Double-DIP has color anomaly in the Cones. In terms of detail enhancement and brightness preservation, our results are more moderated and comfortable. In short, the proposed method is able to achieve better visual perception than other dehazing algorithms under comparison.

3.2 Objective Evaluation

There are many typical image quality objective evaluation indicators for dehazing algorithm evaluation, as follows: Natural image quality evaluator(NIQE) [21], Image Visibility Measurement (IVM) [22], Visual Contrast Measure (VCM) [23], Structural Similarity index (SSIM) [24] and Universal Quality Index (UQI) [25], etc. Through experimental comparison and analysis, NIQE and SSIM are adopted as evaluation indicator in this paper as no-reference and full-reference, respectively.

NIQE is a no-reference image quality evaluation algorithm proposed by Mittal [21], in good consistency with the visual perception of human vision system. The smaller the value is, the better the image quality is. The corresponding results in terms of NIQE are shown in Tables 1 and 2.

Table 1. Indicator NIQE of the images in Fig. 5
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Table 2. Indicator NIQE of the images in Fig. 6
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SSIM is an index to measure the similarity between two images. The structural similarity index defines structural information from the perspective of image composition as independent of brightness and contrast, reflecting the properties of the object structure in the scene. Using the mean as the estimate of the brightness, the standard deviation as the estimate of the contrast, and the covariance as a measure of the degree of structural similarity. The mathematical definition of the SSIM index is as follows:

$$ {\text{SSIM}}\left( {x, y} \right) = \frac{{ ({\mathbf{2}}\varvec{\mu}_{\varvec{x}}\varvec{\mu}_{\varvec{y}} + \varvec{c}_{{\mathbf{1}}} ) ({\mathbf{2}}\sigma_{{\varvec{xy}}} + \varvec{c}_{{\mathbf{2}}} )}}{{ (\varvec{\mu}_{\varvec{x}}^{{\mathbf{2}}} +\varvec{\mu}_{\varvec{y}}^{{\mathbf{2}}} + \varvec{c}_{{\mathbf{1}}} ) (\sigma_{\varvec{x}}^{{\mathbf{2}}} + \sigma_{\varvec{y}}^{{\mathbf{2}}} + \varvec{c}_{{\mathbf{2}}} )}} $$
(15)
$$ c_{ 1} = (k_{ 1} L )^{ 2} ,\;\;c_{ 2} = (k_{ 2} L )^{ 2} $$
(16)

Where x is the dehazing image, y is the ground truth. \( \varvec{\mu}_{\varvec{x}} \) and \( \varvec{\mu}_{\varvec{y}} \) are the average values of x and y. σx and σy are the variances of x and y, respectively. σxy is the covariance of x and y, and L is the gray dynamic range. k1 = 0.01, k2 = 0.03.

In Tables 1 and 2, The result of BASMDE framework have smaller NIQE values, indicating that the method has excellent dehazing effect. Although Meng’s and Double-DIP’s NIQE value is the smallest, combined with subjective perception, their results are not the best. From the above statement, our algorithm is more moderated and natural than others.

500 hazy images were randomly selected from the RESIDE [26] as the SSIM evaluation dataset of this paper. In the dataset, the SSIM values were calculated from the dehazing image of the comparison algorithm and ground truth. Then calculate the SSIM average of 500 images, as shown in Table 3. It can be seen from Table 3 that the SSIM value of our method is the largest. It shows that the BASMDE framework results have higher structural similarity with ground truth than other algorithm results. It also shows that the dehazing framework of this paper can remove the hazy well.

Table 3. Indicator SSIM of the images dataset [26]
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3.3 Computational Complexity

This sections provides a comparison of the computational complexity of this dehazing framework and other classic dehazing algorithms. All these methods are tested using their MATLAB R2016a implementations and run on the same machine with an Intel Core i5-4590 3.30 GHz CPU and 8 GB RAM. The average running times (average of 10 runs per image) of the classic methods for the six test images in Fig. 5 are documented in Table 4.

Table 4. Average running time (In seconds) of different algorithms for enhancing the 6 images
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It can be seen that the dehazing framework proposed in this paper is faster than Meng [10] and Berman [6] in computationally, except the Cai [8]. A closer examination shown that using different EPFs in the framework can make the different calculation times for the algorithm. Therefore, a fast and accurate EPF is especially important for BASMDE framework.

4 Conclusion

An entire image dehazing framework is proposed in this paper with brightness suppression. Global brightness-area suppression could fuse the edge-preserving filtering with the atmospheric veil to protect white objects. Local brightness-area suppression could prevent the sky area or highlight region from over saturation. In addition, a simple but effective procedure of detail and contrast enhancement is designed in this framework. In theory, this framework can integrate all of other dehazing methods. Experiments show this dehazing framework works well with better visual perception.