Defogging algorithms based on dark channel prior have color shift in light color areas because of inaccurate estimation of transmittance. To resolve this problem, a novel improved image clearness method is proposed. Based on the dark channel prior, the essential causes of color shift are analyzed, with two important factors summarized. Then, transmission map is calculated by using 3
In fog weather, due to the influence of atmospheric scattering, image taken by outdoor surveillance system would get serious degradation problems in the color and contrast fidelity. It not only directly affects the safety of sea, land, and air transportation by making the outdoor surveillance system abnormal [
Currently, most of image defogging algorithms are based on image restoration, the core idea of which is as follows: firstly, an imaging mode should be established; secondly, the degraded part of the imaging model is compensated and the interferential part of it is filtered; thirdly, the clear image is restored [
In 2009, Professor Kaiming He proposed a dark channel prior (DCP) theory on CVPR conference [
Other methods are proposed and also have an outstanding effect on dehazing. Zhu et al. [
Based on DCP, this paper proposes an improved algorithm combined with self-adaptive threshold mechanism (STM), which enhances the transmittance in light color area. The remaining parts of this paper are arranged as follows: in Section
In image restoration filed, the following mathematical model is widely used to describe the imaging process of fogging image:
where
Formula (
After observing large numbers of outdoor fog-free images, empirical statistical regularity called dark channel prior theory is proposed by Professor Kaiming He in [
where
Due to the fact that dark channel values of the fogging image are always close to zero in fog weather, the dark channel values obtain certain brightness at the process of imaging. Notice that the dark channel values may be calculated at both sides of (
According to (
There are two unknown parameters in formula (
In fact, atmospheric scattering exists even in a cloudless day. Particles are suspended in air, so the vague area of image will appear when we observe distant objects. On the other hand, images have depth because of atmospheric scattering. If we remove atmospheric light thoroughly, the restoring image may tend to look fake and unnatural. For solving the problem, Professor He introduces parameter
Meanwhile, the defogging model of images may get combined with imaging model (
Therefore, once the transmission map
In practice sense, the value of
Generally speaking, if the fogging images acquired by outdoor surveillance system contain no obvious light color areas, they can obtain a satisfactory defogging effect by defogging algorithm based on dark channel prior theory. This is because the vast majority of the pixels in these images meet dark channel prior theory; i.e., there has to be at least one color channel whose value is close to 0 among these pixels. For example, the original fogging images are shown as Figure
Original images without obvious light color areas.
Clearness images restored from original images without obvious light color areas.
In a real world situation, however, some fogging images may always contain obvious light color areas shown as Figure
Original images with obvious light color areas.
In this case, if we use the defogging method based on dark channel prior theory to restore these fogging images, the color shift problem should appear in light color areas. This is due to the fact that the pixel values in three color channels are very high for all pixels in the light color area, and then the defogging algorithm based on dark channel prior theory is invalid in these light color areas. It is illustrated as Figure
Clearness images restored from images with light color areas.
Notice that, in Figure
To solve the color shift problem, we will first analyze the characteristics of original fogging image and restored image and then figure out the essential cause of image color shift problem. Based on this, a repaired model of inaccurate transmission map in light color is constructed directionally.
In order to analyze the characteristics of original fogging image and restored image, find out the essential cause of image color shift problem; the Histograms of dark channel values between images containing obvious light color areas and images containing no obvious light areas are shown in Figures
Histogram of dark channel values without obvious light color areas.
Histogram of dark channel values with obvious light color areas.
From Figure
However, how do these larger incorrect dark channel values affect the final defogging effect? For answering this question, we rewrite formula (
where
Notice that the dark channel value
To better analyze the problem, the maximum difference of three channels between original fogging images and restored free-fog images by dark channel prior theory is experimented. Figure
Numerical form of three color channels’ maximum difference values.
It can be clearly found that vast majority of three color channels’ maximum difference values of pixels have to be increased several times, which brings a great change for the original color of these pixels, after using defogging algorithm based on dark channel prior theory. To precisely locate these pixels in primary images, the three color channels’ maximum difference values are presented in image form shown as Figure
Image form of three color channels’ maximum difference values.
Obviously, the distribution of these maximum difference values and that of light color areas are coincidental. This indicates that the conclusion is reasonable and fit in with facts. Next, we need to find a method to solve these types of problems.
According to the analysis in previous section, the essential reason of color shift problem in light color areas is the incorrect smaller transmittances generated by the larger dark channel values that come from incorrect calculations. Therefore, the original defogging algorithm can be improved by optimizing these incorrect smaller transmittances. Firstly, we assume that the optimized transmittance and primary transmittance satisfy the following relationship:
In other words, the transmittance can be optimized in light color areas by multiplying a weight coefficient
To improve the effect, Professor Jiang proposed an improvement model to calculate the parameter
Unfortunately, according to the analysis of the pixels in light color area in Figures
(1) The maximum difference values of three color channels are smaller, which can be found by the red curve in Figure
(2) All pixel values in three color channels are close to atmospheric light.
Obviously, Jiang only considered second feature of the light color area, so formula (
To better improve the effect of restored images and meet the dynamical need, the expression of
In reality,
According to the analysis above, the following formula can be used to optimize the primary transmittance:
In addition, there have been cases where the primary fogging image is dim on the whole. Meanwhile, the pixel values in different color channels are close; i.e., the vast majority of three color channels’ maximum difference values of pixels are close to zero. However, the light color areas still exist relatively. In this case, the weight coefficient
The concrete processing steps are as follows.
(1) Locating this situation. Observing the statistical result, it is found that
where
(2) Recalculation for weight coefficient
where
As a result, it not only retains the relative difference of color channels’ maximum difference values, but also increases their absolute difference values. Then we could get a new maximum value
To guarantee the improvement effect of transmittance, the self-adaptive maximum value model of
Based on this information, a final
For verifying the availability of our algorithm, in this section, we will compare it with experimental results of DCP algorithm and Improved DCP algorithm in two ways: subjective visual evaluation and objective quality of defogging images. Here the original images containing large light color areas, which are shown as Figure
The fogging images are restored by using DCP algorithm shown as Figure
Visual comparison of clearness images.
Clearness images obtained by Improved DCP algorithm
Clearness images obtained by STM algorithm
According to formula (
In comparison, the algorithm proposed in this paper prevents artificial arbitrariness of selection for
Considering the limitation of subjective evaluation coming from human visual system, here, we introduce image’s standard deviation that can reflect the contrast of an image to evaluate the quality of restored images defogging by different algorithms. The computing model is as follows:
Meanwhile, the information entropy, which represents the amount of information in an image, is used to evaluate the quality of restored images defogging by different algorithms. And the computing model is as follows:
Normally, if the size of image block is too large, it will result in overly enhanced restoration and then the following problems of restored images arise: image is so saturated that some image details are lost. In addition, our goal is to improve the insufficiency of defogging method based on dark channel prior theory used in light color areas, so a 3
It is generally known that a fogging image always has a low contrast and less depth information. Therefore, the better the algorithm is, the bigger the standard deviation and entropy of the defogging image are. Thus, the performance comparison of quality of defogging images, restored by three algorithms, is listed in Table
Comparison of clearness images quality.
Figure | ||||
Original image | DCP algorithm | Improved DCP algorithm | STM algorithm | |
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Standard deviation | 0.2636 | 0.2878 | 0.3317 | 0.3454 |
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Entropy | 7.6276 | 7.0131 | 7.4399 | 7.5828 |
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Figure | ||||
Original image | DCP algorithm | Improved DCP algorithm | STM algorithm | |
| ||||
Standard deviation | 0.1616 | 0.2498 | 0.2665 | 0.2696 |
| ||||
Entropy | 7.0704 | 6.8523 | 7.2481 | 7.3115 |
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Figure | ||||
Original image | DCP algorithm | Improved DCP algorithm | STM algorithm | |
| ||||
Standard deviation | 0.1495 | 0.2507 | 0.3044 | 0.3076 |
| ||||
Entropy | 6.6060 | 6.7186 | 6.9363 | 6.9744 |
Note. Figures
Observing the above table, we can find that all the algorithms can increase the standard deviation and entropy of the images, i.e., improving the objective quality of images. STM algorithm makes more contribution for standard deviation and entropy of the images, when compared with DCP and Improved DCP algorithm. These results in Table
In this paper, a new improved defogging algorithm based on dark color theory is presented combined with self-adaptive threshold mechanism. First we make a detailed analysis and experimental verification for characteristics of the light color area in image, and then the invalidity of dark channel prior theory in light color is discussed in detail. Based on the dynamical need for defogging image in light color areas, a self-adaptive threshold mechanism is proposed to optimize transmittance. The optimized transmission helps to avoid color shift problem in light color areas. The experiments indicate that our algorithm is in line with practical situation.
On the other hand, we do not consider the situation in which dark prior channel theory is out of work when image contains large range of white objects. It would be worth studying in the future.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The research was sponsored by Natural Science Foundation of China (NSFC) under Grants 61573076, 61663008, and 61703063; the Scientific Research Foundation for the Returned Overseas Chinese Scholars and Program for Excellent Talents of Chongqing Higher School under Grant 2015-49; the Program for Excellent Talents of Chongqing Higher School under Grant 2014-18; Science and Technology Project under Grants KJ1705121 and KJ1705139; and the Chongqing Natural Science Foundation of China under Grant CSTC2017jcyjA1665.