# Proposed Methodology

The proposed algorithm is explained in the following steps:

• 1. Initially, a hazy image is taken as an input image.
• 2. The white balancing procedure, as given in Algorithm 12.1, is applied to the hazy image so as to adjust the color of the input image with reference to a white color, so as to make the image look more natural.
• 3. To improve the visibility of the hazy image, the CLAHE procedure, as given in Algorithm 12.2, is applied to the white balanced image. In this procedure, initially, the image is divided into non-overlapping blocks, and a histogram of each block is calculated. After that a clip limit is chosen to clip the parts of the histogram which are exceeding the limit.
• 4. Finally, the histogram of every region is combined with bilinear interpolation and image gray-scale values are changed according to the new histograms.
• 5. Due to clipping of the histogram in CLAHE, some of the information of the image may get lost. So, to get back that information, GF is used in this step. For GF. a guidance image (/) is considered, using which the filtering process is done.
• 6. The mean of (/), the mean of the CLAHE output image (p), and the mean of (/ x p) is calculated.
• 7. Co-variance of (I,p) is calculated as:

8. The variance of (/) is obtained to get linear coefficients a and b using:

9. The values of a and b are important to get the final result, which can be obtained by:

where e is the regularizing parameter.

10. And finally, the mean of a and b is calculated and the final output of the image, i.e., q, is obtained as:

# Dataset Collection and Analysis

In this chapter, the Haze Realistic Dataset or HazeRD [42] is used for evaluating the proposed algorithm. HazeRD consists of 15 scenes along with their haze-free RGB images of their corresponding depth maps. Five distinct weather conditions are imitated into each of the scenes, which range in ascending order of their visual density,

FIGURE 12.1 Sample of HazeRD having different visual ranges, (a) Ground truth image, (b) image with visual range 50 m, (c) image with visual range 100 m, (d) image with visual range 200 m, (e) image with visual range 500 m, (f) image with visual range 1000 m.

labelled as 50, 100, 200, 500. and 1000. HazeRD is preferred over other dehazing datasets as it provides outdoor scenes, whereas other datasets focus basically on indoor scenes. Another advantage is that this dataset produces haze using real-life parameters, which are more realistic than the prior datasets, using either indoor images or synthetically produced images. In HazeRD, a Matlab function and a demo script is available as well, to create a hazy image with different parameters of haze. It also has the option of noise (by default it is off) for avoiding some unnatural uniformity in the airlight regions. Figure 12.1 shows an example of the dataset image.

# Image Quality Assessment Criteria

## Peak Signal-to-Noise Ratio and Mean Squared Error

Peak Signal-to-Noise Ratio (PSNR) and Mean Squared Error (MSE) [17, 18, 27,41 ] are the two most used error matrices for comparing the quality of the dehazed image. The cumulative squared error among improved dehazed images and the original image is represented by MSE. which can mathematically be represented as:

Here, /,(ш,и) and I2(m,n) are the hazy image and the improved image respectively, MxN is the size of the image, and m, n signifies the x, у location of the image pixel.

A lower value of MSE indicates low error, that is, the lower the value of MSE. the better is the quality of image.

A measure of the peak error is represented by PSNR, which can be described as the reciprocal of MSE. Mathematically, it can be represented as:

where В denotes the bits per sample ranging between 0 to 255. The unit of PSNR is the decibel (dB). The method is considered good if it generates low MSE and high PSNR values.

## Entropy

The entropy of an image identifies its texture and measures the randomness of the image as well. Low entropy specifies that the region is homogeneous, thus a hazy image has lower entropy values compared to a haze free image. Mathematically, it can be estimated as:

where p, indicates the probability of occurrence of one gray level intensity.

## Structural Similarity Index

This index helps in measuring image degradation caused by various processing. Its calculation requires a reference image. Mathematically,

Here, px and p, are the mean of x and у respectively, cr; g; are the variance of x and у respectively, and oxy is the co-variance of x, y. c, and c2 are the variables used for stabilizing the division.

## Contrast Gain

Contrast gain is the mean difference between the contrast of the enhanced image and the original image (hazy image) [6]. It can be calculated by:

where Cf is the mean contrast of the output enhanced image and C, is the contrast of the original hazy image.

The higher the value of the contrast of the enhanced image, the better is the result for the dehazing algorithm.

# Experimental Results and Discussion

Similarly, in Figure 12.3, haze level 100 is considered. In Figure 12.3(c), the output of the white balanced image is given. After applying CLAHE to it, the result obtained seems to be not very appealing, as shown in Figure 12.3(d). To improve the result, GF has been used and its result is shown in Figure 12.3(e). It is observed that the result is quite successful in removing the haze from the background as well.

The experiment has been performed and tested on different hazy images collected from the data set HazeRD. For Figure 12.2, haze level 50 has been considered. Figure 12.2(b) shows that the image is quite hazy. White balancing is performed to adjust the color of the image and the output of the white balanced image is shown in Figure 12.2(c). After applying CLAHE, in Figure 12.2(d), not much visual improvement is observed in the image. So the image is tested by applying GF to it in Figure 12.2(e), where it is observed that, although the visibility of the hazy image has increased, the haze has not been removed totally from the background. Considering haze level 200 for Figure 12.4. it is observed that the result obtained after applying CLAHE. shown in Figure 12.4(d), is not improved much as compared to the resultant image of white balance in Figure 12.4(c). So, to improve the result, GF is applied and the final resultant image is shown in Figure 12.4(e), where haze is seen to be removed and the result obtained is also very appealing. The contrast of the image is also improved as compared to the earlier obtained results.

FIGURE 12.2 Experimental results on hazy Image 50: (a) Ground truth image, (b) Input image, (c) Image after white balancing, (d) Image after applying CLAHE. (e) Image after applying CLAHE+Guided.

FIGURE 12.3 Experimental results on hazy Image 100: (a) Ground truth image, (b) Input image, (c) Image after white balancing, (d) Image after applying CLAHE. (e) Image after applying CLAHE+Guided.

FIGURE 12.4 Experimental results on Hazy Image 200: (a) Ground truth image, (b) Input image, (c) Image after white balancing, (d) Image after applying CLAHE. (e) Image after applying CLAHE+Guided.

FIGURE 12.5 Experimental results on hazy Image 500: (a) Ground truth image, (b) Input image, (c) Image after white balancing, (d) Image after applying CLAHE, (e) Image after applying CLAHE+Guided.

Finally, for Figures 12.5 and 12.6, haze level 500 is considered and the result obtained after applying the proposed algorithm is shown in Figures 12.5(e) and 12.6(e). It can be observed that, the result obtained in both the cases is quite successful in removing haze completely from the image.

So, from the experimental results, it is clear that the proposed algorithm gives a successful result in removing haze from the images having different haze levels.

In Tables 12.1, 12.2, 12.3, and 12.4. the entropy of images, having different haze levels, is calculated individually for each case, that is, for the input hazy image, the WB image, the CLAHE output image, and the proposed algorithm. From the result obtained, it is clearly noticeable that, in every case, the entropy has increased gradually, which further satisfies the definition of entropy as discussed in Section 12.6.

In this chapter, comparison of the contrast gain of the white balanced image, the CLAHE image, and the proposed algorithm is given in Table 12.5, where it can be noticed that the contrast gain is maximum in the case of the proposed algorithm. Similarly, in Table 12.6, a Structural Similarity Index (SSIM) is given and, by comparing the results, it can be observed that the proposed method is better than the individual results obtained from the white balance image and the CLAHE image.

In Tables 12.7,12.8,12.9, and 12.10, PSNR and MSE are calculated for each case, that is, for the white balanced image, the CLAHE output image, and the proposed algorithm. It is observed that the values of PSNR obtained are increasing and the values of MSE are decreasing gradually for all the images having different haze levels. Thus it justifies the definition of PSNR and MSE explained in Section 12.6.

For selecting the value of the clip limit, experiments have been performed by taking different values ranging from 0.001 to 0.02. In Figure 12.7(a), the change in

FIGURE 12.6 Experimental results on hazy Image 500: (a) Ground truth image, (b) Input image, (c) Image after white balancing, (d) Image after applying CLAHE. (e) Image after applying CLAHE+Guided.

TABLE 12.1

Entropy for the Different Images (Haze Level 50)

 Images lnput_lmg WB CLAHE Proposed_Algo 8905 50 4.5328 4.6160 4.1229 5.5894 7033_50 4.7523 4.7523 5.0321 6.1805 8612 50 4.4142 5.0283 4.9598 5.6666 8411_50 4.7069 4.7069 4.9769 5.7104 8602_50 1.0156 1.0156 1.0485 1.3057 9562 50 4.0313 4.3796 4.4768 5.2476 8583_50 6.4290 6.5397 6.6828 7.4777 8895_50 3.5613 3.5613 3.5779 4.1139 7460 50 4.6813 5.0491 4.9275 5.9397 8503 50 5.6430 5.7572 5.8784 6.6873

PSNR values have been plotted against different clip limits, and it is observed that the PSNR values have increased up to 0.004 and, after that, have gradually decreased. It is also observed that from 0.01 the values of PSNR remain almost constant, for all the different haze levels.

Similarly, for Figure 12.7(b), experiments were performed by taking MSE values and different clip limits, and the change in results is plotted in the graph. It can clearly be noted that, considering all the haze levels, MSE values are changing from 0.001 to 0.004 and then increasing; from 0.01 the values are nearly constant. In the

TABLE 12.2

Entropy for the Different Images (Haze Level 100)

 Images lnput_lmg WB CLAHE Proposed_Algo 8905 100 5.4160 5.5104 5.5906 6.3851 7033J00 5.0342 5.4662 5.5616 6.3144 8612 100 4.7288 5.0960 5.4716 5.9133 84I1JOO 5.3070 5.4953 5.6993 6.0931 86O2J0O 1.5804 1.5804 1.8197 2.5705 9562 100 4.4190 4.7700 5.2135 5.7217 8583JOO 6.8261 6.8399 7.0181 7.5408 8895JOO 3.8872 4.3395 4.3820 4.7204 7460 100 5.3353 5.5628 5.8535 6.4265 8503 100 6.0485 6.2272 6.3889 6.7497

TABLE 12.3

Entropy for the Different Images (Haze Level 200)

 Images lnput_lmg WB CLAHE Proposed_Algo 8905 200 5.9866 6.1446 6.2828 6.6998 7033_200 5.1729 5.6113 5.7430 6.2128 8612 200 4.9321 5.5544 5.7897 6.0988 8411_200 5.7225 6.0526 6.2519 6.5294 8602 200 1.8171 1.8171 2.2702 3.5205 9562 200 4.7325 5.3207 5.6718 6.0418 8583 200 7.0706 7.0584 7.2009 7.6185 8895 200 4.0654 4.8206 4.6535 4.9594 7460 200 5.5725 5.9640 6.2490 6.7158 8503 200 6.3318 6.4996 6.7348 6.8685

TABLE 12.4

Entropy for the Different Images (Haze Level 500)

 Images lnput_lmg WB CLAHE Proposed_Algo 8905 500 6.4760 6.6434 6.8270 6.9286 7033 500 5.3028 5.7274 5.9648 6.3246 8612_500 5.1043 5.4662 6.0523 6.2022 8411_500 6.0298 6.3569 6.7168 6.6860 8602 500 1.9799 1.9799 2.5831 3.9649 9562 500 5.0703 5.6726 6.1249 6.4400 8583_500 7.3283 7.2990 7.4185 7.6981 8895 500 4.1707 4.9281 5.0623 5.1402 7460 500 5.7061 6.0856 6.4953 6.7344 8503 500 6.6007 6.7825 7.0328 6.9597

TABLE 12.5

Contrast Gain for Different Images

 Images WB CLAHE ProposecLAIgo 8905 50 0.0094 0.0175 0.2147 8583_50 0.0358 0.0746 0.5171 8612 100 0.0098 0.0497 0.4783 8583_100 0.6488 0.6642 0.8107 8602 200 0.2600 0.2619 0.4303 8503 200 0.0238 0.0679 0.5055 7460 500 0.0308 0.0437 0.3854 8612 500 0.0192 0.0471 0.4381

TABLE 12.6

SSIM for Different Images

 Images WB CLAHE ProposecLAIgo 8905 50 0.3977 0.4325 0.5913 8583_50 0.5753 0.5872 0.7712 8612 100 0.3725 0.3807 0.4922 8583JO0 0.6488 0.6642 0.8107 8602_200 0.2600 0.2619 0.3529 8503 200 0.6596 0.6792 0.7476 7460 500 0.5933 0.6110 0.6772 8612 500 0.5770 0.5960 0.5922

TABLE 12.7

PSNR and MSE for Different Images (Haze Level 50)

 Images WB CLAHE Proposed_Algo PSNR MSE PSNR MSE PSNR MSE 8905 50 60.3165 0.1817 60.3714 0.1793 65.8521 0.0615 7033 50 61.4570 0.1397 61.5453 0.1369 67.2987 0.0364 8612 50 60.6204 0.1702 60.7435 0.1655 63.4328 0.0910 8411 50 62.2395 0.1142 62.4212 0.1119 67.4410 0.0354 8602 50 62.4931 0.1178 62.5186 0.1172 63.1124 0.1036 9562 50 60.8137 0.1622 60.9017 0.1590 63.1684 0.0954 8583 50 64.7303 0.0661 65.3364 0.0575 68.1197 0.0301 8895 50 61.0609 0.1528 61.1456 0.1501 63.5542 0.0866 7460 50 60.0017 0.1960 60.0638 0.1932 61.8371 0.1284 8503 50 62.2970 0.1156 62.5149 0.1100 71.0371 0.0156

same way, considering Figure 12.7(c), (d), and (e), the values of SSIM, entropy, and contrast gain are increasing up to 0.004 and then decreasing, which is clearly visible from the given graphs.

So, considering all the results, discussed in the above section, a clip limit 0.004 is assumed to be the ideal limit for the proposed algorithm.

TABLE 12.8

PSNR and MSE for Different Images (Haze Level 100)

 Images WB CLAHE Proposed .Algo PSNR MSE PSNR MSE PSNR MSE 8905 100 62.4693 0.1108 62.6827 0.1055 72.6006 0.0108 7033 100 64.0733 0.0766 64.2759 0.0731 72.5439 0.0109 8612 100 62.2252 0.1185 62.4898 0.1117 65.1923 0.0629 8411 100 64.7772 0.0651 65.0512 0.0611 71.0179 0.0155 8602 100 62.7623 0.1116 62.8182 0.1055 63.8557 0.0893 9562 100 62.4542 0.1118 62.7117 0.1055 65.8580 0.0538 8583 100 67.0228 0.0391 67.9396 0.0316 69.2701 0.0231 8895 100 62.8090 0.1026 62.9701 0.0989 66.6015 0.0438 7460 100 61.3515 0.1437 61.5766 0.1365 64.8669 0.0641 8503 100 65.1706 0.0599 65.8429 0.0514 73.6977 0.0084

TABLE 12.9

PSNR and MSE for Different Images (Haze Level 200)

 Images WB CLAHE Proposed .Algo PSNR MSE PSNR MSE PSNR MSE 8905 200 65.4788 0.0555 66.2153 0.0469 74.3319 0.0072 7033 200 67.3685 0.0359 67.8051 0.0325 74.3695 0.0075 8612 200 63.8295 0.0832 64.2817 0.0755 66.0236 0.0534 8411 200 67.8332 0.0323 68.6579 0.0267 70.9779 0.0156 8602 200 63.1058 0.1043 63.1808 0.1028 65.1617 0.0680 9562 200 64.4249 0.0721 64.9524 0.0643 68.2702 0.0347 8583 200 69.6355 0.0215 69.2761 0.0131 72.8459 0.0016 8895 200 64.9485 0.0632 65.2555 0.0590 69.6534 0.0237 7460 200 63.3218 0.0915 63.8360 0.0814 69.4296 0.0228 8503 200 68.6587 0.0271 70.1902 0.0190 73.2222 0.0189

TABLE 12.10

PSNR and MSE for Different Images (Haze Level 500)

 Images WB CLAHE Proposed _Algo PSNR MSE PSNR MSE PSNR MSE 8905 500 67.3462 0.0261 69.054 0.0108 75.7431 0.0061 7033 500 69.4035 0.0358 70.5552 0.0186 76.3774 0.0045 8612 500 65.3550 0.0603 65.7849 0.0554 68.4110 0.0059 8411 500 70.4891 0.0221 72.2382 0.0175 75.2609 0.0067 8602 500 63.4477 0.0977 63.5267 0.0962 66.1265 0.0558 9562 500 66.8301 0.0438 67.5183 0.0386 67.5795 0.0386 8583 500 70.2149 0.0205 72.4373 0.0117 75.3941 0.0082 8895 500 67.6465 0.0350 68.2060 0.0312 70.2276 0.0205 7460 500 62.2712 0.0468 67.2298 0.0377 69.3260 0.0235 8503 500 71.8090 0.0287 74.8268 0.0178 78.5556 0.0044

FIGURE 12.7 Experiment results at different clip Limits: (a) PSNR vs clip limit, (b) MSE vs clip limit, (c) SSIM vs clip limit, (d) Entropy vs clip limit, (e) Contrast gain vs clip limit.