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,

Sample of HazeRD having different visual ranges,

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.

Experimental results on hazy Image 50

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.

Experimental results on hazy Image 100

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.

Experimental results on Hazy Image 200

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.

Experimental results on hazy Image 500

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

Experimental results on hazy Image 500

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

Experiment results at different clip Limits

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.

 
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