Comparison with State-of-the-Art Methods

Evaluation on synthetic dataset. Tables5.1,5.4, and5.5 present the quanti- tative comparison of the proposed scheme with 14 state-of-the-art methods using 15 image quality metrics as mentioned in earlier Sub-section 5.2.2. Based on the proposed figure of merit (f om) in Tables 5.1 and 5.4, it can be observed that the proposed scheme has shown a significant improvement over the existing methods [10,61–63]. Despite the fact that SSIMvalue achieved by [61] on SOTS (outdoor) test set is ∼ 1.35% higher, the proposed scheme outperforms [61] by a noticeable margin of ∼ 86% in overall ranking (f om). One of the important aspect of the single image haze removal problem is color restoration. To evaluate this, we have employed CIEDE which essentially measures the color difference between two images. As reported in Table 5.1, the proposed scheme has outper- formed the existing methods [10,48,56,58,60–63] with the lowest CIEDE value of 11.96. Qualitative analysis on outdoor and indoor test sets, as shown in Fig- ures5.5,5.7respectively, proves the supremacy of the proposed scheme over other

Input DCP [48] EIDBR [55] CAP [56] DEFADE [57] MSCNN [60] NLD [58] AOD-Net [61] DCPDN [10] PQC [62] PLD [63] Proposed

Figure 5.4: Subjective comparison of the proposed method with the existing state-of- the-art schemes on the SOTS (Indoor) test images.

Measure Behaviour Input

DCP EIDBR CAP DEFADE MSCNN NLD AOD-Net DCPDN PQC PLD DSIE

Proposed

[48] [55] [56] [57] [60] [58] [61] [10] [62] [63] [64]

TPAMI‘11 ICCV‘13 TIP‘15 TIP‘15 ECCV‘16 CVPR‘16 ICCV‘17 CVPR‘18 TIP‘18 ECCV‘18 CVPRW‘19 SSIM ❛ 0.6942 0.8595 0.7682 0.8171 0.7565 0.7955 0.7775 0.8260 0.7283 0.8513 0.8445 0.6791 0.8598

PSNR ❛ 11.97 20.04 16.13 18.97 17.20 17.12 17.29 19.07 13.19 20.25 20.28 13.78 19.68

VIF ❛ 0.6858 0.7179 0.6782 0.6468 0.6656 0.7305 0.7808 0.6698 0.7148 0.7785 0.7765 0.4563 0.6945

MSE ❝ 4.856 0.776 2.024 0.983 1.531 1.592 1.427 1.144 3.723 0.722 0.728 3.114 0.914

UQI ❛ 0.6435 0.8492 0.7681 0.7879 0.7326 0.7577 0.7698 0.8019 0.6774 0.8228 0.8144 0.7029 0.8406 LPIPS ❝ 0.1999 0.1033 0.1584 0.1108 0.1449 0.1116 0.1432 0.1014 0.1531 0.0771 0.0779 0.2690 0.1128 MS-SSIM ❛ 0.8771 0.9266 0.8767 0.9095 0.8924 0.9269 0.8968 0.9199 0.8915 0.9432 0.9409 0.7858 0.9267 TV-Error ❝ 0.4808 0.7683 0.9635 0.6685 0.8218 0.6657 0.9738 0.6626 0.6302 0.8343 0.7430 1.0559 0.8786 NIQE ❝ 1.8977 1.2869 1.7616 1.3165 1.6364 1.7327 1.7397 1.6264 2.3240 1.6780 1.7007 3.7639 0.9852 FSIM ❛ 0.9112 0.9418 0.8978 0.9309 0.9289 0.9473 0.9203 0.9410 0.9253 0.9569 0.9573 0.8637 0.9613

CIEDE 2000 ❝ 34.73 11.85 18.76 15.24 18.91 21.39 18.34 16.14 29.00 12.41 13.48 23.36 12.14

Haar PSI ❛ 0.7599 0.8313 0.6751 0.8138 0.7764 0.8514 0.7275 0.8336 0.7180 0.8663 0.8797 0.6332 0.8155 GMSD ❝ 0.0879 0.0668 0.1129 0.0793 0.0805 0.0656 0.0935 0.0652 0.1134 0.0582 0.0547 0.1398 0.0517

BRISQUE ❝ 38.92 34.86 33.48 36.33 33.71 35.44 33.42 34.74 41.74 33.78 34.10 29.87 32.95

SpEED-QA ❝ 15.26 15.83 24.14 18.61 17.49 15.16 20.00 14.00 18.46 14.16 12.92 29.54 10.77

f om ❛ - 2 0 0 0 0 0.6 0.4 0.6 3 3.6 0.6 4.2

Table 5.4: Quantitative comparison on the SOTS (Indoor) dataset. Best and second best results are shown in blue and red colors respectively. A figure of merit (f om) decides the final score as number of (0.6×Best+0.4×Second Best)/Total Metrics. TV- Error is 10⁷.

Outdoor

Measure Behaviour Cycle-Dehaze [67] MAMF [65] MS-PPD [159] Proposed

SSIM ❛ 0.7850 0.7502 0.8119 0.8941

PSNR ❛ 12.93 17.81 17.23 20.57

SpEED-QA ❝ 10.64 21.50 14.84 10.17

Indoor

Measure Behaviour Cycle-Dehaze [67] MAMF [65] MS-PPD [159] Proposed

SSIM ❛ 0.7748 0.7269 0.7687 0.8598

PSNR ❛ 17.18 17.16 16.67 19.68

SpEED-QA ❝ 16.86 24.36 18.97 10.77

Table 5.5: Comparison with other existing methods on SOTS.

methods. Unlike [10,64,67,159], the proposed scheme does not suffer from color degradation. As shown in Figure 5.5(c), results obtained by using [60–62] still contain the hazy part and obscured edgy structures. Whereas, the result obtained by using the proposed scheme is free from such artifacts.

The primary reason behind such improvement may be the use of perceptual loss [8] and the introducedLoG difference as the cost functions. Especially, the LoG loss, which may have improved the efficiency of the proposed model by considering the scale-space of the objects from the initial epoch. The proposed method has also been tested on the benchmark images provided by the Fattal et al. [17] and results are tabulated in the Table 5.2.

Evaluation on real-world dataset. The proposed model has been evalu- ated on several real-world hazy images, as shown in Figure5.6. It can be observed

SSIM = 0.7229 SSIM = 0.6822 SSIM = 0.7587 SSIM = 0.8274 SSIM = 0.8763 SSIM = 0.8054 SSIM = 0.7650 SSIM = 0.9344 PSNR = 12.59 dB PSNR = 21.95 dB PSNR = 14.05 dB PSNR = 20.54 dB PSNR = 22.19 dB PSNR = 18.48 dB PSNR = 20.60 dB PSNR = 22.68 dB

Input DCP[48] EIDBR[55] CAP[56] DEFADE[57] MSCNN[60] NLD[58] AOD-Net[61]

SSIM = 0.7590 SSIM = 0.9211 SSIM = 0.9071 SSIM = 0.7039 SSIM = 0.5298 SSIM = 0.6612 SSIM =0.9633 SSIM = 1.0000 PSNR = 12.23 dB PSNR = 21.96 dB PSNR = 23.07 dB PSNR = 14.42 dB PSNR = 14.92 dB PSNR = 17.41 dB PSNR =26.56 dB PSNR =inf

DCPDN[10] PQC[62] PLD[63] DSIE[64] Cycle-Dehaze[67] MS-PPD[159] Proposed Clean (a)

SSIM = 0.7097 SSIM = 0.9024 SSIM = 0.8343 SSIM = 0.8950 SSIM = 0.8787 SSIM = 0.8087 SSIM = 0.8696 SSIM = 0.8791 PSNR = 12.11 dB PSNR = 19.08 dB PSNR = 15.76 dB PSNR = 20.46 dB PSNR = 18.69 dB PSNR = 17.06 dB PSNR = 20.25 dB PSNR = 19.56 dB

Input DCP[48] EIDBR[55] CAP[56] DEFADE[57] MSCNN[60] NLD[58] AOD-Net[61]

SSIM = 0.9065 SSIM = 0.9228 SSIM = 0.9506 SSIM = 0.6358 SSIM = 0.6595 SSIM = 0.7152 SSIM =0.9522 SSIM = 1.0000 PSNR = 21.71 dB PSNR = 21.65 dB PSNR = 23.02 dB PSNR = 12.96 dB PSNR = 11.29 dB PSNR = 17.68 dB PSNR =23.29 dB PSNR =inf

DCPDN[10] PQC[62] PLD[63] DSIE[64] Cycle-Dehaze[67] MS-PPD[159] Proposed Clean (b)

SSIM = 0.6215 SSIM = 0.8134 SSIM = 0.6426 SSIM = 0.8416 SSIM = 0.7774 SSIM = 0.7496 SSIM = 0.8770 SSIM = 0.8454 PSNR = 11.43 dB PSNR = 20.19 dB PSNR = 11.88 dB PSNR = 22.03 dB PSNR = 17.48 dB PSNR = 16.81 dB PSNR = 21.65 dB PSNR = 18.87 dB

Input DCP[48] EIDBR[55] CAP[56] DEFADE[57] MSCNN[60] NLD[58] AOD-Net[61]

SSIM = 0.7042 SSIM = 0.8607 SSIM = 0.8856 SSIM = 0.6705 SSIM = 0.5681 SSIM = 0.6992 SSIM =0.9029 SSIM = 1.0000 PSNR = 13.40 dB PSNR = 20.09 dB PSNR =22.16 dBPSNR = 13.64 dB PSNR = 13.17 dB PSNR = 15.73 dB PSNR = 19.95 dB PSNR =inf

DCPDN[10] PQC[62] PLD[63] DSIE[64] Cycle-Dehaze[67] MS-PPD[159] Proposed Clean (c)

Figure 5.5: Subjective evaluation of the proposed method with existing schemes in terms of SSIM and PSNR(dB) on SOTS (Outdoor) images.

Input DCP [48] EIDBR [55] CAP [56] DEFADE [57] MSCNN [60] NLD [58] AOD-Net [61] DCPDN [10] PQC [62] PLD [63] Proposed

Figure 5.6: Subjective comparison of the proposed model with the existing methods on the real-world hazy images.

DCP [48] EIDBR [55] CAP [56] DEFADE [57] MSCNN [60] NLD [58] AOD-Net [61] DCPDN [10] PQC [62] PLD [63] DSIE [64] Proposed Platform MATLAB [160] MATLAB [160] MATLAB [160] MATLAB [160] MATLAB [160] MATLAB [160] Pycaffe [161] Torch [156] Keras [162] MATLAB [160] Torch [156] Torch [156]

Time 16.37 2.64 0.78 34.84 1.71 5.05 0.48 0.13^† 29 1.68 6.10^‡ 0.05

Table 5.6: Average running time (in seconds) on the test set SOTS (Indoor). †Tested with images of size 512×512. ‡ On CPU.

Input DCP [48]

EIDBR [55] CAP [56] DEFADE [57] MSCNN [60] NLD [58]

AOD-Net [61] DCPDN [10] PQC [62] PLD [63] DSIE [64]

Cycle-Dehaze [67] MS-PPD [159] Proposed Clean

Figure 5.7: Comparison with the existing schemes on a synthetic hazy image (Indoor).

that the earlier existing approaches such as [48], zhu tend to under dehaze the given images whereas schemes such as [55,57,58] have produced the dehazed im- ages with oversaturated tones. It may be because these methods have used a hand-crafted feature such as dark channel prior, to estimate the haze distribu- tion in the images. As a result, the models may not have generalized well on a variety of hazy images. Recent deep learning based approaches such as [60–63]

have been successful compared to the previous models. However, such methods have failed to address the perceptual quality of the dehazed images. The pro- posed scheme has produced visually appealing results compared to other existing methods. More results are shown in Figures 5.9 5.10,5.11.

Run-time comparison and failure case. The runtime comparison of the proposed scheme with existing methods has been shown in Table 5.6. It can be observed that the proposed model takes about ∼ 0.05 seconds to test an image

Input NLD [58] AOD-Net [61]

PQC [62] PLD [63] Proposed

Figure 5.8: Failure case. The proposed model does not perform well on the images with dense haze.

with an average size of 620 ×460. The proposed method fails to address the images with dense haze, as shown in Figure 5.8. However, the perceptual quality of the dehazed image recovered by using the proposed scheme is better than the same by using the existing methods [58,61–63].