Efficient Single Image Dehazing Model Using Metaheuristics-Based Brightness Channel Prior

. Haze degrades the spatial and spectral information of outdoor images. It may reduce the performance of the existing imaging models. Therefore, various visibility restoration models approaches have been designed to restore haze from still images. But restoring the haze is an open area of research. Although the existing approaches perform signiﬁcantly better, they are not so eﬀective against a large haze gradient. Also, the eﬀect of hyperparameters tuning issue is also ignored. Therefore, a brightness channel prior (BCP) based dehazing model is proposed. The gradient ﬁlter is utilized to improve the transmission map computed using the gradient ﬁlter. Nondominated Sorting Genetic Algorithm is also used to optimize the initial parameters of the BCP approach. The comparative analysis shows that BCP performs eﬀectively across a wide range of haze degradation levels without causing any visible artifacts.


Introduction
Images captured in poor environmental conditions, such as haze, fog, and smoggy, suffer from poor visibility issues [1,2]. e haze attenuates the scene radiance with correspondence to an object's distance from the camera [3,4]. e haze imaging model is defined as a linear per-pixel consolidation of an original scene radiance and an airlight [5,6].
Various multiple-images based haze restoration approaches have been implemented [7]. ese approaches require physical characteristics of input images in prior [8][9][10]. But in real life, no physical attributes of input images are available in prior [11,12].
Many techniques have been designed in the literature to remove haze from still images. Oakley and Satherley [13] designed a physical model to restore weather degraded images. e depth map and atmospheric veil were estimated to remove the visibility degradation from weather degraded images. It discovers the law of weather degraded image formation by considering the visual manifestations under various environmental circumstances [14]. Due to the extensive computational complexity of the physical model, He et al. [15] implemented a novel channel prior, that is, dark channel prior (DCP). It assumes that, for an image taken in a sunny environment, the intensity of at least one-color channel approaches toward zero. However, DCP suffers from a number of problems such as sky-region, halo, and gradient-reversal artifacts, color, edges, and texture distortion issues [16]. Recently, researchers have proposed various channel priors to handle the issues associated with standard DCP such as boosting dark channel [17], bounded optimization-based dark channel prior [18], gradient channel prior [19], adaptive bichannel priors [20], sparse dark channel prior [21], and dark channel prior guided variational framework [22]. However, the existing methods perform poorly especially when images contain a large haze gradient. Most of the existing methods suffer from texture distortion issues [23,24].
Guo et al. [25] proposed a fusion model to restore the foggy images. It has shown significantly better edge and color preservation. Yoon [26] implemented a variational minimization based haze restoration model. However, [25,26] are computationally expensive in nature [27]. e primary goal of this research work is to overcome the dehazing artifacts and to preserve significant information of restored images. Brightness channel prior (BCP) is used to obtain the physical attributes of hazy images. e gradient filter is used to refine the transmission map computed using the gradient filter. To optimize the initial parameters of BCP, NSGA is utilized. e comparative analysis is also drawn to evaluate the performance of NSGA based BCP model. e rest of the paper is organized as follows: Section 2 discusses the related work. e proposed model is presented in Section 3. e comparative analysis is presented in Section 4. Section 5 concludes the proposed haze restoration model.

Related Works
Luan et al. [28] proposed a restoration model by using the regression model. Support vector regression is used for regression model learning. Jiang et al. [20] proposed an adaptive bichannel prior to superpixels for removing haze from the single image. e superpixels are used as local regions to estimate the atmospheric light and transmission map by combining bright and dark channel priors. Liu et al. [29] utilized a multiscale correlated wavelet approach for restoring the weather degraded images. In multiscale wavelet decomposition, it has been found that haze mainly presents in the low-frequency spectrum. To remove the haze effect, an open dark channel model (ODCM) is used.
Nair and Sankaran [14] implemented a haze removal approach using a dark channel prior and surround filter. e computational complexity of the approach is due to simple convolution. e surround filter minimizes the memory requirements and enhances the speed of transmission estimation. Wu et al. [30] proposed a restoration model for UAV-based railway images using a densely pyramidal residual network (DPRnet). e loss function is used to preserve the structural information significantly. Shu et al. [31] used a multichannel total variation (MTV) regularizer to restore the hazy images. e alternating direction approach of multipliers is utilized for a nonsmooth optimization problem.
Hodges et al. [32] developed a deep learning-based restoration model (DLR) of weather degraded images. In this, a deep learning model is utilized to train the samples using unmatched images. Zhang et al. [33] solved the problem of bright distortion due to DCP. To eliminate the bright distortion, four parameters, such as mean square error (MSE), mean gradient, program running time, and peak signal-to-noise ratio (PSNR), are evaluated optimally. e logarithmic enhancement approach is used as an optimal approach.
Emberton et al. [34] used haze region segmentation (SRS) to remove haze from images. To address the problem of spectral distortion, a semantic white balancing approach is applied. Guo et al. [35] utilized the deep convolutional network (DCN) to remove the haze from images. Five maps are derived from the original hazy image. e saliency map and exposure map are used to focus on near-region scenes. e gamma correction map and white balance map are applied to gain the components of the intensity and latent color of the scene. e global image contrast is enhanced by using the haze veil map. Alajarmeh et al. [36] proposed an image restoration model based on contrast time airlight and liner transmission (CLT). Two approaches are used such as airlight by image integrals to estimate the airlight value and bounded transmission to estimate the linear transmission maps. Gao et al. [37] proposed a dual-fusion approach (DFT) to restore the hazy images. e segmentation approach is used to divided the regions such as the sky and nonsky. A multiregion fusion approach is used to optimally evaluate the transmission map.

Proposed Brightness Channel Prior-Based
Dehazing Approach is section discusses the designed dehazing model. Figure 1 demonstrates the overall flow of the designed dehazing model.

Depth Map Estimation.
In the first step, BCP is defined to approximate the depth map of a hazy image (H i ) as where Ψ(p, q) defines local patch. δ shows BCP. I c m defines color channels of H i .

Atmospheric Veil.
Atmospheric veil (c) is then estimated as [15]

Coarse Atmospheric
Veil. e coarse atmospheric veil (A v (p, q)) is then computed as [15] 2 Mathematical Problems in Engineering In this paper, a gradient filter is used to improve t as where σ(p, q) defines the standard deviation.

Restoration Model.
In the last step of BCP, a haze-free image (C m ) can be evaluated as

Optimization of Initial Parameters of BCP.
To optimize the initial parameters of BCP, NSGA [46] is used. Flowchart of NSGA based BCP is depicted in Figure 2. NSGA-III [45] has been extensively utilized to solve many computationally complex problems. NSGA-III is preferred over the existing multiobjective optimization approaches as it has good convergence speed and it does not suffer from premature convergence issues [47][48][49]. It utilizes nondominated sorting to sort the nondominated solutions. Table 1 shows the nomenclature of NSGA-III.
Algorithm 1 demonstrates the initial population of NSGA-III based BCP. Initially, a random population is computed. e obtained solutions are then encoded to the range of hyperparameters of BCP. Algorithm 2 demonstrates the working of the proposed NSGA-III based BCP. New visible edges, saturated pixels, and new edge gradients are Mathematical Problems in Engineering used as a fitness function. Dominated and nondominated solutions are then computed. Crossover and mutation operators are then used to compute the child solutions. Nondominated sorting is then implemented by using the dominance relation (). Finally, when termination criteria are achieved, then the optimal initial parameter of BCP is returned. ζ(τ, κ) decompose random individual (τ, κ) to a hyperparameters of BCP.

Performance Analysis
e performance of the NSGA-BCP dehazing model is evaluated on i7 processor with 2.66 GHz and 16 GB RAM. MATLAB 2019a is used to perform the experiments. e patch size is selected as 3 × 3 pixels. Seven well-known dehazing approaches are used for comparative analyses.

Visual Analyses of Proposed Dehazing Model.
e NSGA-BCP based restored images preserve the edge, texture, and color details efficiently.

Mathematical Problems in Engineering 5
values in the table represent the high performance of the given model. Table 2 demonstrates CG analysis. It is found that the proposed NSGA-BCP based dehazing model has significant CG values compared to the competitive dehazing approaches. Overall CG analysis shows that the proposed model achieves an average of 1.9745 CG as compared to the maximum average CG, that is, 1.8932, obtained using the existing dehazing models. Table 3 reveals that the proposed NSGA-BCP based dehazing model has minimum S p values compared to the competitive dehazing models. Overall S P analysis shows that the proposed model achieves an average of 0.0226 S p which is significantly lesser as compared to the minimum average S p , that is, 0.0463 obtained using the existing dehazing models.
Tables 4 and 5 demonstrate that the proposed NSGA-BCP based dehazing model has achieved better e and r values as compared to the existing approaches. Overall e analysis shows that the proposed model achieves an average of 2.9426 e which is significantly better as compared to the maximum average e, that is, 2.7367, obtained using the existing dehazing models. Overall r analysis shows that the proposed model achieves an average of 3.0173 r which is significantly better as compared to the maximum average r, that is, 2.7363, obtained using the existing dehazing models. Table 6 demonstrates execution time (in seconds) analysis. It is observed that the proposed NSGA-BCP based dehazing model is computationally faster than the existing approaches. Overall execution time analysis shows that the proposed model achieves an average of 1.0324 execution time which is significantly minimum as compared to the minimum average execution time, that is, 1.3853, obtained using the existing dehazing models. Table 7 demonstrates haze gradient analyses. It is observed that the NSGA-BCP based dehazing model achieves lesser haze gradient values as compared to the existing approaches. Overall haze gradient analysis shows that the proposed model achieves an average of 1.7483 haze gradient which is significantly minimum as compared to the minimum average haze gradient, that is, 1.9485, obtained using the existing dehazing models. Table 8 shows PSNR analyses of the proposed and the competitive dehazing models. It is found that the proposed NSGA-BCP based dehazing model has significant PSNR values than the competitive dehazing approaches. Overall PSNR analysis shows that the proposed model achieves an average of 27.9136 PSNR which is significantly lesser as compared to the maximum average PSNR, that is, 23.2943, obtained using the existing dehazing models. Table 9 shows SSIM analyses of the proposed and the competitive dehazing models. It is found that the proposed NSGA-BCP based dehazing model has significant SSIM values than the competitive dehazing approaches. Overall SSIM analysis shows that the proposed model achieves an average of 0.8932 SSIM which is significantly lesser as compared to the maximum average SSIM, that is, 0.8395, obtained using the existing dehazing models.

Conclusion
A brightness channel prior (BCP) based dehazing model was implemented. e transmission map refinement was achieved using the gradient filter. e hyperparameters of BCP are tuned using NSGA. e obtained results revealed that BCP outperforms the competitive dehazing models in terms of contrast gain, new visible edges, average gradient, peak signal-to-noise ratio, and structural similarity index metric by 1.9379%, 1.3820%, 1.3289%, 1.9389%, and 1.7392%, respectively. Compared to the competitive models, BCP also minimizes the smog gradient, saturated pixels, and execution time by 1.8382%, 1.2372%, and 0.8272%, respectively.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.
Ethical Approval e research was conducted according to the principles expressed in the Declaration of Hindawi.

Conflicts of Interest
e authors declare no conflicts of interest.