1 Introduction

Satellite imagery has been widely utilized in a variety of remote sensing applications, including astrology, meteorology, earth science, education, agriculture, and Geographic Information System (GIS) mapping. Due to a number of factors including noise interference, uneven illumination, and even the Digital-to-Analog (D/A) conversion process, the visual quality of various of these registered images degrades throughout the image acquisition process. The brightness levels of satellite images, even when they are raw, are usually limited. Because of this, an image quality enhancement strategy is necessary prior to starting the image analysis process as the demand for high-quality images is growing (Kaur and Vijay 2022). Thus, to improve the comprehensibility or the information that people recognize, image enhancement has been utilized as a precursor in almost all applications for image analysis and processing. According to Vyas et al. (2018), image enhancement techniques may be broadly divided into two categories: frequency domain and spatial domain approaches. Contrast enhancement is one of the most popular and successful types of spatial enhancement techniques due to its ability to expand an image’s intensity range and facilitate tasks like object detection and identification. Using lookup tables or transformation functions to change the native image’s intensity figures into a new set of values with optimal parameters is one of the simple yet widely used techniques for increasing image contrast (Mozumi et al. 2022). At the same time as preserving the processed image’s naturalness, the intensity transformation approach should provide effective color replica for multi-band original images. The most often used method for improving global image quality is called Histogram Equalization (HE) (Yoshimi et al. 2024). Among the many study fields where this approach has been broadly utilized are object tracking (Gamal et al. 2023), and various other activities (Can et al. 2021; Acharya and Kumar 2021). HE-based techniques may result in some portions of the processed images being over- or under-saturated since they do not preserve the mean brightness degree of the processed image. A number of enhanced versions have been created, such as the Recursive Mean Separate HE (RMSHE) (Dhal et al. 2021), Bi-Histogram Equalization (BHE) (Bian et al. 2024), and dualistic sub-image HE (Ye et al. 2023). These boosted versions usually approach null processing after several enhancements, which prevents them from offering the best contrast improvement. For this reason, when low-contrast images are enhanced using existing contrast enhancement techniques, particularly for satellite images, they suffer from severe flaws such as brightness aberration, saturation problems, and edge detail distortion. While using an image enhancement technique, it is necessary to minimize these artifacts from the images. A remotely sensed image’s minute details provide crucial information about the spatial positions and intensity degrees. Owing to these important aspects, some Image Contrast Enhancement (ICE) techniques for some images ensure that high- and low-density regions in the images have minimal pixel distortion as well as increase the contrast of the processed image (Dhal et al. 2021). Since most traditional enhancement techniques rely heavily on the input images to be processed, they require manual human intervention. Examples of these techniques are logarithmic image enhancement (Ashish 2020), and histogram equalization (Chaudhary et al. 2022). Automating image enhancement techniques require a reliable assessment technique that works for a range of image datasets across different domains.

A few researchers have recently approached the problem of ICE using a variety of meta-heuristic algorithms. This is because meta-heuristics are prominent and suitable alternatives for successfully addressing a wide range of problems in a wide range of domains (Dinç and Kaya 2023). Among these uses are breast cancer diagnosis (Bourouis et al. 2022), biomedical signal processing (Ahmed et al. 2022), medical image classification (Kumar et al. 2022), and numerous others (Kumar et al. 2022; Dorgham et al. 2022). Meta-heuristic algorithms’ propensity to select a guided random search route has been shown to be highly advantageous in addressing challenging contrast enhancement problems (Khan et al. 2022). By maximizing the fitness function, meta-heuristics for image enhancement seek to identify the optimal set of intensity transformation parameters. According to (Braik et al. 2007a; Braik and Sheta 2011), these parameters ought to offer the best brightness and contrast enhancement in images. Recently, hybridization of optimization methods including path-based and population-based meta-heuristics has also attracted a lot of attention (Bezdan et al. 2021; Braik 2022), aiming to develop a more accurate optimization system for image processing techniques. This method strikes a balance between the elements of exploitation and exploration. Furthermore, a variety of meta-heuristics were integrated with the Incomplete Beta Function (IBF), including differential evolution algorithm (Güraksin et al. 2006) and Particle Swarm Optimization (PSO) algorithm (Rahkar and Ardabili 2021), to automatically determine the optimal parameters of IBF to obtain more enhanced images. However, when the typical IBF expands zones with high or low gray scales, the scopes of processed parameters that may be changed are restricted. This makes image enhancement that is both centrally compressed and has both ends extended completely useless.

1.1 Problem statement

Data gathering in the form of digital images is the foundation of many Image Processing (IP) applications, where rigorous standards for IP are required in many scientific and technical domains, whether seen from the perspective of human or machine vision (Boopathi and Kanike 2023). Captured digital images may have poor contrast throughout the image taking procedure. Some of the factors that cause poor image quality during the image capture phase are uneven ambient light, noise generated during transmission, and non-linear mapping of image intensity (Kaur and Vijay 2022). As mentioned earlier, low-contrast images considerably hinder the functionality of outdoor computer vision systems, which are employed in video surveillance, object detection, and video navigation (Khan et al. 2022). It is in these scenarios that image augmentation techniques show their worth in real-world computer vision applications. For these reasons, it is highly recommended that modest-contrast images in image understanding, and interpretation applications be improved through the use of image enhancement techniques.

It is thus desirable yet challenging to have image analysis methods to derive high-quality images from highly poor-quality images. In this, the goal of ICE is to reduce the influence of unwanted components throughout the capture process, eliminate image deterioration, and ameliorate the visual quality of images. In situations like this, the value of ICE techniques in practical applications becomes evident. Therefore, for such purposes, it is strongly recommended to enhance such low-contrast images using ICE techniques.

1.2 Motives and study goals

As discussed earlier, there is a need for extensive information in satellite and natural imagery, as poor-quality images may result in inaccurate defect detection or defect characterization. Given the difficulty of removing defects using traditional image enhancement methods, this means that it is of paramount importance to maximize the knowledge gained from existing image enhancement methods. In general, image enhancement techniques adjust the pixel data in processed images based on their intended use. Many techniques for improving images have been documented in the literature; nevertheless, certain techniques may be better suited for a specific kind of satellite imagery. While a certain technique might work well for improving low-contrast areas, it might not be the best option for enhancing edge details embedded in the original image. Recent studies have made significant strides in the state-of-the-art for enhancement of satellite and natural images, with certain methods significantly improving the processed images’ quality and contrast (Kaur and Vijay 2022). However, some of the existing image enhancement methods for satellite or natural images do not consider edge information (Kaur and Vijay 2022), and other techniques could struggle with edge localization. They are all not very adaptable when it comes to maintaining edge details. Additional image enhancements are still required, particularly in cases of very low contrast, dim lighting, variable lighting effects, and low edge details. Enhancing the dynamic range of low-resolution images and preserving as much edge information as feasible is also essential. To address the aforementioned issues with existing optimization algorithms in the context of image enhancement, we adopted the Elk Herd Optimizer (EHO) (Al-Betar et al. 2024) in conjunction with other ICE techniques to analyze satellite and natural images in the spatial domain and provide more detailed information about these images.

EHO (Al-Betar et al. 2024) has been used here to carry out the study of interest because of its strong performance in handling a wide range of common benchmark and engineering problems in many disciplines. Though, there are several flaws in EHO, namely its slow rate of convergence and tendency to slip into locally optimal solutions. The more elks travel about in quest of food as well as other activities related to elks, the less diverse it becomes. This suggests that the distribution of solutions over the whole viable region would cause the area to become more localized, which would hinder the elk’s ability to forage. Increasing the range of possible outcomes of this meta-heuristic could therefore boost its variety and prevent it from getting stuck in a local optimality. Here, an Augmented version of the EHO algorithm known as AEGO was proposed to address the previously identified weaknesses of EHO. Then, to create an adaptive ICE technique for natural and satellite images, first, Contrast Limited Adaptive Histogram Equalization (CLAHE) was used as a pre-step to refine the color intensity. Then, the proposed AEHO was fused with IBF to adaptively choose the optimal IBF’s parameters. This will preserve image information and automatically modify the IBF’s gradation transformation curve for a better image enhancement. Following that, an image enhancement strategy was developed using AEHO, with the goal of adjusting the brightness and contrast of low-contrast natural and satellite images. To achieve the satellite image enhancement procedure, a parametrized transformation function was used in this work and assessed using a predetermined fitness function. The processed images’ contrast was then adequately improved by applying Bilateral Gamma Correction (BGC). The purpose of AEHO in this image enhancement method is to determine the optimal combination of intensity transformation parameters to produce appropriate enhancement effects for low-contrast satellite and natural images.

1.3 Contributions of the study

In brief, the key contributions of the proposed work can be briefed as follows:

  1. 1.

    First, an augmented variant of the basic EHO, referred to as AEHO, is developed in a multi-stage process of methods to embrace more exploration and exploitation features of the basic EHO. This in turn improves the convergence rate of EHO and helps to obtain the best possible approximation to the globally achievable optimal solution.

  2. 2.

    Second, the CLAHE method was applied as a pre-processing step to recuperate the color intensity in the processed images.

  3. 3.

    Third, effectively utilize AEHO to obtain the optimal parameters for IBF and use the predefined fitness criterion to enhance the brightness, contrast, and entropy of low-contrast images while keeping maximum edge information locally.

  4. 4.

    Fourth, bilateral gamma correction was used to enhance the visual quality of images without sacrificing edge detail or natural color quality.

  5. 5.

    Fifth, the proposed AEHO-based image enhancement method was assessed using a range of relevant standard assessment measures, and the results were compared with those of other promising image enhancement techniques.

Here is how the remaining work is organized: A comprehensive review of relevant studies in image enhancement is provided in Sect. 2. An exhaustive discussion of the problem formulation and a thorough explanation of the parent EHO algorithm are included in the following Sect. 3. The devised approach for image enhancement is then presented in Sect. 4. Then, in Sect. 5, the quality metrics used to evaluate the algorithms’ quantitative performance are explained in depth. In Sect. 6, the computational and simulation results of the objective tests are presented. The ensuing Sect. 7 highlights the benefits of the created technique for a wider range of future studies and offers concluding remarks and recommendations for more research.

2 Literature review

A review of the literature over the past several years reveals the use of several meta-heuristics for image enhancement in a wide variety of applications. Genetic Algorithm (GA) is one of the oldest algorithms in this field (Munteanu and Rosa 2000). It is noted that Pal et al. (1994) were among the pioneers in using GAs to automatically choose appropriate operators for image enhancement problems to automatically improve image contrast. Next, by measuring the intensity of spatial edges present in the processed image, Saitoh used GA to determine the fitness of the candidate solution (Saitoh 1999). Saitoh also created a transformation relationship that connects the input and output of grayscale images, allowing an initial grayscale image to be turned into a more contrasted one. Although it took longer to process, this strategy was also able to produce enhancement outcomes that were at least somewhat satisfactory when compared to other conventional procedures. In the same year, Munteanu and Lazarescu used a real-coded GA with a subjective objective standard to develop a contrast stretching curve, which they successfully examined on a large set of low-contrast images (Munteanu and Lazarescu 1999).

The authors introduced Gaussian uniform crossover, a potentially useful crossover operator that would allow for more efficient genetic material shuffles throughout evolution. The method’s biggest problem, though, was that the assessment fitness function was very arbitrary in relation to the processed image. Then, based on a real-coded GA procedure, Munteanu and Rosa presented an automated image enhancement method for natural images (Munteanu and Rosa 2000). GA served as a meta-heuristic, or statistical scaling process of sorts, to adapt the parameters of a new expansion to a local enhancement technique. For this reason, a pre-built fitness function was used to improve images’ contrast, entropy, and other characteristics like edge details. Their experimental findings helped to show that their proposed approach of image enhancement may outperform more established techniques like Histogram Equalization (HE) and Linear Contrast Stretching (LCS). Taking into consideration that the enhancement process is a non-linear optimization problem subject to several limitations, Braik et al. developed a promising automatic image enhancement method using the PSO algorithm (Braik et al. 2007a, b). Braik et al. employed PSO to enhance images’ contrast and edge details by maximizing a cost function proposed for that job and modifying several quantifiable parameters. According to the assessment findings, edge details were retained, and the PSO based on the image enhancement technique required less computational efforts than the GA-based approach (Munteanu and Rosa 2000). Gorai and Ghosh (2009, 2011) presented a similar PSO-based image enhancement technique for parameter optimization for grayscale images of a standard dataset. Gorai and Ghosh conducted a comparison and found that their proposed technique outperformed the GA-based image enhancement method in terms of outcomes. Using chaotic sequence evolution techniques, Dos et al. offered many unique approaches to the image enhancement problem (dos Santos Coelho et al. 2009). To guarantee fast convergence, this image enhancement method used a chaotic function to help them avoid early convergence.

The objective criterion described in Gorai and Ghosh (2009) was modified by Dos et al. They conducted a comparative study between the image enhancement problem and the standard Differential Evolution (DE) approach using a set of grayscale images. They thus neglected to provide statistical and analytical research to support the robustness of the image enhancement method. The mean intensity of the processed image is disturbed throughout the enhancement mean procedure, which is a serious issue in many ICE approaches. It makes sense to maintain the image’s average intensity to prevent undesirable artifacts because it also enhances the information in the image.

To increase the contrast of grayscale images while preserving the mean intensity of the processed images, Kwok et al. created the Multi-objective PSO (MPSO) approach (Kwok et al. 2008). The authors have carefully studied gamma correction to preserve density and entropy escalation of the processed image as a fitness criterion. This image enhancement technique was applied to a range of intensities and distributions of grayscale images. Significant contrast enhancement has been successfully accomplished for images using this enhancement technique, especially for images with focused gray levels. Yet, by obtaining peak entropy values with a zero-intensity difference, this method revealed inconsistencies for many of the evaluated images.

Shanmugavadivu and Balasubramanian (2014) assisted in the development of a promising strategy for enhancing image contrast that maintains brightness by averting the abrupt mean shift that arises during the equalization phase of image enhancement. Otsuo’s approach was used to partition the native image’s histogram into two sub-bands, and a set of PSO-obtained optimal weight constraints was used to equalize each band separately. The equalized sub-bands were combined to produce the final contrast-enhanced version of the equalized images. Through experimental analysis, the authors showed that the new method outperformed previous image enhancement techniques in terms of entropy and Contrast Improvement Factor (CIF). The method was less computationally complex and less consistent than previous promising image enhancement techniques. Ye et al. (2015) also introduced an adaptive image enhancement strategy that integrated PSO and Cuckoo Search (CS) algorithms to increase contrast in low-contrast images. To estimate the parameters in the formulation of the intensity transformation function used for that purpose, Ye et al. employed PSO-CS. The quality of the improved image was assessed by computing the improved images’ entropy using a predetermined fitness criterion. The proposed technique for improving images produced high-quality outcomes when compared to previous approaches; nevertheless, the choice of the fitness function, which solely relied on the entropy of the altered images, was deemed to be less appropriate when examined on satellite images in grayscale format.

Bhandariet al. (2015) employed the beta DE approach to optimize the parameters in the transformation matrix modeling. When compared to other cutting-edge image-based enhancement techniques, it produced better quality metric values. yet, it faced a significant issue in amplifying the noisy components embedded in the processed image. Furthermore, the effectiveness of any of the previously described optimization techniques has not been tested on multi-band images. Because hybridization of meta-heuristic algorithms may help ensure that the stages of exploration and exploitation are suitably integrated, it has drawn a lot of interest in many works (Malik 2024).

For image enhancement problems, Hoseini and Shayesteh developed a hybrid approach combining ant colony optimization, GA, and Simulated Annealing (SA) (Hoseini and Shayesteh 2013). Using a promising ICE technique, Gogna and Tayal employed GA, PSO, and DE-SA for enhancing images (Hoseini and Shayesteh 2013; Gogna and Tayal 2013). While using path-based algorithms, like SA, guarantees a thorough search for solutions in favorable regions, it makes the algorithm more computationally intensive and more prone to premature convergence. Using images from the Matlab library, Mahapatra et al. (2015) devised a hybrid approach-which combines the negative selection method with PSO-and evaluated it for image enhancement cases. The method expanded a pre-defined objective criterion to increase the number of pixels of edges compared to HE and LCS as image enhancement techniques. The literature has made extensive mention of the use of nature-inspired algorithms to improve images in the frequency domain (Bhandari et al. 2014). The results were very respectable in terms of the quality metric values obtained. Singh et al. (2016) presented a comprehensive analytical evaluation of the use of several meta-heuristics to enhance contrast in satellite images.

In Khan et al. (2022), an ICE technique for greyscale images is presented, based on the Political Optimizer (PO). To improve PO’s exploitation capability, Adaptive \(\beta\)-Hill Climbing (A\(\beta\)HC), a local search method, was incorporated with it. The best pixel values for low-contrast images were found using the hybridization of PO and A\(\beta\)HC. Utilizing both Kodak and standard image datasets, this enhancement method was examined. The experimental findings demonstrated that this method can successfully outperform many other techniques that were taken into consideration for comparison.

A method for image enhancement based on IBF fusion and BGC is developed in Du et al. (2022). This method used the chimp optimization method to adaptively calculate the parameter values of the IBF. To further increase the contrast of the image, it applied BGC. A set of 12 color images with contrast distortion and a set of 15 contrast approaches were used to test the practicality and effectiveness of this approach. Experimental findings showed that this approach preserves additional image details and has a respectable enhancement impact when blending complex images with numerous characteristics and avoiding over-enhancement.

A novel ICE method for grayscale images is presented in Mukhopadhyay et al. (2022), wherein the optimal or nearly optimal values of the controlling parameters of the IBF are computed with the aid of an optimization algorithm called the Artificial Electric Field Algorithm (AEFA), as opposed to being adjusted empirically. Using the Kodak, USC-SIPI, and MIT-Adobe FiveK datasets, the presented image enhancement strategy was compared to other promising approaches. The acquired simulation results demonstrated that the AEFA-based image enhancement technique improved the overall contrast of images and the inherent information.

In Bhandari et al. (2020), an optimally specified Plateau Limit (PL)-based histogram structure was introduced to preserve brightness and enhance contrast in images without introducing illogical visual degeneration, artificial contrast effects, or structural artifacts. Additionally, it enhances low-light conditions, including backlighting and uneven image illumination, without introducing undesired artifacts. Prior to using the HE method, the disclosed strategy, which was based on clipping operations and sub-histogram, employed PLs to modify the image’s histogram. The Salp Swarm Algorithm (SSA) was used in the enhancement strategy to determine the optimal PLs or adaptive weighted limits. A comparison with other histogram-based processing approaches and state-of-the-art methods documented in the literature was done to confirm the effectiveness of this algorithm.

In Bhandari and Maurya (2020), a brightness-optimized technique for maintaining histogram equalization to preserve average brightness and increase contrast for low contrast images is proposed using the CS algorithm. Extreme enhancement results were realized using a traditional histogram equalization approach, and an artificial look is caused by changing the brightness. To optimize the histogram of the improved image, this approach divided the histogram into two smaller histograms and used the histogram’s statistics to identify the boundaries of the plateaus. The image sub-histograms are equalized and modified based on the estimated plateau boundaries acquired using the CS approach.

Li et al. (2021) presented a Ucolor underwater image enhancement network that uses medium transmission-guided multi-color space anchoring to address color casts and low contrast for underwater images. To improve the visual quality of underwater images, Li et al. used a medium transmission-guided decoder network with several embedded color spaces and physical model-based and learning-based methods. According to the results obtained, the Ucolor technique outperformed other competing approaches.

Oloyede et al. (2022) conducted a comparative study of nine meta-heuristics for Medical Image Enhancement (MIE). The performance levels of these algorithms were assessed using a fitness computation rate. The assessment and transformation functions were combined to generate an objective function that served as the fitness function for the presented methods. For the aim of MIE’s evaluation, samples from various body areas were selected to get the evaluation medical images from the Medpix database. The results indicated that the Whale Optimization Algorithm (WOA) and Grey Wolf Optimizer (GWO) performed marginally better experimentally than other comparative techniques over an average of 1000 Monte Carlo experiments. There was very little statistically significant variance between the comparative techniques.

By determining the best parameters of the IBF, Braik (2022) created a hybrid WOA with the Chameleon Swarm Algorithm (CSA), called HWOA, for image enhancement. To preserve edge detail while improving image contrast and brightness, Braik employed a bilateral gamma adjustment mechanism. Kodak and some landscape images were used to test the HWOA approach, which was evaluated using a range of recognized metrics. The test results indicate that HWOA has effectively outperformed various image enhancement methods. Nevertheless, processing high-resolution images using the HWOA-based image enhancement method necessitates significant computational effort.

Asokan (2023) used a parameter optimization method based on Gabor filter to improve spatial and textural information in satellite images. Asokan proposed a self-adaptable Manta Ray Foraging Optimization (MRFO) for adjusting the filter’s primary parameters in order to remedy the algorithm’s shortcomings in balancing local and global searches. By significantly improving contrast and edge information when compared to other comparative methods on a number of evaluation methods, this method has been shown to be superior to many other image enhancement techniques. By combining PSO with the Black Hole Algorithm (BHA) in two consecutive stages, Pashaei and Pashaei (2023) introduced a hybrid optimization technique for image enhancement that uses an objective function to find the best parameters for a parametrized mapping function. The universal quality index, edge, contrast, and entropy were employed by the objective function to assess contrast and other information in the enhanced images. To evaluate and compare the PSO-BHA-based image enhancement technique with other approaches, a collection of images of various variations was employed. According to the findings, PSO-BHA performed better than all other rival approaches across a range of metrics. An unsupervised learning network and color correction are two components of the sandstorm image enhancement method that Liang et al. developed in Liang et al. (2023). After color compensation, color correction was applied using radical histogram equalization method. Through unsupervised learning, the ambient light with exact initialization, clear image estimate layers, and transmission map were used to remove haze-like effects. Experimental results demonstrated that when tested on a sandstorm image enhancement dataset, this method surpassed a few other competing methods.

Bhandari et al. (2022) divided the input image into two sub-images: low-exposed and high-exposed regions to apply the best weighted multi-exposure histogram equalization model for image contrast enhancement. The input histogram is split into sub-histograms using the exposure information, then clipping and the best weighting technique are employed to limit the amount of over-enhancement. Lastly, to enhance the contrast in dark places, dual gamma correction was used. Based on a predetermined fitness function, the krill herd optimization algorithm was utilized to identify the best constraints for optimizing the degree of enhancement.

Fuzzy Dissimilarity Contextual Intensity Transformation with Gamma Correction (FDCIT-GC) was utilized to enhance color images by either highlighting certain characteristics or reducing unwanted distortions (Veluchamy and Subramani 2020). The following steps make up this method: To determine the average dissimilarity value for every intensity level in the input image, a Fuzzy Dissimilarity Histogram (FDH) was created using the input image. After FDH, clipping was applied to limit the rate of over-enhancement. To improve the display fidelity representation quality, Gamma Correction (GC) was used. The final improved images were obtained by applying Contextual Intensity Transformation (CIT), which restored the image’s inherent qualities. The outcomes showed that the FDCIT-GC algorithm outperformed other existing methods.

A new Bezier curve modification approach was created in Subramani et al. (2021) to enhance the visual quality of undetectable images with contrast degradation. Initially, the salp swarm algorithm was used to determine the optimum threshold value for modifying the transformation in both bright and dark regions independently using a weighted cumulative distribution function. Small features of bright and dark regions are then enhanced using an improved Bezier curve that employs a regularization parameter. Extensive tests on various datasets showed that this approach outperformed other existing approaches in producing improved images with better visual quality for all degrees of contrast-distorted images.

In order to increase the contrast and brightness of satellite images, Malik (2024) combined the Chameleon Swarm Algorithm (CSA) with Crow Search Optimizer (CSO), also known as CCSA. The CCSA method was used to enhance the local contrast, local brightness, and edge details of the processed images with the use of a fitness criterion. Openly available satellite images and a few standard images were used to test the proposed CCSA method. Compared with alternative image enhancement algorithms, the experimental results demonstrated the stability and effectiveness of the CCSA method in consistently improving the brightness and contrast of satellite images.

Trung et al. (2023) introduced a method for enhancing satellite images called Remote Sensing Image Enhancement based on Cluster Enhancement (RSIECE). The fuzzy semi-supervised clustering technique is used to first cluster the input image. Next, based on the cluster, the upper and lower bounds are estimated. A sub-algorithm is then implemented with an enhancement operator for clustering enhancement. To create new equivalent gray levels for every pixel, this sub-algorithm transforms the gray levels for each channel (i.e., Red, Green, and Blue). The RSIECE algorithm outperformed several promising established methods, according to the results obtained.

To improve the soil property maps, a four-step technique called Enhancement and Analysis of Hyperspectral Satellite Images for Soil Study and Behavior (EAHSB) was introduced in Malik et al. (2024). The first step in this method is to enhance the images with better anisotropic filtering. Following that, the areas are divided into regions of interest and regions of non-interest using Fuzzy C-Means (FCM). Several appropriate procedures were used to extract the vegetation index-based characteristics to examine the classification of soil behavior. A hybrid model that combined Deep Residual Network (DRN) and Improved Recurrent Neural Network (RNN) was used to classify soil behavior based on the retrieved characteristics. Computational resources might arise with this method.

2.1 Research gaps

As noticed above, the state-of-the-art in image enhancement is developing, and recent studies have made significant strides (Veluchamy and Subramani 2020; Subramani et al. 2021; Malik 2024; Bhandari et al. 2022). The reviewed image enhancement techniques all performed well in the situations and datasets examined, although they all failed in one way or another, including resistance to illumination variations, low light levels, and the large number of dark areas in the image. Many of them can only do so much with noise and distortion. Additionally, the image enhancement techniques described in Braik (2022), Pashaei and Pashaei (2023), Liang et al. (2023) produced useless artifacts when applied to enhance groups of satellite or natural images. There is still a need for more advancement in image enhancement, particularly for images that have low contrast, low brightness, low visibility, and a large number of dark areas. These issues in image enhancement methods, which include large computational burden, poor results, and lack of promising evaluation methods, need to be addressed in the future.

In order to avoid the negative effects of the above image enhancement methods, this study presents an Augmented version of the Elk Herd Optimizer (AEHO) combined with other traditional image enhancement techniques such as bilateral gamma correction to mend the contrast and brightness of satellite and natural images. Through modifications to the population of EHO, the proposed AEHO was developed to strengthen the global and local searches of EHO while consolidating the exploration and exploitation elements of the original EHO. To demonstrate the effectiveness of the proposed method, a comparison is carried out with other different histogram processing techniques and other similar methods that use the same approach as the proposed method. As will be shown in the results section, the proposed method outperforms other promising techniques in terms of both the objective function and the subjective quality assessment.

3 Background

This section includes a brief synopsis of the related works of the proposed image enhancement technique.

3.1 Bilateral gamma correction

Gamma correction entails adjusting the gamma curve of the processed image to perform nonlinear tone editing, locating the bright and swarthy areas of the image, and increasing the ratio of the two to amplify the contrast impact of the image (Rani and Kumar 2014). The expression of the gamma function can be given as follows (Du et al. 2022):

$$\begin{aligned} I_{o} = cI_{i}^{\gamma } \end{aligned}$$
(1)

where \(I_{o}\) and \(I_{i}\) are the corresponding grayscale values of the target (i.e., output) and raw (i.e., input) images, respectively, and c and \(\gamma\) are two parameters that control the overall luminance of the image and the form (i.e., shape) of the conversion curve, respectively.

When c is set to 1, the values of the input and output images range from 0 to 1. Various variations of the parameter \(\gamma\) will produce distinct stretching effects, as Fig. 1 illustrates. This means that for \(\gamma < 1\), \(I_{o}\) will be brighter than \(I_{i}\), while for \(\gamma > 1\), \(I_{o}\) will be dimmer than \(I_{i}\).

Fig. 1
figure 1

Different curves of the gamma function with various values of the parameter \(\gamma\)

The grayscale value of the image is normalized to fall inside the interval [0, 1] when the value of the parameter c is equal to 1. The gamma functions \(g_a\) and \(g_b\) make up the image enhancement technique on the basis of the global luminosity Bilateral Gamma Correction (BGC) function; their mathematical representations are provided below (Hu et al. 2019; Du et al. 2022):

$$\begin{aligned} g_a(z) = z^{1/r} \end{aligned}$$
(2)

where \(g_a\) is a convex function, represented in terms of the variable z, which is utilized to smooth out dark regions of the processed image, z represents the input image’s gray value, r is an adaptive parameter that controls the amount of image enhancement applied where this parameter is generally equal to 2.5.

$$\begin{aligned} g_b(z) = 1 - (1 - z)^{1/r} \end{aligned}$$
(3)

where \(g_b(z)\) is a concave function, represented in terms of the variable z, which is used to suppress the light regions of the processed image.

Equation 4 provides the last adjustment function produced from weighting the convex and concave functions (Du et al. 2022).

$$\begin{aligned} g(z) = \alpha g_a(z) + (1- \alpha )g_b(z) \end{aligned}$$
(4)

where g(z) is the last adjustment function produced by weighting the convex function, \(g_a(z)\), and the concave function, \(g_b(z)\), and \(\alpha\) is an adjustment variable whose values are within [0, 1].

Equations 2 and 3, respectively, balance the convex, \(g_a(z)\), and concave, \(g_b(z)\), functions, respectively, to get the final adjustment function g(z). Equation 5 can be used to normalize the image before applying the BGC function (Du et al. 2022).

$$\begin{aligned} I_1(x, y) = I(x, y)/256 \end{aligned}$$
(5)

where I(xy) identifies the input image whose intensity values are determined by the coordinates (xy), and \(I_1(x, y)\) stands for the normalized image where the intensity values of its pixel are identified by the coordinates (xy).

Equation 6 can then be utilized to correct the normalized image using the BGC function (Du et al. 2022).

$$\begin{aligned} I_2(x, y) = g(I_1(x, y)) \end{aligned}$$
(6)

where \(I_2(x, y)\) represents the corrected image whose pixel intensity values are given by the coordinates (xy), and g represents the final correction function produced by weighting of \(g_a(z)\) and \(g_a(z)\).

Equation 7 can finally be utilized to determine the range of values in the scope [0, 255] (Du et al. 2022).

$$\begin{aligned} I(x, y) = I_2(x, y)\times 256 \end{aligned}$$
(7)

where I(xy) specifies the final corrected image whose intensity values are adjusted in the range of [0, 255].

3.2 Incomplete beta function

From the perspective of image processing, the relevant transformation functions may be divided into four fundamental categories. These functions are shown in Fig. 2, where different transformation functions frequently used for images of different quality.

Fig. 2
figure 2

Four varieties of analogous gray-scale transformation functions

In Fig. 2, the ordinate displays the grayscale value of the output image, while the abscissa represents the grayscale value of the input image. Every transformation curve may be described by a set of parameters. To automatically fit these four distinct types of transformation functions, Tubbs (1987) created the normalized Incomplete Beta Function (IBF), or F(u), which can be explained as follows (Du et al. 2022):

$$\begin{aligned} F(u) = B^{-1} (\alpha , \beta ) *\int _{0}^{u} t^{\alpha -1}(1-t)^{\beta - 1} \, dt \end{aligned}$$
(8)

where F(u) stands for the normalized IBF, \(0\le u \le 1\), \(\alpha\) and \(\beta\) are the parameters of the IBF, in which \(0< \alpha , \; \beta < 10\), and \(B(\alpha , \beta )\) denotes the Beta function, as defined in Eq. 9 (Du et al. 2022).

$$\begin{aligned} B(\alpha , \beta ) = \int _{0}^{1} t^{\alpha -1}(1-t)^{\beta - 1} \, dt \end{aligned}$$
(9)

where the parameters \(\alpha , \beta > 0\), in which different values of the \(\alpha\) and \(\beta\) parameters can result in different types of transformation curves, as Fig. 2 illustrates.

3.3 Basic Elk herd optimizer (EHO)

In essence, meta-heuristic methods are stochastic population-based models that have emerged from natural adaptation models related to biological computational theories, swarm behavior, and other types. These techniques are frequently strong and useful for solving challenging optimization problems. Each category has many algorithms associated with various behaviors; a thorough examination of these classes and algorithms may be found elsewhere (Al-Betar et al. 2024). The key advantages of such meta-heuristics are their ability to do both local and global searches, as well as their capacity to manage constraints with minimal input needs and a high degree of accuracy. They are therefore very adaptable and capable of handling challenging image processing problems. The mathematical modes of EHO are presented below:

3.3.1 The mathematical model of EHO

Initially, the number of bulls in each family determines how many elks are in the herd. Every family of elks has a bull that leads it throughout the rutting season. The bull’s power determines how many cows or harems the family has. Bulls battle to establish their power via challenges of dominance. Every family then produces calves throughout the calving season that have the same number of family members. The best members of each family are then paired up during the chosen season and invited back for the rutting season. To make sure the resulting elk herd is equipped to handle the difficulties in the surrounding landscape, this process is repeated. Many procedural stages were developed in EHO to connect the elk herds’ breeding cycle with the optimization framework as described below (Al-Betar et al. 2024):

  • Step 1: Initialize the parameters of EHO Two key elements are included in the EHO in order to include the information particular to the problem: the solution representation that elucidates the kind of search space and the objective function that assesses candidate solutions. Generally speaking, the straightforward types of continuous optimization problems where every decision parameter has a range of values. The objective function can be expressed in its general form as in Eq. 10 (Al-Betar et al. 2024).

    $$\begin{aligned} \min _x f({{\varvec{x}}}) \quad {{\varvec{x}}}\in [{\textit{lb}},{\textit{ub}}] \end{aligned}$$
    (10)

    where \(f({{\varvec{x}}})\) is the cost function employed to calculate each elk’s fitness or the solution \({{\varvec{x}}} = (x_1, x_2,\ldots , x_d)\), d is the total number of variables (or solution dimensionality) in each elk’s solution, lb represents the lower bound and ub represents the upper bound. In Eq. 10, each elk has a variable \(x_j\) that refers to one of its attributes indexed by j, where the attribute \(x_j\) lies in the interval \([lb_j, ub_j]\), where \(lb_j\) represents the lower limit at index j and \(ub_j\) stands for the upper bound at index j.

  • Step 2: Create the initial elk herd The population of elk solutions, comprising males and harems, is originally formed as the elk herd (i.e., \({\textbf {EH}}\)). The \(\textbf{EH}\), as expressed in Eq. (11), is a matrix of size \(d \times N\) (Al-Betar et al. 2024).

    $$\begin{aligned} \textbf{EH}=&\left[ \begin{matrix} x^{1}_{1} & x^{1}_{2} & \cdots & x^{1}_{d}\\ x^{2}_{1} & x^{2}_{2} & \cdots & x^{2}_{d}\\ \vdots & \vdots & \cdots & \vdots \\ x^{N}_{1} & x^{N}_{2} & \cdots & x^{N}_{d}\\ \end{matrix} \right] . \end{aligned}$$
    (11)

    where \(\textbf{EH}\) is the initial position of all elks in the search space, \(x^i_j\) represents the ith elk in the jth dimension, and N represents the population size (i.e., number of elks in the herd). Every solution \(x^i_j\) in the continuous domain may be created as presented in Eq. 12 (Al-Betar et al. 2024).

    $$\begin{aligned} x^i_j= lb_{j} + U(0, 1) \times (ub_{j} - lb_{j}) \end{aligned}$$
    (12)

    where \(i = 1, 2, \ldots , N\), \(j = 1, 2, \ldots , d\), \(x^i_j\) represents the position of the ith elk at the jth dimension indicating a potential solution to a problem, and U(0, 1) is a uniformly distributed random value in the range from 0 to 1. Using Eq. 11, the fitness value for every elk’s solution is determined. The elks in \(\textbf{EH}\) are ascendancy ranked on the basis of their fitness scores, such as \(f({{\varvec{x}}}^1)\le f({{\varvec{x}}}^1)\le \ldots \le f({{\varvec{x}}}^i) \le \ldots \le f({{\varvec{x}}}^{N})\), where \(f({{\varvec{x}}}^i)\) is the value of the fitness function of the ith elk.

  • Step 3: Rutting season The EHO algorithm is modeled to generate the families of elks during the rutting season as per Eq. 13 (Al-Betar et al. 2024).

    $$\begin{aligned} \mathcal {B} = \arg \min _{j\in (1,2,\ldots ,B)} f({{\varvec{x}}}^j) \end{aligned}$$
    (13)

    where \(B= |B_r \times N|\) is initially used to compute the overall number of families, \(B_r\) is the bull rate that represents the initial rate of bulls in the herd. In Eq. 13, the bulls in the set \(\mathcal {B}\) begin battling among themselves to form families, where the families of elks are generated during the rutting season according to the bull rate (\(B_r\)). The elks of numbing B with the best fitness values at the top of \(\textbf{EH}\) are considered as bulls, and are chosen from \(\textbf{EH}\). This is intended to simulate combat dominance challenges, in which the stronger elks will be given greater harems after consideration. The roulette-wheel selection method is used to distribute the harems to each bull in \(\mathcal {B}\) as defined in Eq. 14 (Al-Betar et al. 2024).

    $$\begin{aligned} p_j=\frac{|f({{\varvec{x}}}^i)|}{\big |\sum _{k=1}^{B}f({{\varvec{x}}}^k)\big |} \end{aligned}$$
    (14)

    where \(p_j\) identifies the selection probability for each bull \(x^i\) in \(\mathcal {B}\), \(|f({{\varvec{x}}}^i)|\) stands for the absolute fitness value of bull \(x^i\), \(|\sum _{k=1}^{B}f({{\varvec{x}}}^k)|\) represents the total absolute fitness values of all bulls, and B is a parameter used to compute the number of families. In Eq. 14, the harems are assigned to their bulls according to their fitness values in relation to the overall fitness values. To put it technically, the selection probability \(p_j\) for each bull \(x^j\) in \(\mathcal {B}\) will be determined by dividing its absolute fitness value \(f({{\varvec{x}}}^i)\) by the total of all bulls’ absolute fitness values. According to the selection probability \(p_j\) provided by the pseudocode shown in Algorithm 1, the harems will be assigned to the bulls. The harems in the algorithm are reflected in the vector \({\textbf {H}} = (h_1,h_2, \ldots , h_k)\), where the parameter k is equal to \(N-B\). The bull index, which is established by roulette-wheel selection, assigns a number to each harem. For instance, the number of families is represented by \(B=3\) if the elk herd size is ten (\(N = 10\)) and the bull rate is 30%. The formula is \(\mathcal {B}=({{\varvec{x}}}^1, {{\varvec{x}}}^2,{{\varvec{x}}}^3)\), where \({\textbf {H}}=(1, 2, 1, 3, 1, 2, 3)\) is the resulting assignment that can be made to the remaining elks, i.e., (\({{\varvec{x}}}^4, \ldots ,{{\varvec{x}}}^{10}\)), where the first bull has three harems, the second bull has two harems, and the third bull has two harems (Al-Betar et al. 2024).

Algorithm 1
figure a

A pseudo-code describing the roulette-wheel selection method.

  • Step 4: Calving season During the calving season, each family’s calve, \(x^i_j(t+1)\), is generated using the traits mostly taken from their mother harem, \(x^i_j(t)\), and father bull, \({\textit{x}}^{h}_{j}(t)\), according to Eq. 15 (Al-Betar et al. 2024).

    $$\begin{aligned} x^i_j(t+1) = x^i_j(t) + \alpha \cdot \big (x_{j}^h(t) - x_{j}^i(t)\big ) \end{aligned}$$
    (15)

    where \(\alpha\) stands for a random value that falls within the range of [0, 1], \(x^i_j(t+1)\) represents the ith elk at the jth dimension at iteration \((t+1)\), \(x^i_j(t)\) represents the ith mother harem elk at the jth dimension at iteration t, and \(x_{j}^h(t)\) represents the father bull at dimension j and iteration t. In Eq. 15, a calf reproduces (\({\textit{x}}^{i}_{j}(t+1)\)) if it shares the same index i as its bull father in the family. The rate of the inherited qualities from randomly picked elk in the herd \({\textit{x}}^{k}(t)\), \(k \in (1,2,\ldots , N)\), is determined by a random number. As can be inferred from Eq. 15, a large value of \(\alpha\) improves diversity by increasing the chance that random components will participate in the new calf. When a calf’s index matches that of its mother, the elk \(x^i_j(t+1)\) inherits the characteristics of both its father, a bull, and mother, a harem, \({\textit{x}}^j\), as derived from Eq. 16 (Al-Betar et al. 2024).

    $$\begin{aligned} x^i_j(t+1)= x^i_j(t)+ \zeta \big (x^{h}_{j}(t) - x^i_j(t)\big ) + \gamma \big (x_i^r(t) - x^i_j(t)\big ) \end{aligned}$$
    (16)

    where r is the index of a random bull such that \(r \in \mathcal {B}\) in the current set of bulls, \(\gamma\) and \(\zeta\) are two randomly produced values in the range [0, 2], \(x^{h}_{j}(t)\) implicitly stands for the harem bull j, and \(x^i_j(t+1)\) is the ith elk at the jth dimension at iteration \((t+1)\), where this ]represents the calf j’s attribute i at iteration \((t+1)\); this attribute will be kept in \({\textbf {EH}}'\). In rare instances in Eq. 16, if the mother harem bull does not do a good job of defending her, she may also mate with other bulls in the wild. The parts of traits inherited from the previously created calves are randomly determined by the random \(\gamma\) and \(\zeta\) parameters (Al-Betar et al. 2024).

  • Step 5: Selection season The bulls, calves, and harems of each family are united. Technically speaking, the calves’ solutions and the bulls’ solutions are kept in \({\textbf {EH}}'\) and \({\textbf {EH}}\), respectively, and are combined into a single matrix \({{\textbf {EH}}_{temp}}\). Based on their fitness scores, the elks in the \({EH_{temp}}\) will be arranged in ascending order. To ensure that \({\textbf {EH}}^i={\textbf {EH}}_{temp}^i\), for \({i=(1,\ldots , N)}\), the top elks in \({{\textbf {EH}}_{temp}}\) will be retained for the following generation. This kind of selection is known as \(\mu +\lambda\)-selection in the context of evolution strategy, where \(\lambda\) is the offspring population and \(\mu\) is the parent population (Eiben and Smith 2003; Al-Betar et al. 2024).

  • Step 6: Termination criteria The aforementioned steps will be iterated till the termination criteria is satisfied. The maximum number of iteration loops is typically used as the termination criterion. This might represent the maximum reachability of the optimal solution or the maximum number of optimal iterations

Briefly, Algorithm 2 contains the pseudo-code, whereas Fig. 3 provides the flowchart of the basic EHO algorithm (Al-Betar et al. 2024).

Algorithm 2
figure b

A pseudo-code describing the key steps of the basic EHO optimizer

Fig. 3
figure 3

A flowchart describing the basic elk herd optimizer

Since EHO is a superb meta-heuristic optimization method (Al-Betar et al. 2024), it may be used in a variety of contexts, including the one mentioned above. Despite EHO’s effectiveness in achieving an optimum when solving real-world problems, as previously said, its limited search capacity typically traps it in local optima, especially when dealing with complicated optimization problems that have a variety of local optima. This has spurred efforts in this work to enhance EHO’s exploration and exploitation capacities and maintain equilibrium between the previous two aspects to further boost the EHO’s performance. Furthermore, EHO has not been applied to image processing problems, despite its undeniable value in optimization problems. Considering the promising outcomes of EHO in several research fields (Al-Betar et al. 2024), we shall investigate its significance in a significant image processing application in this study. To handle the aforementioned issues in this work, an expanded version of the EHO optimizer is presented for image enhancement problems and applied to determine the best combination of the parameters of the IBF function to improve the images that are being studied. This entails fine-tuning a transformation function’s parameters to adjust the contrast and brightness of satellite and natural images. Detailed mathematical analyses and explanations of the problem formulation and the proposed AEHO algorithm are given in the next section.

4 Proposed AEHO-based image enhancement method

The main goal of the proposed AEHO-based image enhancement approach is to restore and recover detailed information of natural and satellite images in order to improve the low contrast visual appeal of these images. Figure 4 presents the entire block design of the proposed image enhancement method.

Fig. 4
figure 4

Overview of the process flow illustration of the proposed AEHO-based image enhancement method

As observed from Fig. 4, the visual contrast of images in the spatial domain can be strengthened with the help of global intensity modification. To improve the image quality, the intensity values of the original image must be converted to a new set of values using a lookup table or transformation function. This indicates that improving the image histograms and determining a practical intensity mapping transformation function are the most crucial steps in image enhancement techniques. Thus, improving the low contrast visual appeal of images can be achieved by processing and fine-tuning the V element of the image’s HSV color space. This improves the image’s contrast, brightness, and edge details while retaining visual artifacts. This also can lead to the development of a unique transformation function using AEHO and IBF with BGC function as a subsequent fusion function to appropriately alter an image’s contrast to generate the best enhancing impact. This is accomplished by combining the proposed method with a preset objective criterion to identify the optimum parameter settings of IBF based on the characteristics of the original images. More precisely, the proposed image enhancement method, which utilizes the adaptive variables of the IBF found by AEHO, improves and enhances the entropy and details of satellite and natural images. This is achieved by raising the overall contrast of the image while also lowering the gray levels of some bright areas. This implies that the standard deviation, entropy information, and edge details of the treated images are used in the fitness function for each search agent of AEHO to assess the efficacy of the image enhancement approach. To further improve contrast, the BGC function was also used as a last resort.

Below is a detailed explanation of the proposed image enhancement method including the adaptive histogram equalization, related functions, and the AEHO algorithm used for image enhancement.

4.1 Adaptive histogram equalization

4.1.1 Image representation

The input image is first converted from RGB color space (i.e., red, green, channel) to HSV color space space (i.e., hue, saturation, value). Each input image can be represented as: \(o=(H_1, S_1, V_1; \ldots ; H_{M \times N}, S_{M \times N}, V_{M \times N})\). Here, N and M denote the number of pixels in the image’s vertical and horizontal directions, respectively. Each triplet \((H_j, S_j, V_j )\) denotes the intensity of pixel j in each of the corresponding color channels, H, S, and V. Stated differently, the image channels represent the input image o as: \(o=o [x, y]=(H[x, y], S[x, y], V[x, y])^T\), where \(y=1, 2, \ldots , N\) and \(x=1, 2, \ldots , M\). Each detected image’s three-color channels are thought to be statistically independent. The HSV image is then divided into H, S, and V image channels. Because the V channel has more significant information content than the other channels, image enhancement utilizing Contrast Limited Adaptive Histogram Equalization (CLAHE) is only performed on this image component.

4.1.2 Contrast limited adaptive histogram equalization

CLAHE is a type of Adaptive Histogram Equalization (AHE) method (Chakraverti et al. 2024). Using the clip limit and number of tiles parameters, CLAHE figures out the over-amplification issue of the traditional AHE (Zheng et al. 2016). The image is divided into \(M \times N\) local tiles via the CLAHE method. The histogram is calculated separately for every tile. Equation 17 can be first used to get the average number of pixels per area for the purpose of computing the histogram (Kuran and Kuran 2021).

$$\begin{aligned} N_a = (N_x \times N_y)/N_g \end{aligned}$$
(17)

where \(N_a\) represents the average number of pixels, \(N_x\) represents the number of pixels in the x dimension and \(N_y\) stands for the number of pixels in dimension y, and \(N_g\) stands for the number of graylevels. To clip the histogram, we can then specify the clip limit as in Eq. 18 (Kuran and Kuran 2021).

$$\begin{aligned} N_{cl} = N_a \times N_{ncl} \end{aligned}$$
(18)

where \(N_{cl}\) stands for the clip limit and \(N_{ncl}\) stands for the normalized clip limit between 0 and 1. Next, using Eq. 19, the clip limit is established for each tile’s height of the histogram (Kuran and Kuran 2021).

$$\begin{aligned} H_{i}={\left\{ \begin{array}{ll} N_{cl} & if \;N_i \ge N_{cl} \\ N_i & else \end{array}\right. } \end{aligned}$$
(19)

where \(i = 1, 2, \ldots , L-1\), L stands for the number of gray levels, \(H_i\) stands for the height of the histogram of the ith tile, and \(N_i\) stands for the histogram of the ith tile.

Equation 20 can be used to compute the overall number of clipped pixels.

$$\begin{aligned} N_c = (N_x \times N_y) - \sum _{i = 0}^{L - 1} H_i \end{aligned}$$
(20)

where \(N_c\) is the amount of pixels that are cropped. The clipped pixels must also be redistributed once \(N_c\) has been calculated. Redistribution of pixels can be either uniform or non-uniform. The amount of pixels that need to be redistributed may be calculated using Eq. 21 (Kuran and Kuran 2021).

$$\begin{aligned} N_r = N_c / L \end{aligned}$$
(21)

where \(N_r\) represents the amount of pixels that need to be redistributed.

Equation 22 is then used to normalize the clipped histogram.

$$\begin{aligned} H_{i}={\left\{ \begin{array}{ll} N_{cl} & if \; N_i + N_r \ge N_{cl} \\ N_i + N_r & else \end{array}\right. } \end{aligned}$$
(22)

where \(i = 1, 2, \ldots , L-1\)

Equations 20 and 21 are used to calculate the number of undistributed pixels. Repeat Eq. 22 until all pixels have been reallocated. Equation 23 may eventually be used to represent the cumulative histogram of the contextual area.

$$\begin{aligned} C_i = \frac{1}{N_x \times N_y} \sum _{j = 0}^1 H_j \end{aligned}$$
(23)

Following completion of all computations described above, a pre-determined brightness and visual quality are provided by matching the contextual region’s histogram with uniform, Rayleigh, or exponential probability distributions. Assume we have a pixel P(x, y) with a value of s and four center points that are part of the neighboring tiles, which are denoted by the names \(R_1\), \(R_2\), \(R_3\), and \(R_4\). Throughout these four contextual zones, a weighted sum is calculated. Tiles are combined for the output image, and bilinear interpolation is used to remove artifacts across independent tiles. Equation 24 may be used to get the new value of s, which is represented as \(\acute{s}\) (Kuran and Kuran 2021).

$$\begin{aligned} \acute{s}= & (1-y)((1-x) \times R_1(s) + x \times R_2 (s))\nonumber \\ & \quad + y((1-x) \times R_3(s) + x \times R_4(s)) \end{aligned}$$
(24)

After implementing the above steps of CLAHE, lastly, the enhanced image can be acquired, where Fig. 5 shows the enhancement results for an example image using the CLAHE method.

Fig. 5
figure 5

Enhancement results of the CLAHE method: a Input image, b Output image, c Histogram of the input image, d Histogram of the output image

In Fig. 5, CLAHE is used as a pre-step to improve the color intensity of the processed images. The range of intensity levels and the distinction between the lower and upper bounds of pixel values are combined to create the image contrast. Histogram processing is applied to improve the images by supplying a consistent distribution of pixel intensity values, where the primary purpose of an image histogram, which represents the intensity value of the image, is to provide statistical data about the image. For this reason, image enhancements can be made using histograms.

A low contrast image has a limited range of effective intensity. Histogram equalization reorganizes the processed image’s intensity and spreads the intensity distribution. As mentioned above, the Hue-Saturation-Value (HSV) color space is used in this work to convert the input image from the Red, Green, and Blue (RGB) color scheme. Because it is a device-independent color representation format that is perceptually consistent and suitable in situations where color perception is an issue, this color space is a suitable representation for a color image enhancement scheme. A human’s ability to comprehend color images is reflected in the variations in HSV color representation.

The improved V image resulting from the application of the CLAHE method is then used as the input image for the transformation function to do additional processing and enhancement for this image.

4.2 Proposed augmented EHO (AEHO)

The underlying EHO method is supported by a hierarchical population topological structure, which helped to reduce the likelihood of early convergence. Another further issue with EHO is its low exploration and exploitation capacities. Furthermore, the EHO’s search agents will have a strong opportunity to avoid local optimal and pursue the global optimal solution. The hierarchical structure of the proposed AEHO algorithm can be described as follows:

  1. 1.

    Structure hierarchy In AEHO, a four-layer hierarchical design has been developed, which is as follows:

    • Layer 1: Population topology Every search agent in the population is positioned at this stratum. The other layers described below handle the search agents’ motions and positional dispersion at this layer. As a result, this layer primarily offers the AEHO algorithm’s population a full search space, and during the search process, each search agent is free to move about at any.

    • Layer 2: The optimal iteration layer The goal of this layer is to find a large number of the top search agents in the present population so that they can guide Layer 1, or the population topology layer. At this layer, the Q best search agents are selected, which implies that Layer 1 is persuaded to actualize the exploration and exploitation components of AEHO by the best iteration layer, or Layer 2. With the aid of \(B_r\), the crucial EHO’s parameter, at Layer 2, the search agents at Layer 1 are continuously shifting places. Furthermore, the linear decline of the Q best search agents over time dynamically modifies the total number of search agents at this layer.

    • Layer 3: Local optimal layer In order to strengthen the exploration capability and prevent the best search agents M from entering the local optima, this layer was recently added. When it comes to the search process, every search agent has its own historical best position, which is designated as the best search agent. The optimal solution so far is shown by this search agent. It is necessary to locate alternative search agents to help the best search agents Q avoid or escape the local optima, as they are likely to suffer from early convergence only if they just adjust their locations in line with the key parameter (\(B_r\)). Consequently, the personal best search agents that match the best search agents Q are chosen to provide additional information to further guide the search agents at Layer 2. In this, each personal best search agent directly guides the corresponding search agent. Like how the total amount of search agents at Layer 2 changes, so does the amount of search agents at Layer 3.

    • Layer 4: Globally optimal layer At this layer, the AEHO’s exploitation feature aids the population move away from the local optimum and hastens the process of convergence. The population at Layer 1 is further directed by the global best search agent at this layer. The best solution that the population has so far come up with is shown by the global best search agent. Thus, all search agents are moving along the path of the top global search agent to find a better solution, which is the influence of this layer on Layer 1.

    The hierarchy of the proposed AEHO algorithm is intuitively depicted in Fig. 6 as an example. In this figure, there are N search agents at Layer 1 (i.e., \(x_1, x_2, \ldots , x_N\)) and Q best search agents at Layer 2 (i.e., \(I_1, I_2, \ldots , I_Q\)). Layer 2 draws the population at Layer 1 based on the key parameter \(B_r\) of the AEHO. At Layer 2, there is the global best search agent (i.e., gbest) where \(gbest= x_{{opt}(t)}\)), and at Layer 3, there are Q best search agents (i.e., \(lbest_{1}, lbest_{2}, \ldots , lbest_{Q}\)), where \(lbest_{1} = x_{1}^{h_j}\), \(lbest_{2} = x_{2}^{h_j}\), and \(lbest_{Q} = x_{Q}^{h_j}\). The third layer routes the second layer by the top search agents, \(lbest_{1}\), \(lbest_{2}\), and so forth, directs \(I_1\), \(I_2\), and so forth. More guidance for the population topology layer is provided by the global best layer, which implies that gbest offers more routing to the population.

Fig. 6
figure 6

An illustration describing the structure of the developed AEHO optimizer

  1. 2.

    Level-Based Interaction Among the four layers presented in AEHO, there are three different kinds of hierarchical activities, which are described below:

  1. (a)

    The communication between Layers 1 and 2 The parameter \(B_r\) between the Q top search agents at Layer 2 and all search agents at Layer 1 makes them allure. The two layers’ appropriate interaction follows the AEHO’s guiding principles. The purpose of this is to effectively guide the search agents’ process, wherein this layer rates the top-performing pre-defined search agents. The locations of the search agents are updated by Layer 2 telling Layer 1 at each iteration. All search agents correctly need a value of \(B_r\) large enough to accelerate the search process in AEHO. This allows the global exploration of the search space to be done in the first few iterations, and during the iteration loops, this value gradually changes. This infers that a sufficiently big \(B_r\) is needed to increase EHO’s exploration, while a small \(B_r\) is needed to augment its exploitation capabilities. Therefore, to improve the exploration in EHO, the predefined value of \(B_r\) employed in the native EHO was replaced with a plausible formula for this parameter, \(B_r\). Equation 25 defines the mathematical representation of \(B_r\) in AEHO, which is developed using a log-sigmoid function (Braik et al. 2022a).

    $$\begin{aligned} B_r(t) = \frac{B_{r_0}}{1 + e^{\frac{t-\frac{T}{s}}{L}}} \end{aligned}$$
    (25)

    where t denotes the present iteration value, T denotes the maximum iteration value which is 100 in this case, L indicates the curve’s inclination, s is an upper limit that indicates the curve’s center point based on the maximum number of iterations, and \(B_{r_0}\) indicates the biggest likelihood of \(B_r\), which is equivalent to 1. It was obtained after rigorous experimental tests where satisfactory results could be obtained with \(s = 2\) and \(L = 10\). Based on the log-sigmoid transfer function, Eq. 25 demonstrates that the value of \(B_r\)(t) is significantly different from the initial fixed value. Equation 25 displays the graph of the values that change after 100 iterations with \(B_{r_0}\) = 1. As can be shown from Eq. 25, \(B_r\)(t) tends to remain large prior to 50 iterations, after which it rapidly declines to around 0. With enough time to search for the estimated optimum that can be improved upon by subsequent exploitation ability, this impact can ensure that EHO has a high exploration ability in the early phase. Said another way, the newly suggested \(B_r\)(t) can improve EHO’s exploration capacity. This modification is implemented on the medium layer with the intention of altering the search agents’ attraction force, hence influencing their search power and ultimately implementing the development of the bottom layer’s search agent. Additionally, the number of optimal search agents on this layer decreases dynamically as the value of \(B_r\)(t) drops rapidly with iterations. To provide more accurate evolution orientation to all the search agents on the bottom layer, it is advantageous for the global optimum search agent on the top layer to effectively and promisingly lead numerous search agents in the present population (Fig. 7)

Fig. 7
figure 7

The graph of the constant \(B_r\) in AEHO

The reasonable ratio of harems to bulls has a reasonable value in the early stages of the search process to increase exploration capabilities, according to this modified parameter. Following the impact of this parameter, as illustrated by Eq. 25, the search agents at Layer 1 have credible values for this parameter during the iteration loops in which they adjust their locations in accordance with their objective. Because there are fewer and fewer of the best search agents after a certain number of iterations, the number of best search agents becomes fewer and fewer in this layer. To provide an improved pathway for all search agents on Layer 1, it is advantageous for the global optimal search agent on the foremost layer to effectively lead multiple search agents in the present population.

  1. (b)

    Communication between Layers 2 and 3 The personal top search agents are hired to effectively guide the optimal ones. Guidance is given by each personal best search agent at Layer 3 to its counterpart at Layer 2. One-to-one control of this kind can improve each search agent’s search property more in line with its historical best placement. This approach may be expressed as seen in Eq. 26 (Braik et al. 2022a).

    $$\begin{aligned} \eta _{i}(t)= & P_{{opt}^i(t)}+ B_{r}(t) \times N\nonumber \\ & \quad \times \biggl (x_{i}^{h_j}(t) - x_i(t)\biggl ) rand(-1, 1) \end{aligned}$$
    (26)

    where \(i\in Q_{lbest}\), the ith best search agent’s updated position is indicated by \(\eta _{i}\), a uniform random value created in the range \((-1, 1)\) is represented by \(rand(-1, 1)\), and the ith personal best search agent, \(P_{opt}^i\), is the ith best search agent at Layer 2 corresponding to the ith best search agent. The impact among Layers 1, 2, and 3 should occur concurrently to ensure that they interact. To enable the interaction duration between Layers 2 and 3 to be the same as that between Layers 1 and 2, a sigmoid function is used to calculate it. This demonstrates how the Q best search agents are mostly guided by their individual best search agents. Notably, a random value in the range \((-1, 1)\) is used to identify the impact of an individual’s own best search agents on the currently connected search agents. If the random number is positive, it will allow the best search agents Q to migrate closer to their personal best search agents; if the random number is negative, it will force them to move further away from their personal best search agents. As a result, it can guarantee that the best search agents Q are effectively routed and do not become completely stuck in local optima. The best search agents Q receive extra exploration and exploitation skills to change locations based on the connection between these two layers.

  2. (c)

    Communication between Layers 1 and 4 To boost the exploitation potential and hasten AEHO’s convergence in the late search phase, a global best search agent governs the population. As shown in Eq. 27 (Braik et al. 2022a), the concrete control is implemented.

    $$\begin{aligned} \gamma _{i}(t)= & x_{{opt}(t)} + B_{r}(t) \times N \nonumber \\ & \quad \times \biggl (x_{i}^{h_j}(t) - x_i(t)\biggl ) rand(0, 2) \end{aligned}$$
    (27)

    where \(i\in Q_{lbest}\), \(x_{opt}\) denotes the global optimal search agent, rand(0, 2) denotes a uniform random value that falls in the range (0, 2), and \(\gamma _{i}(t)\) signifies the updated location of the instructed search agent \(x_{i}\). + As previously stated, the main purpose of the interaction between Layers 4 and 1 is to improve population performance in the drag search process. As a result, the interactive process between the other layers is characterized using a reverse sigmoid function. More precisely, the aspects of exploration are the emphasis of the interactions between Layers 1, 2, and 3, while the aspects of exploitation are the focus of the interactions between Layers 4 and 1. To ensure that the search agents may move quickly toward the global best search agent, a random number in the [0, 2 is used. Based on this, the population can accelerate even more to improve its position by interacting with these two layers. Eventually, the search agents change their locations as shown in Eq. 28 (Braik et al. 2022a), which is consistent with the three forms of organizational relationships among the four layers.

    $$\begin{aligned} x_{i}(t+1)= x_{i}(t) + \eta _{i}(t) + \gamma _{i}(t)(t) \end{aligned}$$
    (28)

    Consequently, the new exploration positions effectively facilitate and speed up search agents’ efforts, allowing the population to behave more appropriately when searching. To update the search agents’ positions on Layer 1 and effectively reduce EHO’s premature convergence rate while also improving its performance score, Eq. 28 was applied in AEHO.

4.3 Self-adaptation of \(B_r\) in AEHO

A strong exploration component is necessary for the EHO algorithm’s search agents that encounter local optimums in order to eliminate them. In light of this, certain search agents require a sizable value of the parameter \(B_r\) in AEHO to explore the search space, while other search agents just need a modest value to exploit it. Equation 25 was used as the formula for \(B_r\) in AEHO, and this parameter’s self-adaptive in AEHO was employed to address these flaws. The adaptive value of this parameter shows a gradual fading of the exploration feature and a gradual fading of the exploitation feature. If a search agent’s fitness score decreases or stays the same, it means that the search agent can locate the local optimal region of the search space. In view of this, search agents must use a large enough value for this parameter to exit this area. When a search agent becomes more fit, it indicates that there is a greater likelihood that the search agent will find the best solution. For the search agents to become more adept at exploring and exploiting opportunities, the value of \(B_r\) at iteration t has to be raised. In Fig. 8, the self-adaptive \(B_r\) in AEHO is illustrated.

Fig. 8
figure 8

A demonstration of the parameter \(B_r\) in AEHO

In Fig. 8, the sphere, pentagonal, arrowhead, and circle stand in for the local optimal region, global optimal region, and the value of the search agent’s parameter \(B_r\), respectively. As can be seen in this figure, Case 1 leads to the conclusion that in order to enhance a search agent’s capacity to exit a local optimal zone, it needs a sufficient value of \(B_r\). Case 2, on the other hand, demonstrates how a search agent moves swiftly to the ascending global optimal zone. The fitness values of search agent i are recorded using the counters, \(\lambda _i\) and \(\mu _i\), provided in Eqs. 29 and 30 (Braik et al. 2022a), respectively, in order to assess the search agents’ status in AEHO.

$$\begin{aligned} & \lambda _{i}(t)={\left\{ \begin{array}{ll} \lambda _{i}(t-1)+1 & if \;\; f_i^t < f_i(t-1)\\ 0 & if \;\; f_i^t \ge f_i(t-1) \end{array}\right. } \end{aligned}$$
(29)
$$\begin{aligned} & \mu _{i}(t)={\left\{ \begin{array}{ll} \mu _{i}(t-1)+1 & if \;\; f_i^t > f_i(t-1)\\ 0 & if \;\; f_i^t \le f_i(t-1) \end{array}\right. } \end{aligned}$$
(30)

In order to adjust the parameter \(B_r\) in accordance with the fitness values of the fitness criterion, which is used to assess the state of the search agents, Eqs. 29 and 30 are constructed. A search agent has a high likelihood of falling into the local optimum zone if it fails to provide a superior solution quality after several iterations. A search agent may advance to the global optimum if it undergoes several iterations of modification. The modification of the parameter \(B_r\) of the search agents along the iteration route is controlled by a threshold \(\theta\) and a probability \(\rho\). The parameter \(B_r\) will be increased to hasten the convergence rate of search agent i towards the most potent search agent if \(\lambda _{i}(t)\) exceeds \(\theta\). Similarly, the parameter \(B_r\) is enhanced to increase AEHO’s capacity to avoid the local optimum throughout the search phase if \(\mu _i(t)\) exceeds \(\theta\). Equation 31 defines the self-adaptive \(B_{r_i}\) of search agent i (Zhan et al. 2009).

$$\begin{aligned} B_r{_{i}}(t)={\left\{ \begin{array}{ll} B_r{_{i}}(t)\cdot r_{i}^t/2 & if \;\; \tau > \theta \;\; \& \;\;r_z < \rho \\ B_r{_{i}}(t) & else \end{array}\right. } \end{aligned}$$
(31)

where \(r_z\) denotes a random number produced in the interval [0, 1], and the counters \(\lambda _{i}(t)\) and \(\mu _i(t)\) make up the parameter \(\tau\).

In Eq. 31, the search agent requires an extended \(B_r\) to improve its exploration capability when \(\tau\) exceeds \(\theta\) and \(r_z\) surpasses \(\rho\), as it is increased by \(r_{i}^t\).

4.4 Transformation function

A transformation function must be used to change the original intensity of each pixel in low-contrast images to produce images with better contrast. Some methods, as described in Ling et al. (2015), employ a piece-wise linear transformation function to accomplish this goal. Essentially, its purpose is to enhance the contrast of the converted image by optimizing the parameters of the transformation function. Pixels at the point of the subsection may be negative or more than 255 as a result of the transformation procedure. To solve this problem, a continuous curve must be used in place of the piece-wise curve. This study used the improved IBF that was devised by Tubbs (1987).

Due to its continuous and customizable nature, this transformation function may meet the aforementioned criterion. Expanding the image center and condensing both ends has a greater processing impact for the normal IBF but expanding the region with either high or low gray levels results in a more flexible range of parameters. The image enhancement problem for IBF is partially resolved by the BGC function, which uses \(g_a(z)\), a convex function, to boost the dark areas of the image and \(g_b(z)\), a concave function, to dim the bright areas. In this light, the main objectives of this section are to correct the IBF’s parameters with gamma, integrate the BGC function into IBF, and employ AEHO to adaptively optimize the transformation function parameters (\(\alpha\) and \(\beta\)). Achieving adaptive image enhancement, entropy maximization, and crisp edge delineation in low contrast images is the ultimate objective of this effort. The definition of the new Beta function is shown below (Du et al. 2022):

$$\begin{aligned} B_{d}(\alpha _{g(z)}, \beta _{g(z)}) = \int _{0}^{1} t^{\alpha _{g(z)} -1}(1-t)^{\beta _{g(z)} - 1} \,dt \end{aligned}$$
(32)

The definition of the devised IBF can be formulated as shown below (Du et al. 2022):

$$\begin{aligned} F_{d}(u)=\beta _{d}^{-1}(\phi ) *\int _{0}^{u} t^{\alpha _{g(z)} -1}(1-t)^{\beta _{g(z)} - 1}\,dt \end{aligned}$$
(33)

where \(\phi = (\alpha _{g(z)}, \beta _{g(z)})\) and \(0<\alpha , \; \beta < 10\), t indicates the integration parameter and u indicates the intensity of the pixel.

The parameters \(\beta\) and \(\alpha\) in Eq. 33 need to be adjusted for the purpose of obtaining a better fitness value, which results in an enhanced image. As per this, the proposed AEHO algorithm was used to optimize the values of these parameters to obtain a reasonable enhanced image and overcome the issue of over-enhancement, as detailed below.

4.5 Solution representation

Positioning the solution vectors in the search space is carried out by the search agents of the proposed AEHO algorithm. In Eq. 33, \(X^i_j = \alpha\), \(\beta\) represents these search agents, in which these parameters are the input parameters of the new enhanced IBF. In this equation, \(X^i_j\) indicates the contender solution of the ith search agent at the j dimension. Exhaustive exploitation and exploration of the search space is required to find the global optimal solution, which in turn finds the optimal solution vector. The proposed enhancement points embedded into the basic EHO optimizer serve as local and global search strategies to increase the exploitation and exploration capacities of the EHO algorithm. changes.

4.6 Fitness function

Automatic image enhancement technique requires the employment of a suitable fitness function to assess the improved image quality and to determine the best parameter combination for image enhancement. As per this, to ascertain how good a particular candidate is, the fitness of the candidate solution must be assessed subsequent to the development of contender search agents. It is important to remember that different fitness functions might be used as per different standards. The efficacy of the enhanced images is evaluated using a predetermined fitness function. The literature has shown that researchers evaluate the quality of enhanced images created by optimization algorithms using a range of image-related metrics. This research uses certain commonly used image metrics to measure the degree to which an image has been altered and improved, such as:

  1. 1.

    Number of edge pixels (S): An image’s sharpness and quality can be improved by increasing the number of edge pixels. The number of edge pixels in a image, or the number of pixels identified with a Sobel edge detector whose intensity is higher than a predetermined threshold, is indicated by this parameter. Image enhancement requires, among other things, that the edge pixels have a greater intensity than the input image.

  2. 2.

    Image entropy (H): To ascertain the intensity distribution of pixels in an image, the entropy of the image takes into account the image’s histogram. For the enhanced image, the histogram is expected to be more evenly distributed and have better contrast.

  3. 3.

    Standard deviation of the image (Std): It calculates the standard deviation of the edge pixels of the gray level intensity image. After applying an edge detector, like the Sobel edge detector, to the input image, the standard deviation values are calculated and totaled. The contrast of the image is directly related to the value of the Std.

The proposed AEHO optimizer treats image enhancement as an optimization problem, and to automatically enhance the processed image to the required level without requiring human input, a suitable fitness function was used. Consequently, this fitness function is represented by the following (Li et al. 2022; Khan et al. 2022):

$$\begin{aligned} fitness (I_{i}) = \lambda _1H + \lambda _2S + \lambda _3log(Std) \end{aligned}$$
(34)

where \(\lambda _1\), \(\lambda _2\), and \(\lambda _3\) are three constants that represent the weights of different quality criteria, \(I_{i}\) represents the processed image, S denotes the edge content of the analyzed image as determined by the Sobel edge detector and is defined in Eq. 36 (Li et al. 2022), H stands for the image’s entropy, which can be identified according to Eq. 35 (Khan et al. 2022), and Std is the standard deviation of the grayscale values of the image.

In the conducted experiments, the weights of entropy, edge contents, and standard deviation are all the same, or \(\lambda _1 = \lambda _2 = \lambda _3 = 1/3\).

$$\begin{aligned} H (I_{i})= {\left\{ \begin{array}{ll} - \sum _{i = 0}^{255}p_i log_2(p_i) & p_i \ne 0 \\ 0 & otherwise \end{array}\right. } \end{aligned}$$
(35)

where \(p_i\) is the percentage of pixels in the image that have the gray value i, which may be determined in the gray histogram, and \(I_{i}\) is the processed image.

The greater amount of information an image has, and the more level of details are, the higher the entropy value.

$$\begin{aligned} S = \frac{n_edges(E)}{P} \end{aligned}$$
(36)

where P is the total number of pixels in the image, and \(n_edges(E)\) is the number of edge pixels that the Sobel edge detector has detected.

The image has more edge information as a result of the higher the value of S in Eq. 34. Additionally, the test image’s bigger standard deviation (Std) value in Eq. 34 indicates that it has more contrast and is therefore better suited for human vision. Since the enhanced image is intended to have better contrast and uniformly distributed density in its histogram, the proposed AEHO method looks for the candidate solution with the best fitness value. As shown in Eq. 33, each search agent in AEHO provides \(\alpha\) and \(\beta\) as input parameters for the presented IBF. Next, utilizing the newly established IBF found in Eq. 33, these parameters are used to convert the low-contrast image to a high-contrast one by changing the intensity of each low-contrast pixel to an enhanced intensity of the high-contrast image. This image is then used as an input in Eq. 34 to determine the enhanced image’s fitness resulting from the input parameters. As such, there are two phases involved in computing fitness values: Using the enhanced IBF, first, transforming the low-contrast image into a high-contrast one. Second, translating the high-contrast image into Eq. 34 to determine the processed image’s actual fitness.

4.7 Implementation of AEHO-based image enhancement

Using iterative loop processes, the AEHO-based image enhancement approach is put into practice, creating, evaluating, and updating new elk locations. To address image enhancement problems, the developed AEHO added features to the exploration and exploitation aspects of the original EHO algorithm. These activities are performed in each iteration loop up to convergence, at which point the endpoint method is satisfied and the convergence process ends. To put it briefly, Algorithm 3 illustrates the iterative processes of the proposed AEHO algorithm.

Algorithm 3
figure c

A pseudo-code illustrating the proposed method for image enhancement problems

The proposed AEHO algorithm, as it is shown in Algorithm 3, is made to deal with problems related to image enhancement for large-scale, highly complex images as well as satellite and natural images with poor contrast and brightness against both simple and complicated backgrounds. By removing superfluous pixels from the input images and maintaining the relevant information content, the proposed AEHO optimizer seeks to identify the optimum set of transfer function parameters and provide the best enhanced images. Overall, the following key phases may be used to characterize the proposed AEHO-based color image enhancement process for natural and satellite images:

Step 1:

Determine and set up the basic AEHO optimizer’s settings.

Step 2:

Pre-process the native image to be processed. The original image is made up of the following three-color channels: R, G, and B. Its size is \(M \times N\).

Step 3:

Convert the RGB color space of the input image to the HSV color space.

Step 4:

Divide the input image into its three channels (H, S, and V) in the HSV color model space.

Step 5:

Apply the CLAHE method on the V component, and then use the channel V in the proposed AEHO method of image enhancement.

Step 6:

Apply the normalization step to the channel V’s pixel values after using the adaptive histogram equalization process.

Step 7:

Set the AEHO algorithm’s population, or search agents, to their initial values.

Step 8:

Utilize Eq. 33 to figure out the image enhancement approach on the basis of the distribution of the image histogram.

Step 9:

Find the optimal values of \(\alpha\) and \(\beta\) parameters for the IBF using AEHO.

Step 10:

Using Eq. 34, where -fitness is used in this study, determine the population’s fitness score for AEHO and save the best search agent for additional use.

Step 11:

Make use of the optimal settings (\(\alpha , \beta\)) acquired in Step 10 to improve the brightness and contrast of the modified V image.

Step 12:

Incorporate the resulting color components: H, S, and V.

Step 13:

Convert the image from HSV to RGB color representation space, and then evaluate the resulting images using the proposed image enhancement technique.

4.8 Illustration of the proposed image enhancement approach

Figure 9 displays the visual difference between the proposed AEHO algorithm and the fundamental EHO algorithm. This figure shows how the proposed AEHO method, compared with the traditional EHO method, improves the edge and color features in a satellite image, and how the AEHO method displays fine details in the satellite image with fewer artifacts compared to the EHO algorithm.

Fig. 9
figure 9

Enhancement results and convergence study between the basic EHO and the proposed AEHO algorithms: a Original image, b AEHO, c EHO, d Convergence curves

According to the qualitative examination of those images, the proposed AEHO produces the finest effects in terms of boosting brightness and contrast, guaranteeing fine details with little distortion. Figure 9d shows the convergence characteristic plots that illustrate how the proposed AEHO has a very reasonable convergence rate while lowering the chance of early convergence to unsatisfactory solutions. In addition, the convergence results in Fig. 9d help to reveal the consistency of AEHO in enhancing the contrast and brightness of the tested test image.

5 Image quality assessment

This section compares the enhanced images’ quantitative performance to the originals by looking at the full-reference and no-reference quality metrics. In fact, by contrasting the integrity of the enhanced image with the original, the degree of performance of the proposed image enhancement method is evaluated.

5.1 Full-reference quality measures

Image quality assessment primarily focuses on understanding the content and enhancing the contrast and brightness of images (Kaya 2020). Generally, it is vital to evaluate the AEHO-based image enhancement approach to determine its accuracy degree. Put differently, finding objective assessment tools is critical to achieve a sound appraisal of the increased image quality. Based on the computation of a pool of assessment measures between the input images and the corresponding enhanced ones, the performance score of AEHO, which offered the enhancement method for satellite and landscape images, was evaluated. Metrics such as Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Universal Quality Index (UQI), Feature SIMilarity Index (FSIM), Normalized Absolute Error (NAE), and Structural Contrast-Quality Index (SC-QI) are typically used to evaluate the quality of images. The definitions of these evaluation methods are provided below:

  • PSNR: this metric is frequently employed as a quality indicator to gauge how effective an image enhancement technique is (Suresh and Lal 2016). Based on the MSE values computed over the processed image’s pixels, the PSNR value offers a measure of the improved image’s similarity to the original image.

    $$\begin{aligned} PSNR(db) = 10 log_{10}\left( \frac{L^2_{max}}{MSE}\right) \end{aligned}$$
    (37)

    where MSE can be defined as given in Eq. 38.

    $$\begin{aligned} MSE = \frac{1}{MN} \sum _{i=1}^{M}\sum _{j=1}^{N}\left[ O_{i,j} - e_{i, j} \right] ^2 \end{aligned}$$
    (38)

    where e and o denote the processed and original images, respectively, \(M \times N\) denotes the image size, and \(L_{max}\) indicates the value of the highest intensity of the pixel.

  • UQI: this index assessment method is a universal metric measure that can be used for a variety of image processing purposes, which was devised by Wang and Bovik (2002). In general, if the native and enhanced signals are represented as \(\vec {x} = {x_i | i = 1, 2, \ldots , N}\) and \(\vec {y} = {y_i | i = 1, 2, \ldots , N}\), then the UQI method can be calculated as follows:

    $$\begin{aligned} UQI= & \left( \frac{\sigma _{xy}}{\sigma _{x}\sigma _{y}} \right) \left( \frac{2\bar{x}\bar{y}}{(\bar{x})^2 + (\bar{y})^2} \right) \left( \frac{2\sigma _{x}\sigma _{y}}{\sigma _{x}^2+\sigma _{y}^2} \right) \nonumber \\= & \frac{4\sigma _{xy}\bar{x}\bar{y}}{\left( \sigma _{x}^2+\sigma _{y}^2\right) \left( (\bar{x})^2 + (\bar{y})^2\right) } \end{aligned}$$
    (39)

    where the parameters of Eq. 39 can be identified as shown below:

    • $$\begin{aligned} \bar{x} = \frac{1}{N}\sum _{i=1}^{N}x_i \end{aligned}$$
      (40)
    • $$\begin{aligned} \bar{y} = \frac{1}{N}\sum _{i=1}^{N}y_i \end{aligned}$$
      (41)
    • $$\begin{aligned} \sigma ^2_x = \frac{1}{N-1}\sum _{i=1}^{N}(x_i - \bar{x})^2 \end{aligned}$$
      (42)
    • $$\begin{aligned} \sigma ^2_y = \frac{1}{N-1}\sum _{i=1}^{N}(y_i - \bar{y})^2 \end{aligned}$$
      (43)
    • $$\begin{aligned} \sigma _{xy} = \frac{1}{N-1}\sum _{i=1}^{N}(x_i - \bar{x})(y-y_i) \end{aligned}$$
      (44)

The sliding window approach for 2D images should be used to apply this quality index over small regions. Starting from the top left corner of the raw, unprocessed image, a window of size \(v \times v\) glides across each row and column until it arrives at the bottom right corner. The estimated local quality index, \(Q_j\), is then combined to form the UQI for the entire image. Equation 45 may be used to determine the total UQI, given that the total number of steps handled by the gliding window is M.

$$\begin{aligned} Q= \frac{1}{M}\sum _{j=1}^{M}Q_j \end{aligned}$$
(45)

The UQI metric measure was developed to represent the image as a combination of luminance deformation, correlation loss, and contrast deformation components, in contrast to conventional error summation techniques. More appropriately, a higher value of this metric denotes a respectable degree of performance for the algorithm being evaluated.

  • FSIM: this quality metric provides an estimate of the degree of feature similarity between the enhanced and the raw image (Zhang et al. 2011). The mathematical formulation found in Eq. 46 (Bhandari et al. 2016) can be applied to it.

    $$\begin{aligned} FSIM= \frac{\sum _{x\in I}S(x)PC_m(x)}{\sum _{x\in I}PC_m(x)} \end{aligned}$$
    (46)

    where I represents the image, \(PC_m\) is the phase congruity map of the input image and the processed image, where m is \(\in (0, 1)\) which stands for the input and processed images, respectively, and S(x) denotes the similarity between the input and processed images under evaluation. A higher FSIM value suggests that the algorithm performs well in maintaining relevant properties, with FSIM having a value between 0 and 1.

  • NAE: this quality metric measure, which is indirectly related to the quality of the improved image, is used to calculate the effectiveness of the transformation function used for the processed image (Loizou et al. 2006). The mathematical definition of this indicator is given in Eq. 47.

    $$\begin{aligned} NAE= \frac{\sum _{i=1}^{M}\sum _{j=1}^{N}\left| e_{i, j} - O_{i, j}\right| }{\sum _{i=1}^{M}\sum _{j=1}^{N}\left| e_{i, j}\right| } \end{aligned}$$
    (47)

    where \(o_{i, j}\) represents the intensity values of the (ij)th pixel of the raw image and \(e_{i, j}\) denotes the intensity values of the (ij)th pixel of the input image.

  • SC-QI: this measure was developed by Bae et al. (Bae and Kim 2016) and is a potentially comprehensive reference technique for evaluating image quality. The SC-QI score of the processed image may be calculated as shown below.

    $$\begin{aligned} SC-QI_{o, e} = \frac{1}{W}\sum _{m=1}^{B}w\left( o^{(m)}, e^{(m)}\right) f\left( o^{(m)}, e^{(m)}\right) \end{aligned}$$
    (48)

    where o and e represent the input and processed images, respectively; f(oe) represents the local image features; W reflects the normalization element which is derived as a group of all values of w(oe) across all local image blocks B; and finally, w(ow) is the local weight based on the visual foregrounds with respect to its local importance, such as the visual saliency index, degree of information content in the image, and the phase compatibility. A thorough examination of the procedures used to determine the SC-QI score is available in Bae and Kim (2013). Equation 48 indicates that both local and global assessments of visual quality may be accurately described by this evaluation measure. The SC-QI metric value ranges from 0 to 1, where a higher value indicates better performance of the evaluated method for the enhancement problem.

The performance of the image enhancement algorithms is quantitatively evaluated using full-reference quality metrics, which are derived from the aforementioned assessment criteria. As a matter of fact, a well-designed transformation function preserves the important information of the input image, while producing an acceptable enhanced image.

The evaluation metric measures defined above are appropriate for evaluating the enhancement of the processed satellite and natural images, as they can provide an overall measure of performance (Hasan and Kumar 2018; Asokan et al. 2020).

5.1.1 No-reference quality measures

Three no-reference quality criteria were used to objectively evaluate the performance of image enhancement methods. These metrics are defined and discussed below:

  • Discrete entropy (H): Eq. 49 provides a mathematical representation of this metric, which is used to quantify the amount of information contained in an image (Fang et al. 2014).

    $$\begin{aligned} H(e)= - \sum _{i=0}^{L_{max} - 1}p_e(i)log_2\left( p_e(i)\right) \end{aligned}$$
    (49)

    where \(L_max\) is the greatest intensity value obtained in the processed image and \(p_e(i)\) is the probability that a pixel in the processed image e has an intensity value of i. Images with low entropy usually feature many pixels with the same intensity values and very little contrast. This means that this metric may be used to evaluate an image’s contrast in an efficient and appropriate manner.

  • Michelson Contrast (MC) ratio: Eq. 50 (Xueyang et al. 2015) presents the local contrast measure of the image offered by this metric.

    $$\begin{aligned} MC(I)= \frac{I_{max}- I_{min}}{I_{max} + I_{min}} \end{aligned}$$
    (50)

    where the highest and lowest intensity values of the pixels in the \(3\times 3\) window of the processed image I are denoted, respectively, by the variables \(I_{max}\) and \(I_{min}\). A higher value of this metric indicates better contrast for the image under study.

  • Colorfulness Metric (CM): Susstrunk and Winkler (2003) created this no-reference evaluation metric to evaluate the contrast and variety of colors contained in an image, which is defined as given in Eq. 51.

    $$\begin{aligned} CM(e)= \sqrt{\sigma ^2_{\alpha _e} + \sigma ^2_{\beta _e}} + 0.3\sqrt{\mu ^2_{\alpha _e} + \mu ^2_{\beta _e}} \end{aligned}$$
    (51)

    where \(\beta = \frac{R+G}{2} - B\), \(\alpha = R - G\), and \(\mu\) and \(\sigma\) denote the mean and standard deviation of the parameters \(\alpha\) and \(\beta\). The input and processed images are denoted by o and e in each parameter, respectively. The performance level of the analyzed method would be promising, as indicated by the greater value of CM in Eq. 51, which indicates superior image enhancement performance.

The non-reference quality metrics given by Eqs. 49, 50, and 51 are widely used reference norms for estimating the quality of enhanced color images. These metrics are helpful for determining how well the proposed image enhancement approach will be able to enhance the contrast and brightness of satellite and natural color images that are the subject of this study. They can also offer a broad assessment of the precise extent of the image enhancement techniques (Singh et al. 2017, 2019; Sidike et al. 2018; Suresh et al. 2024).

6 Experimental results

The assessment and simulation findings of the image enhancement problem are presented in this section. The characteristics of the image datasets used in the assessment tests are provided in this section. This section also presents the alternative algorithms to the proposed one, together with the parameter configurations that were utilized for the assessment tests. The effectiveness of the proposed image enhancement technique is then demonstrated by comparing the assessment results of the proposed method to others utilizing the evaluation metrics indicated earlier.

6.1 Image datasets

The public benchmark dataset utilized in this section was collected from Satellite Imaging Corp, NASA, and Satpalda Geospatial Services (Suresh and Lal 2017). This benchmark dataset includes more than 50 natural images and more than 100 panchromatic satellite images. As per this, the proposed AEHO-based image enhancement method was tested on a large number of images gathered from the aforementioned locations. While there are significant lighting differences in global space, all the images used in this investigation exhibit modest contrast in the nearby areas. Although several color satellite images were used to evaluate the proposed AEHO-based image enhancement approach, we only include the findings from a small number of these images in this paper. This paper includes the results of enhancing eight satellite images and two natural images.

Images with different illumination levels were selected, which will help to clearly illustrate the strength of the generated AEHO. The basic characteristics of these experimental satellite and natural images are shown in Table 1.

Table 1 Important details regarding the images used in the assessment experiments

As can be seen in Table 1, the experimental dataset employed in this work consists of several images gathered in a variety of locations and settings that can be seen all over the world. This makes the dataset perfect for evaluating the effectiveness of the proposed image enhancement method. The dimensions of these images are detailed in Table 1. The selection of this broadly available benchmark dataset enables us to assess the proposed image enhancement method using real-world satellite images and natural images, which can be useful for a number of remote sensing applications. Although this dataset provides a large number of test cases, only a subset of the experimental findings are shown and illustrated in Table 1 due to the scope of the paper.

6.2 Comparative methods

Studies were carried out using well-established state-of-the-art enhancement techniques, including Low-light IMage Enhancement (LIME) technique (Guo 2016), Regularized-Histogram Equalization and DCT (RHE-DCT) (Xueyang et al. 2015), Low Color Correction (LCC) (Lisani et al. 2016), Tone Mapping Method (TMM) (Lisani et al. 2016), and Linking Synaptic Computation Network (LSCN) (Zhan et al. 2017). This is to make a comparison regarding the optimization ability and quality of enhancement of the proposed AEHO-based image enhancement method. Additionally, utilizing the same image enhancement procedures as the proposed AEHO, the parent algorithm of the proposed AEHO, known as the Elk Herd Optimizer (EHO) (Al-Betar et al. 2024), was adopted to build an image enhancement method. Differential Evolution (DE) algorithm (Storn and Price 1997), Artificial Bee Colony (ABC) algorithm (Nouria and Farhad 2020), White Shark Optimizer (WSO) (Braik et al. 2022b), Particle Swarm Optimization (PSO) algorithm, Electric Eel Foraging Optimization (EEFO) algorithm (Zhao et al. 2024), Walrus Optimizer (WO) (Han et al. 2024), Newton-Raphson-Based Optimizer (NRBO) (Sowmya et al. 2024) are some examples of meta-heuristic algorithms that were used to develop other comparative image enhancement algorithms. Notably, the image improvement technique employed by the proposed AEHO was the same as that of the image enhancement approaches established based on these population-based algorithms. It is important to note that some of the comparative algorithms including EHO, DE, ABC, WSO, PSO, WO, NRBO are general-purpose optimization methods known as population-based algorithms. Many of these algorithms such as DE, ABC, and PSO have proven effective in solving a variety of combinatorial optimization problems as broadly reported in the literature. It is also important to notice that each of these algorithms may belong to a different category of inspiration such as evolutionary theory, swarm intelligence, physics, or others. In general, population-based meta-heuristics are good at exploring the search space but are not always so good at exploiting each potential area of the search space.

The RHE-DCT-based image enhancement method regulates the histogram of the original input image to submit it to the initial global contrast enhancement phase. Next, a distribution function of the original raw image is created by combining a sigmoid function with the histogram. Next, the traditional HE method is applied to produce a new image with improved global contrast. To improve the local details in the processed image, the DCT coefficients are dynamically modified (Xueyang et al. 2015). The LCC method is thought to be an extension of Land’s Retinex hypothesis, which describes how people naturally perceive color as being about constant under various lighting circumstances. By focusing on the computational aspects of the problem, it lessens the fragile nature of the Retinex theory (Lisani et al. 2016). An appropriate Tone-Mapping Operator (TMO) may be found using the statistical TMM approach (Mai et al. 2010), which can greatly improve the overall quality of the reconstituted image. To find the optimal tone curve that reduces the expected Mean Square Error (MSE) and, consequently, the overall computational load complexity, the model formulates an optimization problem (Xueyang et al. 2015).

The developed connecting synaptic computing in the visual cortex through local coupled synaptic modulation is inspired by gamma-band oscillations. Through the connected synaptic process, the fusion of spatiotemporal information may be absorbed into the network. The LSCN approach uses the final state of the linking synaptic process (Zhan et al. 2017) to extract the enhanced image from the input image. The LIME technique was specifically developed to enhance images taken in low light. This approach is based on a model that decomposes each of these collected images into the illumination (shading) images and the whiteness of the scene (Guo 2016). To obtain an image with more enhanced details, the method uses a raw illumination map estimating pace that is continuously modified while taking advantage of local consistency.

Based on an intensity transformation function akin to the one proposed in AEHO, the EHO and other competing image enhancement methods, including DE, ABC and others, work to amplify a particular fitness standard. Eventually, the method yields an optimal set of parameters depending on the transformation function, which may effectively improve the raw images. The transformation function-based fitness criterion, which is amplified to create a new set of pixel intensity values for converting the input image to an enhanced version, is utilized in the optimization process. The other competitor optimization algorithms, like WO, NRBO, and PSO, also optimize different and district parameters used to convert the low-contrast input image into a better one by adhering to the previously stated procedures. In reference to the above-discussed proposed AEHO, an appropriate arrangement of the exploration and exploitation phases increases its versatility in enhancing low contrast images for image processing applications.

6.3 Experimental settings

All of the aforementioned image enhancement techniques were started with a fixed population size of 30 and run for a given number of iterations, with a value of 100, in order to provide a good comparison of the outcomes between the various techniques. Table 2 displays the parameter settings for the additional parameters applied by the different image enhancement methods. Using Matlab R2022a under Microsoft Windows 16 platform, all of the previously described methods were implemented and created on an Intel Core i3 PC with a 64-bit operating system, a 2.3 GHz processor, and 4 GB of RAM.

Table 2 Parameter settings used in each comparative meta-heuristic optimization algorithm

The number of images to be processed, the time required to enhance each image under study, and the algorithm’s complexity all affect the computational speed. The outcomes of the proposed image enhancement technique are documented using the previously mentioned performance criteria and contrasted with a few well-known conventional and cutting-edge methods presented in the literature. The specs for the hardware, software, and programming language were given to show how effective the developed image enhancement methods in terms of computational efforts. The parameter settings for each competing algorithm in Table 2 were chosen as published in their original works. The common control parameters including number of iterations, search agents, and number of experiments were used based on what is reported in the relevant literature. This is intended to ensure a fair comparison between all competing meta-heuristic algorithms used for image enhancement.

6.4 Computational and simulation results

This section presents the comprehensive image enhancement results obtained by comparing the created AEHO with the other previously mentioned methods. Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13 display the findings from the analysis conducted to compare the proposed AEHO with other twelve enhancement algorithms, taking into account all of the previously mentioned metrics, for the given image dataset. Note that the bold results in tables refer to the best solutions obtained). The best possible conclusion in each scenario is reinforced in bold. AEHO outperforms all other comparative techniques by a reasonable margin, as demonstrated by the assessment of the stated metric values for each method.

Table 3 Overall edge intensity acquired using AEHO and other image enhancement algorithms
Table 4 The quantity of edgels found using AEHO and other methods for enhancing images
Table 5 Fitness values produced by various image enhancement techniques as well as AEHO
Table 6 PSNR values from several image enhancement techniques, including AEHO
Table 7 MSE values acquired by different image enhancement techniques and the proposed AEHO method
Table 8 NAE values produced by AEHO and various other methods for image enhancement
Table 9 UQI values produced by AEHO and additional techniques for image enhancement
Table 10 FSIM values produced by various image enhancement techniques as well as the proposed AEHO algorithm
Table 11 SC-QI scores produced by AEHO and other image enhancement techniques
Table 12 Discrete entropy (H) scores produced by AEHO and other techniques for image enhancement
Table 13 CM values produced by AEHO and other techniques for image enhancement

Table 3 shows that the intensities of the improved images produced by the proposed AEHO algorithm are higher than those of other methods. This is evident in every case considered. In addition, in most test instances, the sum of the edge pixel intensity values of the enhanced images generated by AEHO are significantly higher than those of other competing methods.

The number of edge pixels in each image is represented by the edgels metric, as Table 4 illustrates. As mentioned earlier, edge information was factored into account while applying the proposed AEHO to enhance the images. The numbers of edge pixels in the enhanced images are significantly higher than those of the original images, as Table 4 makes evident. This suggests that the image enhancement techniques examined in this study are successful. The enhanced images produced by AEHO have a significantly higher number of edge pixels than the similar enhanced images produced by other competitors. This indicates the superior robustness and dependability of the proposed approach over other competitors.

In comparing the proposed AEHO with those of rival techniques, the fitness criterion is also employed. In the event that the enhanced images’ edge pixels, entropy, and intensity surpass those of the matching raw images, the fitness measure’s values are raised. As can be seen from Table 5, the enhanced images have greater fitness values than the raw images. This shows that the edge details and other information content in the images may be effectively boosted by the image enhancement techniques examined in this study. In addition, the proposed AEHO algorithm’s fitness values significantly outperform those of competing approaches, demonstrating the strength and resilience of AEHO.

The PSNR values produced for each image utilizing the proposed AEHO-based image enhancement approach are shown in Table 6, and indicate a significant improvement in the processed images’ quality when compared to the associated input images.

For the proposed AEHO method, the evaluation results of MSE and NAE criteria are substantially lower than those of other competing approaches, as shown in Tables 7 and 8, respectively. This demonstrates how well the proposed AEHO algorithm optimizes the set of parameters used in the intensity transformation procedure.

The UQI measure, a highly useful statistic for evaluating the efficacy of image enhancement techniques, provides the foundation for the image enhancement findings in Table 9. Upon examining the findings in this table, it is evident that AEHO outperforms other rival techniques, which consistently yielded extremely respectable outcomes for every satellite image and landscape image examined.

The results of the FSIM measure, as shown in Table 10, demonstrate how well the proposed AEHO method preserves important characteristics that appear in the input images. These results support AEHO’s adoption for other pertinent image processing uses.

For every image taken into consideration in this investigation, the proposed AEHO algorithm has the higher values for the SC-QI metric in Table 11. These values are substantially better than those of certain competing methods and marginally better than those of other methods. This attests to AEHO’s capacity to enhance the visual characteristics of both local and global images.

Table 12 presents the discrete entropy score results that provide insight into the image’s information content. In this case, the enhanced images will have higher entropy values than the original images if they have more balanced histograms than the native images. This is because an equalized histogram increases the entropy of the modified image. While the findings of those comparable approaches are promising with a reasonable degree of performance, it is clear from reading Table 12 that AEHO is the best contender for image enhancement among the others.

The results shown in Tables 12, 13, and 14, respectively, for no-reference performance measures like discrete entropy, MC, and CM show the encouraging level of performance of the proposed AEHO algorithm when compared to other conventional image enhancement techniques and other meta-heuristics that employed the same enhancement method of the proposed AEHO algorithm.

Table 14 MC values acquired using different image enhancement techniques and the proposed AEHO method

6.5 Visual assessment of the enhanced images

For the purpose of evaluating the proposed AEHO-based image enhancement against other image enhancement methods for enhancing contrast and brightness information of images, Figs. 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 show the subjective evaluation of satellite and natural images processed using different image enhancement methods.

Fig. 10
figure 10

Enhancement outcomes of image A a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 11
figure 11

Enhancement outcomes of image B a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 12
figure 12

Enhancement outcomes of image C a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 13
figure 13

Enhancement outcomes of image D a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO. Color figure online

Fig. 14
figure 14

Enhancement outcomes of image E a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 15
figure 15

Enhancement outcomes of image F a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 16
figure 16

Enhancement outcomes of image G a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 17
figure 17

Enhancement outcomes of image H a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 18
figure 18

Enhancement outcomes of image I a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Fig. 19
figure 19

Enhancement outcomes of image J a Original, b RHE-DCT, c LIME, d LCC, e TMM, f LSCN, g DE, h ABC, i WSO, j PSO, k WO, l NRBO, m EEFO, n EHO, o Proposed AEHO

Figures 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 show the visual enhancement outcomes of various competing approaches and the proposed AEHO algorithm. The input images are shown in the upper left corner, the findings of the proposed AEHO are shown in the bottom right corner, and the results of the competing techniques are shown in the remaining images. The visual evidence of these figures clearly shows that the proposed AEHO method adequately enhances each feature of the original images. These graphical results also demonstrate how the proposed AEHO method regularly maintains the mean intensity of the images it works on, while maintaining their normalcy. The results show that AEHO is suitable for satellite and natural imaging and emphasize its advantages even further.

Figures 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 show that the brightness and contrast were improved to a reasonable degree by the proposed AEHO algorithm. The images have smooth overall brightness, with just the appropriate amount of darkness and exposure. Further explanations of the visual results displayed in Figs. 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 are found below. The contrasts of the images produced by the standard approaches-RHE-DCT, LIME, and TMM-are clearly inferior even after enhancement, as Fig. 10 makes clear. In contrast, the image exhibited in Fig. 10o for the developed approach has a better contrast with higher edge details. Furthermore, the algorithms’ final outputs-which include WO, NRBO, EEFO, and EHO-have reasonable brightness and contrast.

The contrast and brightness of the processed image in Fig. 11o were much better than those of the original image and every other competing method shown in Fig. 11. Figure 12o displays the enhanced image obtained by AEHO. It is highly detailed and contains vivid natural color information. In contrast, the image generated by RHE-DCT is darkish, but the image generated by LIME is white. Furthermore, there are faint edge features and moderate contrasts in the enhanced images created by WO, NRBO, EEFO, and EHO algorithms.

As seen in Fig. 13, the proposed AEHO method removed the satellite image’s overall dark tint and created a suitable color with better contrast. However, the RHE-DCT findings’ black color stayed virtually unchanged, giving them an unappealing visual look. Furthermore, the contrast and brightness of the images produced by LIME and PSO are still inadequate even after the images have been increased. Although not as excellent as those of AEHO, the enhancement results for the images obtained by NRBO, EHO, and EEFO are nevertheless good. Compared with the images created by the WO, WSO, and PSO algorithms, the one produced by AEHO has a better contrast and brighter color.

It is evident from Fig. 14n and o that the proposed AEHO method and the basic EHO algorithm can successfully improve the color of the input images, respectively. Moreover, compared with other competing techniques, the contrast of the image generated by AEHO in Fig. 14o is sharper and more efficient. Nevertheless, images that have been enhanced by RHE-DCT method have noticeable dark tones. The brightness and details of the images created by WO, EEFO, NRBO, and PSO are much better than those of AEHO, albeit not quite as much.

According to the results displayed in Fig. 15, the proposed AEHO enhances low-light regions’ brightness in an adaptive way, and the enhancement characteristics are commensurate with those observed in actual satellite images. Figure 15o displays AEHO’s brightness and enhancement characteristics in a highly realistic manner with exquisite details. While the contrast of the images produced by RHE-DCT, LSCN, and TMM were all somewhat enhanced, the contrast of the image produced by LCC was only marginally better than the original image.

Even if the image created by TMM is whiter, the end produced image is still very noticeable. The clarity, adequate contrast, brightness, and edge detail of the enhanced images generated by NRBO and EEFO are commendable but fall short of AEHO’s outcomes. Even while the TMM approach produces a considerably whiter image than the original, the benefits of the enhancement are still extremely evident. While they do not quite reach the levels of the intended AEHO method, the images produced by WO, PSO, and EHO deliver clear enhanced results with respectable contrast, brightness, and edge detail.

The AEHO enhancement results, as shown in Fig. 16, have sharper contrast and are more visually acceptable than other competing algorithms. It is apparent that the contrast enhancement produced by WO, NRBO, and PSO has a reasonable level of improvement over the contrast enhancement produced by RHE-DCT and LCC techniques. Figure 17o shows the completely satisfactory enhancement results of AEHO, with no negative effects on the enhanced image. The improved images created by RHE-DCT, LIME, LCC, TMM, and LSCN are not as good as those created by the proposed AEHO method.

The contrast of the image formed by AEHO is greatly boosted and is superior to that of the RHE-DCT, LIME, LCC, TMM, and LSCN methods, as shown by the enhancement findings in Fig. 18. This figure shows a considerable improvement in illumination compared to the enhanced images of WO, NRBO, EHO, EEFO, and PSO. These images show greater detail but tend to have low contrast in some local places. This suggests that AEHO may adaptively decrease the influence of uneven scene illumination on image quality when compared to existing standard methods.

The images produced by RHE-DCT and LSCN in Fig. 19b and f show only slight enhancements in brightness and detail compared to the equivalent images, and no discernible overall contrast. Although there is an excessive enhancement in bright locations, Fig. 19c and e for the LIME and TMM approaches, respectively, show excellent overall outcomes; in contrast, LCC produces unsatisfactory augmentation in numerous regions. The final enhancement results of WO, EEFO, and NRBO algorithms are commendable with high contrast and detail when compared to AEHO. Nonetheless, compared to RHE-DCT, LIME, LCC, MSR, TMM, and LSCN approaches, some meta-heuristics, such as EHO and PSO, have far stronger enhancement effects.

Traditional image enhancement methods like LIME, LCC, TMM, and LSCN may have issues with over-enhancement as there is no regularization component to balance the required amount of enhancement in these methods. However, the experimental findings show that the definitions of \(\alpha\) and \(\beta\) in the incomplete beta function designed in Eq. 33 accommodate the variations in content across the various images in the adopted dataset. The enhancement outcomes are more consistent across many images when adaptive values of the parameters \(\alpha\) and \(\beta\) are used. The values of these parameters were adapted through the iteration loops of the proposed AEHO algorithm to prevent over-enhancement for each considered image, which might lead to a high level of performance with improved edge information.

Finally, these visual findings clearly demonstrate that the proposed AEHO method effectively enhances each and every minute feature in the input images, and as a result, eliminates image artifacts, as seen in Figs. 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19. These visual results further illustrate that the proposed AEHO method consistently maintains the processed images’ mean intensity, hence maintaining their normalcy. The findings demonstrate that AEHO is suitable for satellite and natural images and highlight its advantages even more.

6.6 Complexity analysis and implementation time

In this subsection, we statistically investigate the complexity of the previously stated techniques for the enhancement of images of size \(M \times N\). The order of time complexity of the RHE-DCT method is calculated to be \(\mathcal {O}(N \text {Log} N)\). When compared to the Lands Retinex method, which had an overall complexity level of \(\mathcal {O}(N^4)\) and \(\mathcal {O}(N^2)\) with a processed region dimension of \(M \times N\), where this is achieved by the LCC algorithm. With respect to the LSCN technique, its efficiency lies in its ability to handle a computational complexity problem of the order of \(\mathcal {O}(Rw^2MN)\), where R denotes the total number of iterations and \(v\times v\) denotes the size of the filter window used to produce the same dynamic range inside the input image. The local variance and local mean values must be computed using a window of size \(v \times v\), where v = 3, according to a threshold in the initialization stage of this approach. Based on this, a total computational complexity of \(\mathcal {O}(2\times 3^2MN)\) may be represented. Using a complexity order of \(\mathcal {O}(M \times N)\), the histogram of the image must be calculated as the final step in the gray level stretching process. Consequently, \(\mathcal {O}(Rw^2MN + 19MN)\) is the order of the total time complexity of the LSCN approach for image enhancement problems. The LSCN approach demands a time complexity of the order of \(\mathcal {O}(MN)\); in contrast, the LIME method has a computationally easier time complexity. The meta-heuristic techniques employed in this work have a higher computational complexity than the conventional methods under study, but their complexity increases as they try to find the best possible solutions for the intricate image enhancement problem under consideration.

When solving the image enhancement problems under study, the computational complexity of the aforementioned meta-heuristics-PSO, WO, NRBO, EEFO, EHO, and AEHO-is determined by several factors, including the number of iterations, population size, fitness criterion cost, and problem dimensionality, which represents the size of the images. The overall time complexity of these algorithms is evaluated in concrete terms using the termination method, with estimates of the order \(\mathcal {O}((v(K(cn+nd + n))) + nd)\); here, nd denotes the number of indiscriminate candidate solutions initially found and the dimensionality of the problem, and v, K, c, n, and d denote the number of evaluation experiments, iterations, fitness function cost, population size, and problem size, respectively. It is interesting to observe that EHO and PSO are slower than WO, NRBO, and EEFO due to their modest complexity differences. Furthermore, because AEHO is made up of some enhancement procedures applied to parent EHO algorithm, each of these procedures along with EHO increase the AEHO algorithm’s complexity, making it somewhat more complicated than the other compared algorithms. While the majority of meta-heuristics have a constant algorithmic cost, the computational complexity of the several phases of the random solution search differs when examined separately. Even though the parent algorithm, EHO, has distinct exploration and exploitation phases, it requires different amounts of computational burden efforts. In short, the complexity issue of the proposed AEHO algorithm can be written as: \(\mathcal {O}((v(K(cn+nd + n))) + nd)\).

Table 15 shows the average implementation time results of the proposed AEHO-based image-enhancement algorithm as well as the results of various rival methods for image A over 30 independent runs, 100 iterations, and a population size of 30.

Table 15 Implementation time results of the proposed AEHO-based image enhancement algorithm and other competing methods

Even though the proposed AEHO algorithm is more complex than WO, EEFO, EHO, and a few other competing algorithms, its implementation time increase is manageable as it is within the range of these other competing algorithms. The highest possible number of iterations of the meta-heuristics used for the image enhancement problem under study was set to 100 in all test cases, taking into account the running time and enhancement consequences for the processed images.

As the basic EHO lacks distinguished exploration and exploitation stages, AEHO is proposed to boost these two features. In this, the proposed AEHO algorithm tends to be more exploitative and exploratory than the basic EHO algorithm and other competing algorithms such as WO, WSO, and EEFO. The accelerated rate of convergence towards the global optimal solutions may be attributed to AEHO’s quicker and more effective exploration capacity as compared to EHO. Consequently, the integration of the phases of exploration and exploitation of AEHO is guaranteed by combining EHO with promising operators and other procedures applied to this algorithm to devise the proposed AEHO algorithm. This eloquently shows AEHO’s computational prowess in improving low-contrast images. By establishing a termination assessment method based on a sufficient tolerance span of the global fitness scores achieved at each experimental runtime, it is possible to avoid the restriction of the basic EHO-based optimization technique to function for an ongoing number of iterations. This will demonstrate the computational power of AEHO in enhancing low-contrast images in an elegant way. While WO, ABC, EEFO, and NRBO have reasonable exploration and exploitation features, AEHO is more explorative and exploitative than these algorithms. Compared with these competing algorithms, the exploration and exploitation capabilities of AEHO are better and more effective than those of other rival algorithms, which contributes to the rapid pace of convergence of AEHO towards the global optimal solutions.

While enhancing the brightness and contrast of the analyzed satellite and natural images showed encouraging results and satisfactory trajectories for the proposed AEHO algorithm, this algorithm would need some relatively large computational burdens. As such, there may be several limitations to this proposed method in computer vision applications such as autonomous automobiles and video navigation. Meanwhile, its computational costs remain comparable to those of rival methods, such as EHO, WSO, and WO as described above, which utilized the same enhancement procedure as AEHO. For the image enhancement problems under discussion, the proposed AEHO algorithm is restricted to continuous search spaces, which makes sense; nevertheless, it faces difficulties with binary search spaces, such as feature selection. Although AEHO performs well in most of the test images, it may fail in some images such as the one in Fig. 17 which drops to a local optimum. Therefore, to get beyond these limitations, more initiatives can be considered to boost the degree of performance of the proposed AEHO algorithm.

It is noteworthy to note that the proposed AEHO algorithm is slightly more complex than other comparative algorithms such as WO, NRBO, EEFO, and thus slower than these competing algorithms. Moreover, AEHO is a bit more complex than the basic EHO algorithm since it is formed by a combination of EHO and other embedding procedures. Although the algorithmic complexity of most meta-heuristics is got to be the same, the computational complexity of the stages of searching for random solutions varies when analyzed individually.

The great performance of the proposed AEHO algorithm in improving the contrast and brightness of humble and extremely low-contrast satellite and natural images makes it adequate for integration into a broad range of real-world applications, such as medical image processing, signal processing, video processing, remote sensing analysis, and image classification. Additionally, sand-dust images might be improved using the proposed AEHO algorithm for computer vision applications such as object recognition, video surveillance, intelligent transportation, and aviation. Additional uses of the proposed image enhancement technique could be used in processing the low contrast of haze, fog, and underwater images.

7 Conclusion and future works

In this study, a multi-stage approach for enhancing the brightness and contrast of satellite and natural images has been presented, using Contrast Limited Adaptive Histogram Equalization (CLAHE) and an Augmented version of the Elk Herd Optimizer (EHO), or referred to as AEHO. To accomplish both local and global search activities, AEHO incorporates new and effective strategies with the mathematical model of EHO. To do so, EHO was enhanced by the addition of several deliberate actions aimed at balancing these two aspects and enhancing exploration and exploitation. The goal is to get an approximate match to the optimal solution in relation to the basic EHO optimizer, while also securing a promising convergence feature. The proposed AEHO algorithm was used for adaptive image enhancement technique by adaptively choosing the optimal values of the incomplete beta function using a predetermined fitness function. To enhance the contrast and other features in the dark regions of satellite and natural images, a bilateral gamma correction function was then used. To evaluate the efficacy and suitability of the proposed image enhancement technique compared to existing state-of-the-art techniques, both quantitative and qualitative findings were presented on a variety of image datasets. The proposed AEHO algorithm was developed into a more stable algorithm than the original basic one, helping to preserve the processed image’s average intensity, improving the processed image’s clarity and naturalness, and the way humans perceive the natural scenes. Assessment metrics that considered the improvement of brightness and contrast revealed the advantages of the proposed method compared to its competitors. Regarding the visual assessment of the outcomes, it is revealed that AEHO can clearly discern fine features inside the resultant image without creating space for undesired artifacts. The proposed AEHO algorithm was shown to be highly effective in producing reasonably improved images, with generally higher scores of efficiencies for all the images evaluated, when compared to other well-researched and high-performance enhancement methods. In every image under consideration, the AEHO-based image enhancement method resulted in higher edge pixel count and edge intensities than the original images and images generated by other competing methods. Specifically, the average values of these two evaluation criteria on all test images using AEHO are 4.08E+05 and 2.046E+06, respectively, which are better than the values of the original images, which are 4.046E+05 and 7.12E+05, respectively. The generalization of the AEHO-based image enhancement method to a broader range of images such as large-scale satellite images as well as large-scale natural images would be valuable. Further study is demanded to adapt AEHO to address computer vision and image processing applications, such as object recognition, intelligent transportation, remote sensing imaging, video processing, and video surveillance. The extension of AEHO to other areas related to signal processing to test its usefulness would be beneficial. As AEHO experiences a flaw of being computationally complex, a potential next step would be to combine its features with those of promising meta-heuristics. A particular challenge would be to make the proposed image enhancement method work in real-time.