Modified clipping based image enhancement scheme using difference of histogram bins

IET Image ProcessingVolume 13, Issue 10 p. 1658-1670 Research ArticleFree Access Modified clipping based image enhancement scheme using difference of histogram bins Pankaj Kandhway, Pankaj Kandhway Department of Electronics and Communication Engineering, National Institute of Technology Patna, 800005 IndiaSearch for more papers by this authorAshish Kumar Bhandari, Corresponding Author Ashish Kumar Bhandari bhandari.iiitj@gmail.com orcid.org/0000-0001-9842-8125 Department of Electronics and Communication Engineering, National Institute of Technology Patna, 800005 IndiaSearch for more papers by this author Pankaj Kandhway, Pankaj Kandhway Department of Electronics and Communication Engineering, National Institute of Technology Patna, 800005 IndiaSearch for more papers by this authorAshish Kumar Bhandari, Corresponding Author Ashish Kumar Bhandari bhandari.iiitj@gmail.com orcid.org/0000-0001-9842-8125 Department of Electronics and Communication Engineering, National Institute of Technology Patna, 800005 IndiaSearch for more papers by this author First published: 15 July 2019 https://doi.org/10.1049/iet-ipr.2019.0111Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this study, an image enhancement algorithm based on the modified histogram clipping scheme using a difference of histogram bins (MCDHB) has been proposed. The core idea of the proposed method is to ascertain the difference between the number of pixels' in histogram bins of an input image and that of the traditional histogram equalised (HE) image. The calculated difference of each bin is partitioned into different blocks based on range criteria. The proposed algorithm can be attested as a global HE approach and mainly focuses on maintaining peaks in the histogram. The proposed MCDHB framework provides a good trade-off among contrast enhancement, shape of histogram, detailed information, and natural colour. Furthermore, the MCDHB framework is also incorporated with gamma correction for further improvement. The subjective and objective assessment confirms that both the proposed techniques can efficiently enhance the images, in a better way than those produced by classical techniques. 1 Introduction Image enhancement techniques play an important role in the restoration of degraded images. Owing to low-quality, low cost imaging sensors, poor illumination condition, users' inexperience and operational errors, the contrast of the captured images may not be satisfactory. Contrast enhancement algorithms are widely used for the restoration of degraded media and used as a pre-processing stage in texture synthesis, medical imagery, and many other image/video processing applications. A number of histogram equalisation (HE)-based, fusion-based, transfer domain-based, and retinex-based approaches have been developed to enhance the contrast of low-light images. Among them, HE is the most famed method for producing a better visualisation of enhanced images. Histogram equalisation-based algorithms are extensively used for contrast enhancement techniques because of their convenient implementation and effectiveness. In recent years, the performance of low contrast image enhancement has become a crucial quality measure of multimedia devices. Consequently, distortions of the image quality are not tolerable in the multimedia era. The traditional HE stretches the dynamic range of the original histogram and tries to produce uniform probability distribution function. Thus, the HE enhanced image suffers from over-enhancement and under-enhancement conditions due to the existence of dominant grey levels. Moreover, it creates undesirable artefacts and also alters the mean brightness. Kim et al. [1] proposed a technique named brightness preserving bi-histogram equalisation (BBHE), which preserves the mean brightness and also improves the contrast of an image. In recent years, there has been a trend of using histogram-based technique to design more robust image enhancement algorithms for various applications. Wan et al. [2] introduced a framework, i.e. dualistic sub-image histogram equalisation (DSIHE). Unlike BBHE [1], this algorithm uses median intensity value for histogram partition. Chen and Ramli [3] presented an approach where histogram partition is done by the threshold value obtained by computing minimum absolute mean brightness error and afterwards they [4] have devised an algorithm to get scalable brightness preservation. In BBHE, the partition is done only once, whereas, in this technique, the division is performed recursively. Abdullah-Al-Wadud et al. [5] suggested a dynamic histogram equalisation (DHE) where the local minimum of the histogram is used for histogram partitioning. Ooi et al. [6] proposed a quadrant DHE (QDHE) for better contrast enhancement where DHE and clipping process are performed simultaneously for enhancing the contrast of grey-level images. Recently, Kuldeep and Rajiv [7] introduced an approach for contrast enhancement of images [8] based on the sub-histogram and clipping process. In 2015, another enhancement of low exposure images via recursive histogram equalisation algorithms [9] was introduced. The discussed methods are very effective for low-light images such as underwater sequences or night vision images. Santhi et al. [10] proposed an adaptive contrast enhancement using modified histogram equalisation (ACMHE). It minimises the problems of over-enhancement, saturation artefacts and changes in mean brightness. Tang and Isa [11] proposed an approach, which obtained mean brightness preservation and control enhancement rate by minimising the supremacy effect of high-frequency bins. Bin et al. [12] proposed a framework for contrast enhancement using a local histogram equalisation (LHE) variant in which an input image is divided into numbers of non-overlapped sub-blocks and the histogram projection is performed separately. A new method was designed for LHE that uses the bilateral Bezier curve for histogram modification and gradient information for transformation function [13]. Ibrahim et al. [14] proposed an algorithm to smooth the original histogram with a Gaussian filter by dividing the smoothed histogram based on its local maxima. A novel technique [15] was introduced by the authors to segment the histogram into two or more sub-histograms, where, they have used six plateau limits for the clipping process. Kim and Paik [16] proposed an approach to perform adaptive contrast enhancement using the clipping process with controllable gain. A new algorithm was proposed for enhancement of mammogram images [17] where adaptive histogram equalisation is explored to improve the mammographic images. Chen et al. [18] introduced a framework to improve three parameters, which are contrast enhancement, visual distortion reduction, and embedding capacity increment. Xiao et al. [19] designed a technique on grounds of grey-level and gradient magnitude histogram where Fibonacci quantised gradient magnitude is performed to describe space information effectively. Shanmugavadivu and Balasubramanian [20] presented an enhancement algorithm, which divides the original histogram into two sub-histograms through Otsu's thresholding mechanism. In 2016, Niu et al. [21] proposed a framework for contrast enhancement based on tone-preserving entropy maximisation and high entropy contained in the enhanced image. Few more HE-based approaches [22-26] were proposed by the authors based on histogram modification [22], grey-level grouping [23, 24], two-dimensional (2D) histogram [25], and unsharp mask filtering [26], are also available in the literature. However, these methods improve the contrast without considering the histogram pattern. In recent years, several fuzzy-based [27-30] enhancement techniques have been proposed. Fuzzy dissimilarity histogram (FDH) is generated using a fuzzy similarity index and a histogram equalisation mechanism is incorporated on normalised FDH [29]. Deng et al. [30] introduced an enhancement approach where the intuitionistic fuzzy set is used to improve images with feeble edges. Owing to significant improvement in contrast and brightness enhancement areas, the histogram-based method [31, 32] continuously attracts many researchers to solve image enhancement-related problems. Contrast enhancement approaches have been widely used to enhance the billions of digital images which are captured by multimedia devices. The major intent of all HE-based methods is to achieve several significant properties which are uniform contrast enhancement, noise tolerance during the enhancement process, preserving the natural colour, and convenience to implement. All algorithms are concentrated on determining intensity value(s) for the sub-histogram operation to achieve the above-mentioned significant properties. This study presents a modified histogram clipping process based on the difference of histogram bins (MCDHB) technique to obtain good contrast enhancement while preserving the original histogram pattern. Furthermore, the proposed framework is combined with gamma correction (GC) to achieve better perceptual quality. The rest of the paper is organised as follows. Section 2 gives a comprehensive study of the traditional histogram equalisation method and motivation. Section 3 provides a detailed discussion about the proposed MCDHB technique. Simulation results and discussions are presented in Section 4. Finally, Section 5 concludes the proposed technique by highlighting the merits and future scope of the work. 2 Histogram equalisation and motivation 2.1 Histogram equalisation In this section, the traditional histogram equalisation method [33] is discussed in brief. Consider an image X = {X(i, j)} and (i, j) are the spatial coordinates of the pixel, where X(i, j) represents the grey level and the size of the image is M × N. A total number of pixels in the entire dynamic range, (X0, XL−1) is 'n', i.e. n = M × N. The value of L is equal to 2b. Here, b is 8 for the b-bit digital format. The probability density function (PDF) is written as (1)for k = 0,1,…, L − 1, where nk represents the number of pixels at intensity level Xk and cumulative density function (CDF) can be expressed as follows: (2)Histogram equalisation is a technique that maps the original image into the complete dynamic range by using CDF as a transform function. The transform function f(Xk) is computed as (3) (4)where Xeq(i,j) is an HE-enhanced image. 2.2 Motivation All HE-based methods have been used for the contrast enhancement by using different operations such as sub-histogram, histogram clipping process, DHE etc. However, these methods are not concerned about the shape of histogram (peaks in the histogram) preservation. The contrast of an image is improved by altering peaks of the histogram, by all HE-based methods available in the literature. Hence, these methods remove crucial details or information contained in the image. These histogram peaks are also widely used in digital image processing for other operations such as image thresholding and segmentation. The proposed MCDHB method is focused on preserving peaks in the histogram with the adaptive improvement of the contrast. The main objectives of the proposed framework are to produce both uniform contrast enhancement and maintain natural colour casts without introducing unfavourable artefacts and colour in the enhanced images. In [1, 2, 6, 10, 29], the sub-histogram approaches provide better enhancement results than HE approaches. In this study, better results are obtained using the HE approach in comparison with previously established techniques. 3 Proposed methodology The complete framework of the proposed MCDHB is presented in Fig. 1. The proposed approach has an adaptive feature that cuts off input histogram peaks. Furthermore, the clipped histogram is obtained with the help of both input histogram and histogram of HE equalised image. Fig. 1Open in figure viewerPowerPoint Flowchart of the proposed MCDHB method The proposed approach mainly consists of the following three operations: (1) Histogram of HE image. (2) Modified histogram clipping process. (3) The difference of histogram bins (DHB). 3.1 Histogram of HE image A traditional HE method is applied to an input image X(i,j) to get HE-enhanced image Xeq(i,j). The histogram of HE-enhanced image Xeq(i,j) is also calculated, which is represented as heq(k). All HE-based methods are using the traditional HE method as a comparison method, however, the proposed MCDHB method uses the properties of over-enhancement and under-enhancement of the traditional HE method to improve the quality of an image to get better contrast and natural appearance of an image. 3.2 Modified histogram clipping process The idea behind the modified histogram clipping operation is to control the enhancement rate. Modified self-adaptive plateau histogram equalisation [34] was presented to ascertain the median value of the histogram bins (non-empty) as clipping threshold Tc. The modified clipped histogram is computed as described in (6) and (7) (5) (6) (7)where hc(k) and h(k) are clipped histogram and input histogram, respectively. 3.3 Difference of histogram bins In the HE-based methods, we have to find the intensity values for sub-histograms and the obtained transform function is used for each sub-histogram individually, which generates undesirable viewing artefacts and also reduces information contents. To overcome these drawbacks, the proposed method uses the DHB technique. The difference of the histogram bin is calculated using (8) as (8)where heq(k) and h(k) are HE and input histogram, respectively, and D(k) represents a difference of the number of pixels at each intensity value. In range criteria, D(k) is divided into several parts [R(0), R(1), R(2), R(3), R(4), and R(5)] and a new histogram is created with the help of both original and HE-enhanced histograms. The DHB technique is described as (9) After obtaining the modified histogram hc(k), histogram equalisation is used, where pc(k) denotes the PDF which can be expressed as (10)where n is a total number of pixels in the image and cc(k) represents CDF and it is defined using (11) as (11)The transform function fc(k) is based on the CDF as (12)where X0 and XL−1 are the intensity values of an image and Xmc(i, j) is an MCDHB-enhanced image. The selection of the several constants for the range criteria [R(0), R(1), R(2), R(3), R(4), and R(5)] has been manually opted after numerous trials for different images and the constant values are universal for all images. These threshold values are considered to produce a novel PDF. This PDF is used to generate transform function closer to the original/ideal curve (Xk = f(Xk)). Generally, the HE-based enhancement algorithms use a monotonic transform function to map the grey levels of the input images and reshape the output histogram. Transform function also provides some important idea about the behaviour of the method which results in over/under-enhancement, artefacts, uniform contrast enhancement, and natural colour appearance in the enhanced image. With this transform function, the input intensity values are mapped to output intensity values. The proposed method lies in the category of the global HE method due to its use of a single mapping or transform function. The proposed method has several advantages compared to sub-histogram-based methods. In sub-histogram equalisation methods, determining the number of sub-histograms or intensity values are the major problem, which directly affects the output image quality and the computational complexity of the methods. Sub-histogram-based contrast enhancement methods generally follow the histogram partition technique, which improves the contrast as well as noise in the image. Traditional HE emphasises the domination of histogram bins with a large number of pixels, histogram bins having less number of pixels tend to be phagocytised by dominance bins in the neighbourhood. In general, HE shifts the intensities towards the extreme left or the extreme right region of the histogram because it stretches the high histogram portions and compresses the contrast level of the low histogram portions. This intensity shifting property is considered as level saturation effects. This disadvantage of the HE method is subdued by the calculation of D values, and an adaptive average between the original histogram and HE-enhanced histogram is used for both high- and low-frequency histogram bins. Equation (9) is derived by using the properties or behaviours of the HE method to maintain the shape of input histogram. By using a specifically designed algorithm, the presented method generates a good contrast-enhanced image with a preserved detail information and histogram pattern. 3.4 Algorithm steps The detail steps of the proposed algorithm are described below (Fig. 2). Fig. 2Open in figure viewerPowerPoint Algorithm steps 3.5 MCDHB with GC Moreover, the proposed MCDHB framework is made more effective by using a GC [33] technique that aims to improve the contrast and visual quality. An optimal adaptive gamma value is applied to slightly improve the contrast and abbreviate the generation of adverse effects. The proposed MCDHB with GC is formulated as follows: (13)GC scheme is incorporated in the enhanced image, Xmc, where the value of the gamma parameter is opted as 1.01 for greyscale images and adaptive gamma value in the case of colour images (14) (15) (16) (17)The maximum intensity value of each colour (R–G–B) channel is used to achieve adaptive gamma value as described in (14)–(17). 4 Experimental results In this section, the performance of various image enhancement methods has been evaluated with the proposed algorithms. All the experiments were performed on a system with MATLAB having a 3.6 GHz Intel Core i7 processor and 8 GB memory. In this study, the proposed frameworks, as well as compared approaches [1, 2, 6, 8, 29, 33], were implemented by the same rule for greyscale and colour images that are mentioned in Section 3.4. 4.1 Subjective assessment Enhancement results and their corresponding histograms using different methods for test images are shown in Figs. 3 and 4. It can be observed that the proposed MCDHB technique is showing better colour appearance and well-enhanced results as compared to different HE-based algorithms for each image. This framework has also shown the best histogram similarity between the original and the proposed histograms as well as a good contrast for almost all cases. Fig. 3Open in figure viewerPowerPoint Enhancement results and their corresponding histograms(below) using different methods for test images (a) Original image and HE [4],(b)BBHE [5] and DSIHE [6],(c) QDHE [10] and ACMHE [14], (d) FDHE [29] and proposed MCDHBmethod Fig. 4Open in figure viewerPowerPoint Enhancement results and their corresponding histograms(below) using different methods for test images (a) Original image and HE [4],(b) BBHE [5] and DSIHE [6], (c) QDHE [10] and ACMHE [14],(d) FDHE [29] and proposed MCDHBmethod 4.2 Objective assessment For comparative analysis among HE-based methods, fidelity parameters are used which are mentioned in Table 1 for a quantitative study. The objective of the proposed algorithm is to maximise entropy, Contrast Per Pixel (CPP), Structural Similarity Index Measurement (SSIM), Feature Similarity Index Measurement (FSIM), and peak-signal-to-noise ratio (PSNR). Tables 2 and 3 show the matrices of CPP and entropy, respectively, the CPP value of the proposed framework is the highest for most of the images. The entropy value of the MCDHB is the closest to the original value, which indicates the minimum information loss. Table 1. Different metrics to test the efficiency of the algorithms Parameters Formula Remarks constant per pixel [36] measures the average intensity difference between a pixel and its neighbouring pixels entropy [10] measures the richness of information associated with grey levels in the image structural similarity index [36, 37] measures the structural similarity for an enhanced image with respect to the reference image feature similarity index [28] computes the similarity in features between the processed and input image mean square error [37] measures the average of the squares of the errors of the enhanced and original image PSNR [37] the ratio of maximum possible power of the signal to the noise power in an image Table 2. Comparison of CPP computed by the different algorithms CPP Image HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 6.275 3.968 4.468 3.586 3.920 3.392 4.697 Couple 7.403 4.397 5.182 3.235 3.862 3.868 4.996 Lady2 9.140 9.148 9.428 9.091 9.420 8.563 9.444 Lady3 8.201 7.887 7.876 7.591 7.903 6.727 7.911 Pepper 2.291 2.298 2.292 2.122 2.221 2.092 2.306 Lake 1.828 1.805 1.795 1.796 1.849 1.541 1.857 F16 2.244 3.219 2.77 3.048 3.079 2.674 3.389 House 5.005 5.497 5.123 5.486 5.755 4.194 6.150 Barbara 2.252 2.079 2.089 2.033 2.104 1.424 2.083 Lena 2.828 2.845 2.828 2.747 2.856 2.586 2.807 Car 1.872 2.011 1.978 2.015 2.095 1.813 2.172 Beans 4.503 8.774 6.415 8.144 7.952 8.822 8.930 Table 3. Comparison of entropy computed by the different algorithms Entropy Image Original HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 7.052 5.944 6.903 6.901 6.947 6.540 5.987 7.044 Couple 6.420 5.676 6.193 6.158 6.317 6.285 5.011 6.418 Lady2 5.593 4.675 5.282 5.270 5.518 5.382 5.616 5.558 Lady3 7.257 5.961 7.004 7.040 7.125 7.117 6.337 7.229 Pepper 7.593 5.976 7.432 7.431 7.505 7.524 7.110 7.593 Lake 7.484 5.971 7.292 7.292 7.372 7.362 6.795 7.481 F16 6.702 5.709 6.602 6.584 6.642 6.650 6.444 6.698 House 6.496 5.448 6.245 6.254 6.377 6.379 6.174 6.468 Barbara 7.443 5.977 7.344 7.336 7.388 7.369 6.867 7.441 Lena 7.445 5.970 7.333 7.348 7.384 7.369 6.848 7.434 Car 7.233 5.919 7.048 7.060 7.115 7.165 7.003 7.231 Beans 5.728 5.015 5.699 5.545 5.702 5.704 4.858 5.717 Tables 4 and 5 present the values of SSIM and FSIM, respectively, which show structural and feature similarity between input and enhanced images. MCDHB has the highest value for both cases and is closest to one. PSNR and execution time (ET) are shown in Tables 6 and 7, respectively. The proposed method has the highest value of PSNR for a maximum number of images. Table 4. Comparison of SSIM computed by the different algorithms SSIM Image HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 0.590 0.859 0.768 0.934 0.909 0.714 0.944 Couple 0.297 0.683 0.603 0.871 0.786 0.559 0.914 Lady2 0.317 0.422 0.338 0.897 0.899 0.859 0.959 Lady3 0.780 0.796 0.793 0.948 0.936 0.540 0.969 Pepper 0.917 0.920 0.923 0.961 0.960 0.865 0.976 Lake 0.902 0.911 0.910 0.960 0.970 0.669 0.980 F16 0.557 0.901 0.738 0.949 0.956 0.716 0.968 House 0.562 0.623 0.583 0.938 0.921 0.676 0.975 Barbara 0.871 0.880 0.879 0.945 0.950 0.623 0.940 Lena 0.874 0.903 0.892 0.956 0.960 0.753 0.960 Car 0.771 0.887 0.856 0.955 0.971 0.803 0.973 Beans 0.539 0.906 0.695 0.931 0.931 0.870 0.975 Table 5. Comparison of FSIM computed by the different algorithms FSIM Image HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 0.803 0.898 0.863 0.930 0.915 0.883 0.979 Couple 0.698 0.789 0.760 0.876 0.837 0.817 0.967 Lady2 0.591 0.644 0.606 0.926 0.908 0.927 0.960 Lady3 0.861 0.867 0.866 0.954 0.928 0.854 0.977 Pepper 0.950 0.947 0.950 0.983 0.979 0.941 0.989 Lake 0.952 0.955 0.956 0.979 0.983 0.903 0.989 F16 0.753 0.930 0.838 0.969 0.972 0.832 0.974 House 0.780 0.811 0.794 0.959 0.949 0.886 0.984 Barbara 0.935 0.939 0.939 0.970 0.963 0.857 0.968 Lena 0.927 0.939 0.936 0.972 0.965 0.910 0.976 Car 0.873 0.926 0.908 0.967 0.977 0.872 0.980 Beans 0.701 0.912 0.772 0.930 0.931 0.898 0.975 Table 6. Comparison of PSNR computed by the different algorithms PSNR Image HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 49.658 35.965 35.675 58.406 63.808 29.275 74.908 Couple 58.344 58.801 58.549 59.473 60.378 28.546 72.816 Lady2 26.891 29.551 27.723 28.349 32.881 31.874 33.396 Lady3 31.182 31.288 30.281 33.637 34.063 31.599 34.693 Pepper 29.693 29.581 29.594 37.585 44.649 30.262 64.517 Lake 30.374 30.213 30.213 32.611 37.211 28.131 35.007 F16 25.123 30.369 27.431 29.596 31.106 28.654 36.521 House 27.135 26.601 27.143 30.079 31.888 31.877 33.084 Barbara 29.552 27.992 28.088 31.545 33.360 31.207 34.383 Lena 27.812 28.568 27.943 30.806 32.568 28.122 30.343 Car 25.377 28.168 27.589 29.883 31.367 28.295 39.696 Beans 25.470 31.038 27.259 30.955 30.750 25.264 33.703 Table 7. Comparison of ET computed by the different algorithms ET Image HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 0.040 0.048 0.046 0.084 0.086 1.713 0.049 Couple 0.043 0.045 0.042 0.083 0.084 1.593 0.045 Lady2 0.042 0.045 0.044 0.081 0.083 1.569 0.044 Lady3 0.042 0.045 0.043 0.083 0.086 1.560 0.045 Pepper 0.425 0.490 0.488 0.571 0.634 11.454 0.491 Lake 0.415 0.470 0.466 0.576 0.581 11.487 0.471 F16 0.405 0.468 0.461 0.570 0.562 11.747 0.460 House 0.359 0.405 0.415 0.467 0.484 3.997 0.415 Barbara 0.403 0.481 0.485 0.548 0.567 12.795 0.481 Lena 0.415 0.492 0.481 0.562 0.578 11.443 0.492 Car 0.401 0.477 0.498 0.558 0.581 11.437 0.476 Beans 0.351 0.413 0.404 0.439 0.453 3.979 0.412 The ET of the proposed method is approximately equal to BBHE. The low computational complexity and time of the method can be best utilised by energy-aware multimedia applications. Table 8 represents the round values of maximum forward difference (MFD) of transform function, where MCDHB has the minimum value for all test images. The forward difference value of transform function (f(k) − f(k − 1)) should be minimum to preserve the naturalness of the image and also conserve peaks in the histogram. The larger forward difference is caused by the spikes in the histogram and produces over the enhanced and unnatural looking image [22]. The best value of quantitative results for each case has been indicated in bold. Table 8. Comparison of MFD computed by the different algorithms MFD Image HE BBHE DSIHE QDHE ACMHE FDHE Proposed Lady1 5 3 8 4 3 3 2 Couple 15 7 7 5 4 4 2 Lady2 29 19 27 5 4 10 2 Lady3 5 4 4 3 3 7 2 Pepper 3 3 3 3 3 3 2 Lake 4 4 4 2 3 3 2 F16 8 4 8 13 9 4 2 House 19 21 19 4 4 8 2 Barbara 3 3 4 3 3 3 2 Lena 3 3 3 3 2 3 2 Car 8 5 5 9 4 3 2 Beans 16 7 12 4 9 6 2 4.3 Evaluation of the experimental results In this study, the performance of the proposed approach is compared with six different existing methods such as HE [33], BBHE [1], DSIHE [2], QDHE [6], ACMHE [10], and Fuzzy Dissimilarity Histogram Equalization (FDHE) [29]. These frameworks are mainly focused on sub-histogram, histogram clipping, DHE, and FDH equalisation schemes, which are closely related to the proposed MCDHB algorithm. The original images with their histograms are depicted in Figs. 3a and 4a, and the enhanced images and their corresponding histograms are shown in Figs. 3a–d, 4a–d. For contrast enhancement and naturalness preservation, the images are perceptually visualised and verified with the help of enhanced image and their histogram. HE enhanced images suffer from level saturation effects and noticeable artefacts as shown in Figs. 3a and 4a. Over-enhancement, under-enhancement, and noticeable artefacts can be seen at 'background' and 'hair' regions of Lady2 and Lady3 images. Whereas, both BBHE and DSIHE improve contrast globally they tend to degrade pictorial features due to over-enhancement. These methods provide enhancement at the cost of information loss and unnatural colour appearance as represented in Figs. 3b and 4b. The enhanced results of BBHE and DSIHE appear to be similar in terms of visible aspect because both methods are based on bi-histogram equalisation technique. The existing limitations within the HE method are improved in BBHE and subsequently in DSIHE. The enhanced images using QDHE and ACMHE, control over-enhancement as they use the histogram clipping process. On the other hand, these algorithms generate unwanted artefacts, which are clearly visible in the enhanced images as depicted in Figs. 3c and 4c. ACMHE produces slightly over enhanced images. QDHE also generates effective contrast enhancement, but the detail information achieved by this method is unclear. These methods eradicate original appearance and also heighten the noise component in the enhanced images. These methods also alter some important features such as edge sharpness, natural looks, and visual clarity which can be noticed in the House and Barbara images. The enhanced images of FDHE does not show adept visual results. This method generates a degraded image with visual artefacts. FDHE reduces the visual clarity of small details because it approximately follows the properties of the sigmoid function. The sigmoid function causes dark pixels to be even darker, and the bright pixels to be even brighter. The edge details of FDHE enhanced image are not