Image Contrast Enhancement by using Histogram Clipping and 2-D Histogram

Subject Areas : Signal Processing; Image Processing

Mahdis Golabian ¹ , Azar Mahmoodzadeh ^{2 *} , Hamed Agahi ³

1 - the Department of Electrical Engineering,Shiraz Branch, Islamic Azad University, Iran, Shiraz
2 - Electrical Engineering,Islamic azad University,Shiraz Branch,Shiraz,Fars,Iran
3 - Department of Electrical Engineering,Shiraz Branch, Islamic Azad University, Iran, Shiraz

Received: 2023-10-21 Accepted : 2024-01-06 Published : 2024-05-08

Keywords: Skewness, Contrast Enhancement, Visual machine algorithm, 2-D Histogram, clipped Histogram,

Abstract :

Several factors are affected images' contrast and eliminated details in images. Therefore, contrast enhancement is a critical process for any visual machine algorithms. To achieve this purpose, in this paper, a novel algorithm based on 2-D histogram and clipped histogram is introduced. To improve the performance of the algorithm, the histogram is divided into three sub-histograms based on mean and standard deviation. For each sub-histogram image, clipped histogram is calculated, separately. The threshold for clipping of histogram is obtained based on median of 2-D histogram of image. Based on the pervious researches we know that the desired distribution for 2-D histogram is Gaussian distribution. Hence, we introduce a novel iterative algorithm for transforming the available histogram to desired histogram. On the other words, our method modifies image histogram to improve its contrast. Our proposed method is based on Skewness, where algorithm is attempted to minimize the absolute value of Skewness. The performance of the algorithm is compared by several algorithms based on different factors. Simulation results indicate the proposed algorithm has the best performance than other algorithms.

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Signal Processing and Renewable Energy, Month XX   Year XXXXXX

 

Signal Processing and Renewable Energy Month–Year-(pp XX - XX )  ISSN: 2588-7327 eISSN: 2588-7335

 

 

 

 

 

 

 

 

Image Contrast Enhancement by using Histogram Clipping and 2-D Histogram

Mahdis Golabian1, Azar Mahmoodzadeh*1, Hamed Agahi1

 

Department of Electrical Engineering, Shiraz Branch, Islamic Azad University, Iran, Shiraz (*Corresponding Author’s Email: [e-mail]).

 

ABSTRACT

Several factors are affected images' contrast and eliminated details in images. Therefore, contrast enhancement is a critical process for any visual machine algorithms. To achieve this purpose, in this paper, a novel algorithm based on 2-D histogram and clipped histogram is introduced. To improve the performance of the algorithm, the histogram is divided into three sub-histograms based on mean and standard deviation. For each sub-histogram image, clipped histogram is calculated, separately. The threshold for clipping of histogram is obtained based on median of 2-D histogram of image. Based on the pervious researches we know that the desired distribution for 2-D histogram is Gaussian distribution. Hence, we introduce a novel iterative algorithm for transforming the available histogram to desired histogram. On the other words, our method modifies image histogram to improve its contrast. Our proposed method is based on Skewness, where algorithm is attempted to minimize the absolute value of Skewness. The performance of the algorithm is compared by several algorithms based on different factors. Simulation results indicate the proposed algorithm has the best performance than other algorithms.

 

 

Keywords:

Visual machine algorithm, Contrast enhancement, 2-D Histogram, clipped Histogram, Gaussian distribution, Skewness

 

 

1.          INTRODUCTION

Contrast is defined as a difference between luminance in gray or color images. Extracting features and details are too difficult in low contrast images. The contrast of images is affected by several factors such as defect in camera or transmission systems, environment effects such as shadow, light or etc. Contrast is a vital factor in images and it is so important for any machine visions systems. Visual image quality is actively enriched using contrast enhancement approaches, which are increasingly essential for the design of consumer electronic devices and digital multimedia systems. Image contrast enhancement is an important process to improve dynamic intensity range of pixels. In this process, an intensity of images is changed to increase contrast of image[1].

Conventional contrast enhancement such as histogram equalization (HE) method is used widely in many practical applications. These methods usually increase image contrast at peaks values and may cause noisy effect on images[2]. In pervious papers, researchers introduced some methods. Such as, Brightness preserving bi-histogram equalization (BBHE)[3], Dominant Orientation-based Texture Histogram Equalization (DOTHE) [4]exposure based sub-image HE algorithm (ESIHE) [5]to overcome these challenges. Whole above algorithms divide image histogram to several partitions and use

 

HE algorithm to process sub histograms. The main disadvantage of these methods still is intensity saturation at some of the sub histograms. In some recent papers, researchers use histogram clipping methods such as CLAHE [6]to prevent intensity saturation. Clipped histogram equalization technique is a novel version of HE methods that control undesired increasing of contrast and avoiding image saturation[7]. In[8], histogram is clipped based on median of histogram. This median is named threshold and calculated adaptively for any images. In both papers, if the value of histogram is more than the threshold value, histogram is clipped. In [9]histogram of image is divided to several sub-histogram based on the mean and variance of histogram. In[10] authors used adaptive gamma correction for improving image contrast. Gamma correction is a nonlinear method for enhancing luminance and contrast in images. Another method for improving image contrast is a method based on discrete cosine transform (DCT). This method is introduced in[11], where the method operates in the DCT domain and is computationally efficient, which makes it suitable for real-time imaging systems.

Due to the importance of contrast improvement, in addition to the above research, contrast improvement has also been considered by scientists. For instance, in[12], researchers used Fuzzy logic method for improving image contrast which adaptive fuzzy inferencing system determines the pixel value of the output based on the contrast measure of the input image. In[13], authors introduced a method based on the adaptive non-linear contrast stretching. Contrast stretching improves the contrast in an image by stretching the range of intensity values. Optimization algorithm still used by researchers for this purpose. For instance, in[14], Artificial Bee Colony Algorithm is used for introducing adaptive image contrast enhancement. This research investigates the system performance based on the different metrics such as peak signal to noise ratio (PSNR), SSIM (Structural Similarity Index), SNR (Signal to Noise Ratio), MSE (Mean Squared Error). Wavelet transform can be used for image contrast enhancement. In[15], researchers introduced an algorithm in the wavelet domain. In that paper, a contrast sensitivity function is obtained for each sub-band which is applied to weight the wavelet coefficients in the sub-band.

All pervious papers are based on one dimensional (1-D) histogram modification for contrast enhancement. In some recent papers, authors use 2-D histogram. The main advantage of 2-D histogram is that, it can counts the pairs of adjacent pixels with gray levels and represent the gray level difference between the pixels of an input image and their neighbors[16]. As a comparison, a 1-D histogram is nothing more than counting how many voxels with a particular intensity occur in the image. The intensity range of the image is divided in bins. A voxel then belongs to the bin if its intensity is included within the range the bin represents. Therefore, we use 2-D histogram in our paper. In addition, we use clipped histogram equalization technique to avoid any undesired increasing pixel intensity. We use three level thresholds for clipping histogram. Three level thresholds cause to eliminate outlier values and increase image contrast algorithm. As mentioned above, for 2-D histogram, a desired distribution is Gaussian distribution. For ideal Gaussian distribution, the amount on Skewness is equal to zero. Therefore, in our proposed algorithm, we attempt to minimize the value of Skewness for 2-D histogram of image. Hence, the algorithm is an iterative algorithm improves image quality, adaptively.

The rest of this paper is organized as follows; in the section 2, we introduce our proposed algorithm, mathematically. In the section 3, simulation results are presented and discussed, conclusion is explained in the section 4.

2.       PROPSED ALGORITHM

In this section, the proposed algorithm is described. The proposed algorithm flowchart is shown in the figure 1. In the proposed algorithm the image contrast is improved based on the iterative algorithm. Skewness of the histogram is used as decision metric. The algorithm is repeated until the Skewness be less than threshold value. In the first subsection, 2-D histogram is introduced. In the second subsection, the Clipped histogram is presented mathematically and in the third subsection, the proposed algorithm is described. The proposed clipped histogram algorithm is obtained based on the standard division and mean of the image histogram.

 

 

Figure 1. Flowchart of the proposed algorithm

 

2.1       Sub-section Head Style

As mentioned before, 2-D image histogram gives more information than 1-D image histogram. Therefore, in this research, uses 2-D histogram for improving image contrast. For calculating 2-D image histogram, assume color or gray level image with low contrast quality. For gray image, the histogram intensity has values between zeros to 255. Color images have three channels for main colors (i. e. Blue, Green, Red) which each one has values between zeros to 255. Letting  as input image where  and  are number of pixels in row and columns, respectively.  as a sorted k distinct gray level of image . 2-D histogram is defied mathematically as follows[16]:

 

(1)

Where

The  in the above equation is defined as follows:

(2)

 Where w is odd number. For each pixel a square neighborhood pixels are considered, and:

(3)

To understand difference between 1-D and 2-D histogram, figure 2 indicates 1-D and 2-D histogram for a typical image. In this image, the value of window, , for 2-D histogram is assumed to be 3.

 

 

Figure 2. gray image, 1-D and 2-D histogram

 

As mentioned in[17], the desired 2-D histogram has Gaussian distribution. Therefore, we attempt to transfer 2-D histogram of input image to Gaussian distribution. Skewness indicates the degree of asymmetry in the probability distribution. If the data are symmetric to the mean, the skewness will be zero. Skewness has been normalized to the third torque. The skewness is actually a measure of the degree of symmetry of the distribution function. The Skewness is defined as follows[14]:

(4)

Based on the above discussion, in our paper, we attempt to minimize absolute value of Skewness. On the other words, the algorithm is finished when the amount of Skewness to be less than specified value. The details of the proposed algorithm are described in next sections.

 

2.2       Clipped histogram

Figure 3 indicates the idea behind clipped histogram. As shown in this figure, the histogram values more than threshold value is clipped to avoid image sturation. Similar to recent researches, we use median of histogram to calculate the threshold value. The main advantage of median is that it cannot be affected to outlier values. Therefore, by assuming  as thereshold level, it is defined as follows:

(5)

 

 

Figure 3. Threshold Level

 

Most papers use a single threshold for images. But, due to Non-uniform distribution of image pixels, a single threshold does not have enough performance for image contrast enhancement. Therefore, we use three threshold levels to increase the algorithm performance. In this method, the image histogram is divided into three parts and for any parts the value of threshold (i.e. median) is calculated separately. Figure 4 indicates the histogram is divided to three sub-histograms. For simplicity, in this image, we show our idea in 1-D histogram.

 

Figure 4. sub-histogram image

As shown in figure 3, the image is divided into three partitions base on the standard deviation and mean of histogram. Therefore, we divides image in three parts at first. The metrics for division are standard deviation and mean of 2-D image histogram that are calculated as follows:

(6)

At the second step, for all parts, the value of the threshold is calculated as follows:

	(7)
	(8)

In the third step, for any three areas, a new value for histogram is updated as follows

(9)

Finally for any intensity value, , and the mapping function is calculated as follows:

(10)

Where  and  are lower and upper band of any areas and  is cumulative distribution function (CDF) and for each area is calculated as follows:

(11)

2.3       Iterative Algorithm

As mentioned before, the desired distribution for 2-D histogram is Gaussian distribution. In addition, for Gaussian distribution, the value of Skewness is zero. Skewness can be positive or negative. Therefore, we want to reduce the absolute value of Skewness for achieving desired 2-D histogram. In the proposed iterative algorithm, in the each iteration the values of mean, median and standard deviation are updated. Therefore, although, the number of sub-histograms is constant but their borders are changed. Unless to [9], the process is applied to all pixels in the each iteration, hence, the all pixels have opportunity to receive the optimal value.

It is obvious Skewness may not be exactly zero and the algorithm gets stuck in the infinite loop. Therefore, we define a threshold for avoiding this problem as follows:

(12)

Based on the above explains, the proposed algorithm is presented as follows.

 

 

 

 

 

 

(13)

Input: image Output: image 1.       Calculate Skewness based on Eq. 5 2.       While    upper than threshold value do 3.       Calculate 2-D histogram based on Eq. 2 4.       Calculate mean and standard deviation based on Eq. 7 and Eq. 8, respectively 5.       Divide histogram into three parts 6.       Calculate median of histogram based on Eq. 9 for each parts 7.       Calculate new value for 2-D histogram based on Eq. 10 8.       For each intensity value, calculate a new value for pixels based on Eq. 11 9.       Check the value    for output image 10.       If condition in Eq. 13 is satisfied the algorithm is finished, otherwise return to step 1                                 2.4       Sub-section Head Style   To evaluate the performance of the algorithms; we need to examine our proposed algorithm's performance by different metrics. Nowadays, there are a several metrics that are used by researchers for investigating their algorithms. In this research, we use five metrics including PSNR, SSIM, AMBE, Entropy and spatial frequency. The first one is peak signal-to-noise ratio (PSNR) where is used widely in many researches. PSNR is defined as follows[18]:  Where MSE is Minimum square error and is defined as follows:   (14)   Higher PSNR indicates the image has the better performance. On the other words, for two algorithms, the algorithm which one has higher PSNR is better algorithm. The second metric is structural similarity index (SSIM). SSIM is used for measuring the similarity between two images. The SSIM index is a full reference metric; in fact, the measurement of image quality is based on an initial uncompressed or distortion-free image as reference that is defined as follows [13]:   (15)   Where  and  are mean of original image, mean of improved image, standard deviation of original image, standard deviation of improved image and covariance of both images, respectively. In addition,  and  are constant values. The third metric is absolute mean brightness error (AMBE) that is indicates the change of gray levels between the input and output images. AMBE is defined as follows[19]:   (16)   Where  and are the means of input and output images of algorithms. For two algorithm, each algorithm has the less AMBE is better and it has the higher performance. The forth metric that is used in this research by us is entropy. In the information theory, the entropy can be interpreted as the average level of "information", "surprise", or "uncertainty" inherent in the variable's possible outcomes. The higher entropy shows the image has the more information and the algorithm has the better performance. The entropy can be defined as follows [16]:   (17) Where  is a probability of ith intensity in the histogram.  The last metric that is used by us is spatial frequency (SF). Spatial frequency is a property of any structure that is periodic across position in space. This metric calculates sinusoidal components per unit of distance. This metric is obtained as follows:   (18)   Where  is wavelength. For image contrast enhancement algorithms, higher value of SF indicates the algorithm has the better performance. 3.         experiment and results In this section we evaluate the performance of our proposed algorithm by employing our algorithm to different images. The images are downloaded from Contrast Enhancement Evaluation Database (CEED2016) database[20]. Five metrics including SF, SSIM, PSNR, Entropy and AMBE are established for comparing the performance of all algorithms. In this research, the performance of our proposed algorithm is compared with CLAHE, DCT, DOTHE and ESIHE algorithms. Figure 5 indicates the original, low contrast and improved images. The values of metrics are described in table 1. It is observed the proposed algorithm has the best performance than other algorithms. The performance of other algorithms is shown in these table and figure. It is observed for different metrics, different algorithms have different performance. In fact, the best algorithm should be selected based on the usage of the algorithm and its applications.   Figure 5. original, low contrast and reconstructed images by different algorithms. Table 1: the metrics results for different algorithms   (19)   SF SSIM PSNR Entropy AMBE   2.936 0.823 13.432 5.623 34.680 Proposed algorithm 1.935 0.535 9.007 5.786 89.430 CLAHE 2.823 0.745 11.537 5.597 65.871 DCT 3.509 0.754 13.202 4.390 53.520 DOTHE 2.672 0.701 14.468 5.607 42.231 ESIHE   Figure 6 and table 2 indicate the results for the second image test. For this image it is observed the performance of the proposed algorithm has the better than other algorithms. It is worth to note that, it may possible our algorithm has the worth performance than a spatial algorithm in one metrics but it has better than that algorithm in other metrics. Indeed, we should consider the performance of algorithms in whole metrics. For more investigating, we apply different images in our algorithm and other algorithms. In the following figures and tables, the results for other images are presented. It is observed for all images, our proposed algorithm has the best performance.     Figure 6. original, low contrast and reconstructed images by different algorithms for the second image test Table 2. the metrics results for different algorithms for the second image test SF SSIM PSNR Entropy AMBE   4.228 0.906 19.394 6.958 16.628 Proposed algorithm 3.780 0.476 12.222 6.229 58.323 CLAHE 4.228 0.856 18.764 6.965 23.758 DCT 4.141 0.646 15.440 6.130 22.730 DOTHE 4.817 0.605 17.358 5.930 31.452 ESIHE   Figure 7. original, low contrast and reconstructed images by different algorithms for the third image test Table 3. the metrics results for different algorithms for the third image test SF SSIM PSNR Entropy AMBE   2.303 0.851 23.393 5.947 8.098 Proposed algorithm 1.961 0.454 14.676 5.889 44.917 CLAHE 2.315 0.785 21.169 6.887 4.189 DCT 2.127 0.692 17.004 5.816 10.666 DOTHE 1.607 0.487 16.593 5.647 31.888 ESIHE   Figure 8. original, low contrast and reconstructed images by different algorithms for the fourth image test Table 4. the metrics results for different algorithms for the fourth image test SF SSIM PSNR Entropy AMBE   2.537 0.790 21.229 6.278 17.912 Proposed algorithm 3.173 0.488 14.054 6.048 48.971 CLAHE 1.356 0.752 19.130 7.100 2.860 DCT 1.619 0.489 12.701 6.244 11.344 DOTHE 2.633 0.438 14.951 5.816 28.384 ESIHE     Figure 9. original, low contrast and reconstructed images by different algorithms for the fifth image test Table 5. the metrics results for different algorithms for the fifth image test SF SSIM PSNR Entropy AMBE   2.284 0.612 11.499 5.239 9.851 Proposed algorithm 1.988 0.213 8.243 5.129 93.149 CLAHE 2.083 0.475 10.114 5.527 73.519 DCT 1.743 0.496 13.991 5.291 62.025 DOTHE 1.750 0.481 13.999 5.118 39.358 ESIHE 4.       Conclusion       We proposed a novel method for contrast enhancement in this research. The proposed algorithm is used 2-D histogram and divided it into three parts based on the statistical parameters. In addition, the clipping histogram method is used in this algorithm. Clipping method is a procedure to avoid image saturation. The main idea behind this research is to use Skewness to transform histogram distribution to Gaussian distribution. An iterative method is designed in this paper to minimize the Skewness of the histogram. At the end, the performance of the proposed algorithm is compared with different algorithms based on the different metrics and it is observed the proposed algorithm has the better performance than other investigated algorithms.     References 1.       Gonzalez R. C. and Woods R. E., “Digital Image Processing”, 2nd ed. Englewood Cliffs, NJ: Prentice- Hall, 2002 2.       Mousania, Younes, Salman Karimi, and Ali Farmani. 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Al., Brightness and contrast controllable image enhancement based on histogram specification, Neuro computing 2018; 275: 2798-2809 16.       Mittal H, Saraswat M, An optimum multi-level image thresholding segmentation using non-local means 2D histogram and exponential Kbest gravitational search algorithm, Engineering Applications of Artificial Intelligence 2018; 71: 226-235 17.       King K.M, Kim D. S, McCabe C. j, Random responses inflate statistical estimates in heavily skewed addictions data, Drug and Alcohol Dependence 2018; 183: 102-110 18.       Borda, Monica, Fundamentals in Information Theory and Coding. Springer. 2011. 19.       Ponticorvo A, et. al., Spatial Frequency Domain Imaging (SFDI) of clinical burns: A case report, Burns Open 2020; 4: 67-71 20.       https://data.mendeley.com/datasets/3hfzp6vwkm/3                       Authors   Mahdis Golabain received the B.Sc. and M.Sc. degrees in Electrical Engineering from the Islamic Azad University, Shiraz, and Neyriz  branches, Iran, in 2013 and 2016, respectively. She is a Ph.D. student in Electrical Engineering at Shiraz University, Shiraz, Iran. Her research interests include image processing and computer vision.                       e-mail: [e-mail]         Azar Mahmoodzadeh received B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering from University of Shiraz, University of Shahed and University of Yazd, Iran, in 2005, 2008 and 2013, respectively. From 2009, she was with the Islamic Azad University, Shiraz Branch, Shiraz, Iran. Her research interests include pattern recognition and image and signal processing. corresponding author. e-mail: [e-mail]   Hamed Agahi received B.Sc. M.Sc. and Ph.D. degrees in Electrical Engineering from University of Shiraz, Amirkabir University of Technology and University of Tehran, Iran, in 2005, 2008 and 2013, respectively. From 2009, he was with the Islamic Azad University, Shiraz Branch, Shiraz, Iran. His research interests include pattern recognition, image and signal processing, and fault detection and diagnosis applications. e-mail: [e-mail]

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