Computational Intelligence and Neuroscience

Volume 2017 (2017), Article ID 6029892, 12 pages

https://doi.org/10.1155/2017/6029892

## Image Enhancement via Subimage Histogram Equalization Based on Mean and Variance

^{1}School of Communication and Information Engineering, Shanghai University, Shanghai, China^{2}Faculty of Electronic and Information Engineering, Huaiyin Institute of Technology, Huai’an, China^{3}Key Laboratory of Advanced Displays and System Application, Ministry of Education, Shanghai, China

Correspondence should be addressed to Yepeng Guan

Received 30 August 2017; Accepted 8 November 2017; Published 18 December 2017

Academic Editor: Silvia Conforto

Copyright © 2017 Liyun Zhuang and Yepeng Guan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper puts forward a novel image enhancement method via Mean and Variance based Subimage Histogram Equalization (MVSIHE), which effectively increases the contrast of the input image with brightness and details well preserved compared with some other methods based on histogram equalization (HE). Firstly, the histogram of input image is divided into four segments based on the mean and variance of luminance component, and the histogram bins of each segment are modified and equalized, respectively. Secondly, the result is obtained via the concatenation of the processed subhistograms. Lastly, the normalization method is deployed on intensity levels, and the integration of the processed image with the input image is performed. 100 benchmark images from a public image database named CVG-UGR-Database are used for comparison with other state-of-the-art methods. The experiment results show that the algorithm can not only enhance image information effectively but also well preserve brightness and details of the original image.

#### 1. Introduction

Enhancement technology is regarded as one of the most active fields of digital image processing. It improves the quality and appearance for low contrast image, and it can be used in monitoring, imaging systems, human-computer interaction [1–3], and many other areas [4–9]. The histogram equalization (HE) technique is simple and easily implemented, which is most extensively utilized for contrast enhancement. HE utilizes the cumulative density function (CDF) of image for transferring the gray levels of original image to the levels of enhanced image. The main drawback of HE is that it tends to change the mean brightness of the image to the middle level of the dynamic range and results in annoying artifacts and intensity saturation effects. This drawback makes HE technique unsuitable for many consumer electronics applications, for example, TV and cameras.

In order to overcome the shortcomings mentioned above, many other HE-based methods have been proposed, such as the brightness preserving bihistogram equalization (BBHE) [10], dualistic subimage histogram equalization (DSIHE) [11], and minimum mean brightness error bihistogram equalization (MMBEBHE) [12]. BBHE [10] partitions the histogram based on the image mean while DSIHE [11] uses image median to segment. MMBEBHE [12] recursively divides the image histogram into multiple groups based on mean brightness error (MBE). Although these methods have made great progress, they still have their own drawbacks, including failing with images having nonsymmetric distribution [10], failing to preserve mean brightness [11], producing more annoying side effects [12], and losing structural information [13]. In these techniques, however, desired improvement may not always be achieved, and the difference between input and output image is minimal [14].

Chen and Ramli proposed the method called recursive mean-separate histogram equalization (RMSHE [15]), in which the authors suggested recursive division of histograms based on the local mean. The mean brightness of processed image approaches towards the mean brightness of input image. Wang et al. improved DSIHE [11] into recursive subimage histogram equalization (RSIHE [16]) based on contrast enhancement, by introducing recursive segmentation in the similar manner as Chen and Ramli proposed in [15], although this method is similar to RMSHE [15] but it uses median values instead of mean values to divide histogram into subhistograms.

Adaptively modified histogram equalization (AMHE) [17] method is developed by Kim et al., which can modify the probability density function (PDF) of the grayscale as well as apply histogram specification to the modified PDF. Unfortunately, the entire redistribution to the original histogram by those methods can cause overenhancement, underenhancement, and some artifacts appearing in some smooth regions. Although the AMHE [17] does not produce any degradation, it darkens the bright areas of the sky and fails to boost the brightness of the dark regions.

In addition, some other methods based on histogram equalization for contrast enhancement with brightness enhancement have also been proposed, such as the dynamic histogram specification introduced by Sun et al., which preserves the shape of the input image histogram but does not enhance it significantly [18]. Tsai et al. suggested a contrast enhancement algorithm for color images [19, 20]. Huang et al. proposed an adaptive gamma correction with weighting distribution (AGCWD [21]) to enhance the contrast and preserve the overall brightness of an image; in the method, the gamma correction and a probability distribution for luminance pixels were used. The AGCWD technique may not give desired results when an input image lacks bright pixels since the highest intensity in the output image is bounded by the maximum intensity of the input image, because the highest enhanced intensity will never cross the maximum intensity of the input image [22]. Besides, AGCWD [21] leads to loss of information in processed image due to its sharp increasing resultant transformation curve described below.

An image enhancement technique using the idea of exposure value, named image enhancement using exposure-based subimage histogram equalization (ESIHE [23]), was advanced. The method divided the clipped histogram into two parts by using the precalculated exposure threshold [24]. The effects of using intensity exposure in histogram segmentation before histogram clipping were studied in [25]. Through simulation on standard images, low contrast images, and noisy images, the study showed that [25] could yield a certain enhancement results; however, the method usually causes underenhancement. Tang and Mat Isa introduced an algorithm named bihistogram equalization using modified histogram bins (BHEMHB) [26], which segmented the input histogram based on the median brightness and altered the histogram bins before HE is applied, but it made limited improvement for contrast.

In order to effectively increase the contras of the input image with brightness and details well preserved, an efficient algorithm named Mean and Variance based Subimage Histogram Equalization (MVSIHE) is developed in this paper. The proposed method is more effective for preserving the mean brightness and details of the enhanced image while improving the contrast compared with some other state-of-the-art methods. According to the experiments based on 100 images for our method, we know that the MVSIHE technique can achieve the multiple objectives of entropy maximization, details, and brightness preservation as well as control on overenhancement. The main contributions of this paper are as follows. Firstly, we introduce the mean and variance based algorithm to divide the histogram of the image. Secondly, a novel transformation called hyperbolic tangent transformation is developed to modify the histogram bins to overcome this domination problem. Thirdly, we put forward a normalization transformation, which can make the brightness component of the output image have a wider dynamic range and the output image look more natural and clearer. Furthermore, results indicate that the proposed method is a better approach compared to the state-of-the-art methods.

This paper is organized as follows: Section 2 describes the proposed MVSIHE method. Data samples and performance evaluations are given in Section 3. Section 4 shows experimental results and comparisons with state-of-the-art methods, and our concluding remarks are included in Section 5.

#### 2. Proposed Image Enhancement Method

##### 2.1. Threshold Calculation Based on Mean and Variance

The histogram of an image is divided into four parts with three thresholds which are adaptive and obtained by the same method. The procedure to obtain the thresholds will be presented in detail as follows.

An input image is given; let be the global histogram of the input image , where and represent lower and uppermost intensities of the image . is the histogram of the gray level , which is described aswhere is the of gray level in the image , the pdf of the image, pdf, can be defined as where is the total number of pixels in the input image .

The threshold value for histogram segmentation can be obtained. First, we divide the whole histogram into two parts by an adaptive threshold . Then the two parts can be presented as and . The probability of each part can be solved by

Next, the mean value of each part can be calculated by

Therefore, the mean of the whole image is described as

Then, we can seize the variance between the two parts by

Then the optimization model can be defined asWe can obtain the optimal threshold by (7), which is utilized to segment the histogram of image. Note that we set ; the optimal thresholds and of the two parts up and down the threshold can also be obtained in the same way as the above, respectively. Finally, the histogram is segmented into four subhistograms; that is, and are the boundary values of the luminance range within the th segmentation. Hence, the all subimages are captured bythe pdf of th subhistogram is represented by where is the number of pixels of the th segmentation. After the segment of input image histogram, the next stage of processing procedure is histogram modification. As mentioned in the introduction, CHE emphasizes the domination of high-frequency histogram bins, thus resulting in loss of details in the image. Low-frequency histogram bins tend to be swallowed by high-frequency bins in the neighborhood. MVSIHE modifies the histogram bins to overcome this domination problem. Histogram bin modification is performed using (11) for the subhistogram [27]. where is the total number of pixels in the th subimage.

##### 2.2. Histogram Equalization

CHE involves mapping an input gray level using transformation function , which can be defined as where and represent the minimum and maximum gray levels, respectively. As observed in (8), the remapping of the input image is within the entire dynamic range [] after applying CHE. The proposed method equalizes the modified subhistograms by (14); thereafter, the equalized subhistograms are integrated to produce the final enhanced output image.

##### 2.3. Normalization of Intensity Levels

In our proposed method, each segment is equalized independently and output image is obtained by adding the equalized subsegments. This may result in saturation of intensities and interference caused by nonuniform light; in order to solve the problems, we utilize the normalization of intensity levels of the processed image. The normalization transformation is defined aswhere is a matrix of the input image’s luminance component and and are the maximum and the minimum values of , respectively. and are the boundary values of the luminance range within , without loss of generality, is set as 0, and is 255 to obtain a maximum luminance range for 256 gray levels.

After normalization of intensity levels, for the sake of getting a more comprehensive and informative information output image, we fuse and together by the following: where is image obtained after applying (15), is input image, and is finally output image. Parameter is between 0 and 1. Figure 1 shows the statistical results (100 test images) with different parameters . From Figures 1(a), 1(b), and 1(c), we can know that the average values of Peak Signal-to-Noise Ratio (PSNR), Discrete Entropy (DE), and Absolute Mean Brightness Error (AMBE) can obtain optimum value when is roughly to 0.6.