Histogram shape based Gaussian sub-histogram specification for contrast enhancement

Abstract

Contrast enhancement is an essential primary part of computer vision in all fields of engineering including aerospace, agriculture, electrical, mechanical, medical, surveillance, etc. Annoying side effect in the enhanced images due to variation of gray levels is a key concern in the existing contrast enhancement techniques. In this paper, a new method for contrast enhancement is proposed, which captures the variation in the gray level distribution using skewness of the pixels distribution of the input image to avoid annoying side effects in order to produce contrast enhanced image with entropy close to that of the input image. In the proposed method, the given image is decomposed into two sub-images using a bisecting gray scale value which is determined based on the shape of the histogram of the input image. The desired Gaussian based histograms for sub-images are determined dynamically by controlling the parameters (mean and standard deviation). The performance of the proposed Histogram shape based Gaussian Sub-Histogram Specification technique (HGSHS) is evaluated on the images taken from standard databases and NASA database using the quality metrics: contrast, entropy and gradient. The performance of the proposed technique is found to be better than that of the existing contrast enhancement techniques.

Keywords

Contrast enhancement histogram specification Gaussian distribution skewness entropy

1. Introduction

Image enhancement is an inevitable process to transform the original or acquired image more appropriate for specific applications by altering certain features of the image such as contrast, brightness, etc. [1]. Contrast being one of the key feature used in image processessing such as classification, segmentation, object recognition [2], etc., the requirement for contrast enhancement is significant. Usually, enhancement of contrast is attained by histogram processing technique, which is majorly categorized into Histogram Equalization (HE) and Histogram Specification (HS). The concept of enhancing the contrast of an image by spreading the intensity levels of the image into a wider range of intensity scale to attain a uniform histogram is well known as histogram equalization [1]. While spreading the intensity levels during histogram equalization, the shifting of mean of the original image becomes unavoidable, due to which contrary effects such as over-enhancement [3, 4] with augmented noise and intensity saturation, come to existence [5]. To overcome these problems, researchers working in contrast enhancement (CE) techniques have proposed various techniques.

In an attempt to get rid of the problem of over-enhancement due to mean shifting, Kim [6] has proposed mean preserving Bi-HE (BBHE) technique in which the input image is segmented into two subimages using the mean as bisecting point before equalization. Even then, the problem of intensity saturation was not fully resolved, hence Wang et al. [7] have proposed a Dualistic Sub-Image HE (DSIHE) technique, in which two sub-images are formed by equally dividing the image using the median as bisecting point and equalized separately. In order to address the same intensity saturation problem, Chen and Ramli [8] have proposed Minimum Mean Brightness Error Bi-HE (MMBEBHE) method in which a calculated threshold level is used as splitting point for HE. Further, to reduce the problem of augmented noise, the concept of dividing the histogram recursively into preferred sub-histograms before HE is used by Chen and Ramli [9] in their technique: Recursive Mean-Separate HE (RMSHE). Sim et al. [10] have used medians instead mean for segmentation of subimages in their Recursive Sub-Image HE (RSIHE) technique. However, both the recursive type HE techniques RMSHE and RSIHE are found to be inefficient with increased number of recursive. To avoid the problem of over amplification, the concepts of bisecting and clipping the histograms are hybridized in the technique Bi-HE Plateau Limit (BHEPL) proposed by Ooi et al. [11]. Later, an efficient algorithm for enhancing different natural gray scale images called Adaptive CE Based on modified Sigmoid Function (ACEBSF), has been proposed by Lal and Chandra [12].

It is observed from the existing techniques [3, 4, 5, 6, 7, 8] that creating uniform histogram alone does not always provide the best solution, instead, the transformation of the histogram into a specified histogram known as Histogram Specification (HS) or matching is well suited for providing better solutions especially for contrast enhancement problems. As an attempt of refining the accuracy of HS, Zhang [13] has proposed a new grey-level mapping law for direct HS, which is found to be a universal version of HE technique. Later, to enhance contrast without modifying the original histogram distribution features, Chi-Chia et al. [14] have developed a Dynamic HS (DHS) algorithm. Further, to preserve the information content of images during image enhancement, Coltuc et al. [15] have proposed a technique of exact HS using strict ordering.

To accomplish exact HS concurrently with better image enhancement, Wan and Shi [16] have developed a wavelet-based histogram specification technique. To maximize the structural similarity index of the output image, Nasiri et al. [17] have developed a gradient ascent based exact global HS technique. To obtain increased image information after modifying the histogram, an automatic exact HS technique has been developed by Sen and Pal [18]. In an effort to reduce noise through attainment of strict ordering by quantization, Nikolova et al. [19] have developed an exact HS with variational approach. To obtain well-approximated target histogram, Jung [20] has proposed a two-dimensional HS technique with 2D cumulative distribution function based pixel-value mapping.

However, the problems of identifying the optimum desired histogram and appearance of undesirable checkerboard effects on the enhanced images are not fully addressed by the above mentioned histogram specification techniques. Hence an algorithm, which utilizes the contextual information of the histogram to control the brightness and contrast using two parameters known as Brightness and Contrast Controllable HS (BCCHS), has been developed by Xiao et al. [21]. In BCCHS, as the information of neighbouring pixels are gathered for computing the contextual information of the image, the computational part became more complicated. From various existing CE techniques, it is observed that appearance of annoying side effects in the enhanced images due to variation of gray levels is a major issue in the existing CE techniques. Hence, to eradicate this major issue, the proposed work, called as Histogram shape based Gaussian Sub-Histogram Specification (HGSHS) technique, formulates a novel contrast enhancement model using the shape of the histogram of the input image, which helps in avoiding the appearance of annoying side effects in the enhanced image. In the proposed technique, initially, the given image is classified based on its histogram shape by determining the skewness (symmetry, left skewed and right skewed) of the statistical distribution of gray scales in the image.

Based on the nature of the skewness, the given image is segmented into two sub-images namely lower and upper sub-histograms using appropriate Bisecting Gray Scale (BGS). The concept of Sub-Histogram is evolved based on Brightness preserving Bi-Histogram Equalization (BBHE) [6]. Where as in order to increase the search for better enhancement in a wider range, in the proposed work apart from the original mean, the BGS values (i.e. dividing gray scale values) are taken as $(L-1)/{4}$ , $(L-1)/{2}$ and $3(L-1)/{4}$ , where $L$ is the maximum gray scale value of the input image. After bisecting, desired specified Gaussian histograms for the sub-histograms are determined dynamically by controlling the specification parameters such as lower mean, lower standard deviation, upper mean, and upper standard deviation. Further, the sub-images are enhanced using the desired histograms by applying histogram specification method. For experimental evaluation, the proposed technique is evaluated on various images taken from standard databases and NASA database. Finally, the performance of the proposed technique is compared with the various existing techniques. The overall diagram illustrating the complete work is also given in Fig. 1.

Figure 1.

Overall diagram illustrating the complete work.

The rest of the paper is organized as follows. The proposed technique is presented in Section 2. Experimental results are discussed in Section 3. Section 4 concludes the paper.

2. Mathematical model of the proposed contrast enhancement technique

Let $P=\{p(i,j)|1\leqslant i\leqslant R,1\leqslant j\leqslant C\}$ be the digital input image defined by gray scales in the range $[0,(L-1)]$ . Where, $p(i,j)$ is the intensity value for the coordinate $(i,j)$ , $R$ and $C$ are the number of rows and columns of the given image, and $L$ is the maximum value of the intensity.

The main aim of the proposed technique’s is to attain an enriched image $Q_{e}=\{q(i,j)|1\leqslant i\leqslant R,1\leqslant j\leqslant C\}$ with image quality enhanced than that of the input image ‘ $P$ ’. Initially, in order to determine the histogram shape of the input image, skewness ( $S_{P}$ ) of the image is calculated using Eq. (1).

$\displaystyle S_{P}=\frac{{E(p(i,j)-{\mu}_{P})}^{3}}{{{\sigma}_{P}}^{3}}$ (1)

where, ${\mu}_{P}$ and ${\sigma}_{P}$ are the mean and standard deviation of the intensity values of the input image $P$ , and $E$ is the expectation operator.

The mean ( ${\mu}_{P}$ ) of the intensity values of the input image ‘ $P$ ’ is calculated using Eq. (2).

$\displaystyle{\mu}_{P}=\frac{\sum^{R}_{i=1}\sum^{C}_{j=1}p(i,j)}{n}$ (2)

where, $n$ is the total number of pixels in the input image ‘ $P$ ’.

The standard deviation ( ${\sigma}_{P}$ ) of the intensity values of the input image ‘ $P$ ’ can be determined using Eq. (3).

$\displaystyle{\sigma}_{P}=\sqrt{\frac{\sum^{R}_{i=1}\sum^{C}_{j=1}(p(i,j)-{\mu% }_{P})^{2}}{n}}$ (3)

The histogram shape of the input image is determined using the skewness ( $S_{P}$ ) value obtained from Eq. (1), as follows:

$\displaystyle S_{P}=\left\{\begin{array}[]{ll}0,&\textit{Symmetry}\\ <0,&\textit{Left skewed}\\ >0,&\textit{Right skewed}\\ \end{array}\right.$ (4)

In order to split the input image ‘ $P$ ’ into subimages based on the skewness ( $S_{P}$ ), for case (i) symmetrical histogram $(S_{P}=0)$ , the BGS values are taken in a way to explore the stretching on either side along with the input mean $({\mu}_{P})$ . Hence, the selected BGS are $\{{\mu}_{P},{(L-1)}/{4},{(L-1)}/{2}\}$ . For case (ii) left skewed histogram $(S_{P}<0)$ with bright features, the input mean being in the extreme right, the major stretching is done towards the dark side, but excessive movement is avoided by not using the BGS values ${(L-1)}/{4}$ as it produces annoying artifacts. Hence, the selected BGS are $\{{\mu}_{P},{(L-1)}/{2},{3(L-1)}/{4}\}$ . For case (iii) right skewed histogram $(S_{P}>0)$ with dark features, the input mean being in the extreme left, the major stretching is done towards the bright side. Hence, the selected BGS are $\{{\mu}_{P},{(L-1)}/{4},{(L-1)}/{2},{3(L-1)}/{4}\}$ . The BGS values other than values given in Eqs (2)–(2) are found to have very little variation, which adversely increases the time of searching the best enhancement. Hence, the selection of BGS is done as per Eqs (2)–(2).

$\displaystyle\textit{If }(S_{P}=0);$ (5) $\displaystyle\quad\textit{BGS}\in\left\{{\mu}_{P},\frac{L-1}{4},\frac{L-1}{2}\right\}$ $\displaystyle\textit{If }(S_{P}<0);$ (6) $\displaystyle\quad\textit{BGS}\in\left\{{\mu}_{P},\frac{L-1}{2},\frac{3(L-1)}{% 4}\right\}$ $\displaystyle\textit{If }(S_{P}>0);$ (7) $\displaystyle\quad\textit{BGS}\in\left\{{\mu}_{P},\frac{L-1}{4},\frac{L-1}{2},% \frac{3(L-1)}{4}\right\}$

Based on the BGS value, the input image ‘ $P$ ’ is disintegrated into two subimages $P_{L}$ and $P_{U}$ as

$\displaystyle P=P_{L}\cup P_{U}$ (8)

where,

$\displaystyle P_{L}=\{p(i,j)|p(i,j)\leqslant\textit{BGS},\forall p(i,j)\in P\}$ $\displaystyle P_{U}=\{p(i,j)|p(i,j)>\textit{BGS},\forall p(i,j)\in P\}$

The probability distributions of the subimages $P_{L}$ and $P_{U}$ are computed using Eqs (9) and (10).

$\displaystyle f(p^{k}_{L})=\frac{n^{k}_{L}}{n_{L}}$ (9)

where $k=0,1,2,\dots,\textit{BGS}$

$\displaystyle f(p^{k}_{U})=\frac{n^{k}_{U}}{n_{U}}$ (10)

where $k=(\textit{BGS}+1),(\textit{BGS}+2),\dots,(L-1)$ .

In Eqs (9) and (10), $n^{k}_{L}$ and $n^{k}_{U}$ are the number of $k^{\text{th}}$ intensity values and, $n_{L}$ and $n_{U}$ are the total number of pixels in the subimages $P_{L}$ and $P_{U}$ respectively. The cumulative distributions of the subimages $P_{L}$ and $P_{U}$ are computed using Eqs (11) and (12).

$\displaystyle F(p^{k}_{L})=\sum^{k}_{j=0}{f(p^{j}_{L})}$ (11)

where $k=0,1,2,\dots,\textit{BGS}$

$\displaystyle F(p^{k}_{U})=\sum^{k}_{j=(\textit{BGS}+1)}{f(p^{j}_{U})}$ (12)

where $k=(\textit{BGS}+1),(\textit{BGS}+2),\dots,(L-1)$ .

To determine the specified Gaussian distributions for the subimages, the lower and upper means ( ${\mu}_{L}$ & ${\mu}_{U}$ ) and standard deviations ( ${\sigma}_{L}$ & ${\sigma}_{U}$ ) corresponding to the subimages are obtained using Eqs (13)–(2)

$\displaystyle{\mu}_{L}=\left(\frac{\textit{BGS}}{2}\right)$ (13) $\displaystyle{\mu}_{U}=\left(\textit{BGS}+\left(\frac{(L-1)-\textit{BGS}}{2}% \right)\right)$ (14) $\displaystyle\textit{If }(S_{P}\leqslant 0);{\sigma}_{L}\in\left\{0,1,2,\dots,% \frac{L-1}{2}\right\},$ (15) $\displaystyle\quad{\sigma}_{U}\in\left\{0,1,2,\dots,\frac{L-1}{2}\right\}$ $\displaystyle\textit{If }(S_{P}>0);{\sigma}_{L}\in\left\{0,1,2,\dots,{\mu}_{p}% \right\},$ (16) $\displaystyle\quad{\sigma}_{U}\in\left\{0,1,2,\dots,\frac{L-1}{2}\right\}$

It is noted from the Eq. (2) that the sigma values for both symmetrically skewed and left skewed histogram are selected as 1 to ${(L-1)}/{2}$ . For symmetrically skewed histogram, the value is limited to half of the total gray scale value $(L-1)$ to avoid excessive darkening or brightening. Whereas, in case of left skewed histograms with bright features, the major stretching is to be done towards the darkening side but excessive stretching in darker side is avoided by limiting the sigma value up to ${(L-1)}/{2}$ , as sigma value above that produces annoying artifacts. Hence, the $\sigma$ values used for generating specified histograms are obtained as per Eqs (2) and (2).

The probability distributions of the specified Gaussian distributions of the subimages are computed using Eqs (17) and (18).

$\displaystyle f(g^{k}_{L})=\frac{1}{{\sigma}_{L}\sqrt{2\pi}}\left[e^{\frac{{-% \left(g^{k}_{L}-{\mu}_{L}\right)}^{2}}{{2{\sigma}_{L}}^{2}}}\right]$ (17)

where $k=0,1,2,\dots,\textit{BGS}$

$\displaystyle f(g^{k}_{U})=\frac{1}{{\sigma}_{U}\sqrt{2\pi}}\left[e^{\frac{{-% \left(g^{k}_{U}-{\mu}_{U}\right)}^{2}}{{2{\sigma}_{U}}^{2}}}\right]$ (18)

where $k=(\textit{BGS}+1),(\textit{BGS}+2),\dots,(L-1)$ .

In Eqs (17) and (18), $g^{k}_{L}$ and $g^{k}_{U}$ are the $k^{\text{th}}_{L}$ and $k^{\text{th}}_{U}$ intensity values from 0 to BGS and $(\textit{BGS}+1)$ to $(L-1)$ respectively.

The cumulative distributions of the specified Gaussian distributions of the subimages are determined using Eqs (19) and (20).

$\displaystyle F(g^{k}_{L})=\sum^{k}_{j=0}{f(g^{j}_{L})}$ (19)

where $k=0,1,2,\dots,\textit{BGS}$

$\displaystyle F(g^{k}_{U})=\sum^{k}_{j=(\textit{BGS}+1)}{f(g^{j}_{U})}$ (20)

where $k=(\textit{BGS}+1),(\textit{BGS}+2),\dots,(L-1)$ .

After deciding the range of ${\mu}_{L},{\mu}_{U},{\sigma}_{L}$ and ${\sigma}_{U}$ for the specified Gaussian distributions using Eqs (13)–(2), in order to obtain the transformed image with histogram similar to the specified histogram, the input gray level $(P)$ is mapped to the specified gray level $(G)$ using Eqs (21)–(24).

$\displaystyle F(G_{L})=F(P_{L})$ (21) $\displaystyle F(G_{U})=F(P_{U})$ (22)

Where, $F(G_{L})$ and $F(G_{U})$ and $F(P_{L})$ and $F(P_{U})$ are the cumulative distributions of specified distributions and the subimages respectively.

The transformation functions used to map each gray level in the input subimages to the specified gray level to obtain the desired output subimages with the histogram similar to the specified histogram are given in Eqs (23) and (24).

$\displaystyle G_{L}=F^{-1}[F(P_{L})]$ (23) $\displaystyle G_{U}=F^{-1}[F(P_{U})]$ (24)

The decomposed subimages with respect to BGS are enriched independently using Eqs (23) and (24) that can be combined together to obtain enhanced output image.

The enhanced output image $(Q_{e})$ of HGSHS is expressed as

$\displaystyle Q_{e}=\{q(i,j)\}=G_{L}\cup G_{U}$ (25)

2.1 Assessment criteria

To evaluate the performance of the proposed technique and compare with the existing techniques, the performance metrics such as contrast, entropy, and gradient given in Eqs (26)–(29) are used in this paper.

2.1.1 Contrast

The metric, $C_{\textit{contrast}}$ [22] provides the measure of dynamic range of gray levels of any image. In general, larger dynamic range of gray level provides better contrast. The $C_{\textit{contrast}}$ of the images before and after enhancements are determined using Eqs (26) and (27).

$\displaystyle C_{\textit{contrast}}=\frac{1}{RC}\sum^{R}_{i=1}\sum^{C}_{j=1}{q% _{e}}^{2}(i,j){}-\left|\frac{1}{RC}\sum^{R}_{i=1}\sum^{C}_{j=1}q_{e}(i,j)% \right|^{2}$ (26)

Where, $R$ and $C$ are the rows and columns of the images respectively, $q_{e}(i,j)$ is the pixel intensity at coordinate $(i,j)$ .

Taking logarithm of $C_{\textit{contrast}}$ , the contrast is converted into decibel ( $d B$ ) unit as in Eq. (27).

$\displaystyle C^{\#}_{\textit{contrast}}=10\text{ log}_{10}C_{\textit{contrast}}$ (27)

2.1.2 Entropy

The measure of richness of information known as entropy [23] in an image is normally modified during contrast enhancement. In general, entropy higher than that of the original image is not anticipated, as the increase in information more than that of the original image, which leads to increase in file size leading to complication in compression of the image and sometimes even higher entropy produces undesirable artifacts. The decrease in entropy is also not anticipated, as it may lead to loss of details pertaining to the quality of the image.

Owing to the above concepts, during analysis of entropy, instead of directly using the value of entropy before and after enhancements, the nearness of the entropy value of the enhanced image to the entropy value of the input image is calculated for evaluation of optimum contrast enhancement. In other words, the degree of preservation of details in an image is determined by evaluating the Difference In Entropy (DIE) using the entropies of the images before and after enhancements. The image enhancement is said to be better if the value of the DIE is close to zero. To calculate DIE, the entropy of the image is determined using Eq. (28).

$\displaystyle\textit{Entropy }E(Q_{e})=-\sum^{255}_{k=0}f(Q^{k}_{e})\text{log}% _{2}(f(Q^{k}_{e}))$ (28)

Where, $f(Q^{k}_{e})$ is the probability of kth intensity value of image $Q_{e}$ .

2.1.3 Gradient

The measure of sharpness of the image called gradient [24] is computed using Eq. (29)

$\displaystyle\textit{Gradient}=\frac{1}{RC}\sum^{R}_{i=1}\sum^{C}_{j=1}{}\sqrt% {{\nabla}^{2}_{i}(i,j)+{\nabla}^{2}_{j}(i,j)}$ (29)

where, $R$ and $C$ are the rows and columns of the images respectively, ${\nabla}_{i}(i,j)=q_{e}(i,j)-q_{e}(i+1,j)$ , ${\nabla}_{j}(i,j)=q_{e}(i,j)-q_{e}(i,j+1)$ and $q_{e}(i,j)$ is the pixel intensity at coordinate $(i,j)$ , are the horizontal and vertical gradients. Higher the value of gradient denotes an anticipated sharp image.

The optimal values of the parameters BGS, ${\sigma}_{L}$ and ${\sigma}_{U}$ for specified Gaussian distributions to be used for contrast enhancement using the proposed HGSHS technique are determined using Algorithm 1.

Algorithm 1: Histogram shape based Gaussian Sub-Histogram
Specification (HGSHS)
Input: Input Image $P$
Output: Output Image $Q_{e}$
1:	Initialize $\textit{entropy\_ max}=$ 0, $\textit{contrast\_ max}=$ 0, enhanced image $Q_{e}$ , bisecting gray scale BGS, standard deviation lower ${\sigma}_{L}$ , standard deviation upper ${\sigma}_{U}$ , maximum gray level $L$ .
2:	Compute gray mean $({\mu}_{P})$ & standard deviation ( ${\sigma}_{P}$ ) of the input image
3:	Calculate the skewness ( $S_{P}$ ) of the input image using Eq. (1)
4:	if $(S_{P}=0)$ ; $\textit{BGS}\in\left\{{\mu}_{P},\frac{L-1}{4},\frac{L-1}{2}\right\}$ ;
5:	${\sigma}_{L}$ & ${\sigma}_{U}\in\left\{0,1,2,\ldots,\frac{L-1}{2}\right\}$
6:	else if $(S_{P}<0)$ ; $\textit{BGS}\in\left\{{\mu}_{P},\frac{L-1}{2},\frac{3(L-1)}{4}\right\}$
7:	${\sigma}_{L}$ & ${\sigma}_{U}\in\left\{0,1,2,\ldots,\frac{L-1}{2}\right\}$
8:	else if $(S_{P}>0)$ ; $\textit{BGS}\in\left\{\mu_{p},\frac{{L-1}}{4},\frac{{L-1}}{{2}},\frac{{3(L-1)}% }{{4}}\right\}$
9:	${\sigma}_{L}\in\{0,1,2,\ldots,{\mu}_{P}\},{\sigma}_{U}\in\left\{0,1,2,\ldots,% \frac{L-1}{2}\right\}$
10:	foreach value of BGSdo
11:	for each value of ${\sigma}_{L}$ do
12:	for each value of ${\sigma}_{U}$ do
13:	Perform Histogram Specification ( $Q$ ) using Eqs (8)–(25)
14:	Compute contrast & entropy using Eqs (26)–(28)
15:	if $(\textit{entropy\_max}<=\textit{entropy})$ then
16:	$\textit{entropy\_max}=\textit{entropy}$
17:	$Q_{e}=Q$
18:	$\textit{contrast\_max}=\textit{contrast}$
19:	end of if
20:	next value of ${\sigma}_{U}$
21:	next value of ${\sigma}_{L}$
22:	next value of BGS
23:	return $Q_{e}$

3. Experimental results and analysis

The experimental evaluations for the proposed HGSHS are carried out on various images taken from USC-SIPI [25], LIVE [26], CSIQ [27], Toyama [28] and Kodak [29] and the results are compared with the existing contrast enhancement techniques. In HGSHS, the images are classified as symmetry, left skewed and right skewed based on the skewness of gray scale distribution of the images, then the histogram of the given image is bisected to obtain the sub-histograms of the image. To bisect the histogram of the given image, the Bisecting Gray Scale (BGS) values are identified. As the distribution of gray scale in an image is not always uniform, the selection of BGS should be done by considering the distribution of gray scale of the image.

It should also be noted that even if a BGS falls outside the gray scale range of distribution of any image, limited stretching of gray scale occurs in the sub-histogram containing the distribution, which reduces the occurrence of undesirable over enhancement. Hence, for an effective sub-histogram bisection, the choice of BGS is done based on the skewness of the given image as per Eqs (2)–(2) given in Section 2. The standard images used for implementation are all 256 grayscale images. Hence the BGS values for symmetrically skewed $(S_{P}=0)$ images are input mean, 64 and 128. Whereas for the left skewed $(S_{P}<0)$ images the BGS values are input mean, 128 and 192. Finally for right skewed $(S_{P}>0)$ images the BGS values are input mean, 64, 128 and 192. After bisecting, to decide the Gaussian histogram specification for the sub-histograms, Gaussian histogram specification parameters: lower mean $({\mu}_{L})$ and upper mean $({\mu}_{U})$ corresponding to the lower and upper sub-histograms are obtained using Eqs (13) and (14). Similarly, the parameters, lower standard deviation $({\sigma}_{L})$ and upper standard deviation ( ${\sigma}_{U}$ ) are obtained using Eqs (2) and (2). The standard deviations values used for implementation on 256 grayscale images for left and symmetrically skewed $(S_{P}\leqslant 0)$ images are ${\sigma}_{L}\in\{0,1,2,\ldots,128\}$ and ${\sigma}_{U}\in\{0,1,2,\ldots,128\}$ . Whereas for right skewed $(S_{P}>0)$ images ${\sigma}_{L}\in\{0,1,2,\ldots,\textit{input mean}\}$ and ${\sigma}_{U}\in\{0,1,2,\ldots,128\}$ .

The specified Gaussian sub-histograms along with parameters for differently skewed images are shown in Fig. 2, in which it is witnessed that higher standard deviation of the specified sub-histograms widely stretches the range of distribution of grey level of the sub-histograms, which apparently results in contrast enhancement.

Whereas, the increase in the standard deviation higher than ${(L-1)}/{2}$ leads to intensity saturation and the efficiency of contrast enhancement gets reduced. Hence, there arises a necessity for identifying suitable standard deviations $({\sigma}_{L}$ & ${\sigma}_{U})$ for the respective means ( ${\mu}_{L}$ & ${\mu}_{U}$ ) up to which the contrast enhancement is proficient. The values of BGS, ${\sigma}_{L}$ and ${\sigma}_{U}$ obtained from the experiments by the proposed HGSHS for standard and NASA images are given in Tables 1 and 2.

Table 1
Statistical parameters of input histogram and specified Gaussian sub-histograms

Image name	Skewness ( $S_{P}$ )	Histogram	Input image		Specified gaussian parameters
			Mean ( ${\mu}_{P}$ )	SD ( ${\sigma}_{P}$ )	Bisecting Gray
Scale (BGS)	Mean ( ${\mu}_{L}$ )	SD ${}_{L}$
( ${\sigma}_{L}$ )	Mean ( ${\mu}_{U}$ )	SD ${}_{U}$ ( ${\sigma}_{U}$ )
Pollen grain	0	Symmetry (S)	109	11	64	32	5	160	26
Boston	0	Symmetry (S)	128	6	64	32	9	160	30
Roadside	0	Symmetry (S)	125	27	64	32	7	160	33
Child	0	Symmetry (S)	120	7	64	32	9	160	19
Foxy	0	Symmetry (S)	109	16	64	32	9	160	24
Plane	$-$ 2	Left skewed (LS)	194	32	128	64	55	192	35
Aerial	$-$ 2	Left skewed (LS)	181	39	128	64	49	192	34
F16	$-$ 1	Left skewed (LS)	178	46	178	89	49	217	17
Aerial1	$-$ 1	Left skewed (LS)	197	37	128	64	34	192	34
Lady_liberty	$-$ 1	Left skewed (LS)	213	30	192	96	50	224	20
Seashore	2	Right skewed (RS)	32	46	128	64	32	192	24
U2	3	Right skewed (RS)	33	25	128	64	33	192	14
Plant	3	Right skewed (RS)	27	35	192	96	44	224	22
Couple	2	Right skewed (RS)	32	31	192	96	38	224	13
Cat	1	Right skewed (RS)	57	73	128	64	56	192	29

Figure 2.

The histograms of input and enhanced images with specified Gaussian sub-histograms for (a) symmetrically (Roadside) (b) left (Aerial1) and (c) right (Plant) skewed images.

Table 2

Statistical parameters of specified Gaussian sub-histograms for NASA database [30]

Image no.	Histogram	Specified gaussian parameters
		Bisecting Gray Scale (BGS)	Mean ( ${\mu}_{L}$ )	SD ${}_{L}$ ( ${\sigma}_{L}$ )	Mean ( ${\mu}_{U}$ )	SD ${}_{U}$ ( ${\sigma}_{U}$ )
1	RS	192	96	38	224	34
2	RS	192	96	42	224	20
3	RS	192	96	44	224	18
4	RS	192	96	44	224	17
5	RS	192	96	43	224	24
6	RS	192	96	40	224	20
7	RS	192	96	35	224	24
8	RS	192	96	30	224	24
9	RS	192	96	35	224	25
10	RS	192	96	40	224	20
11	RS	192	96	50	224	15
12	RS	192	96	43	224	17
13	RS	192	96	35	224	20
14	RS	192	96	45	224	20
15	RS	192	96	35	224	40
16	RS	192	96	44	224	35
17	RS	192	96	47	224	13
18	RS	192	96	40	224	30
19	RS	192	96	40	224	80
20	RS	192	96	43	224	17
21	RS	192	96	30	224	25
22	RS	192	96	42	224	23
23	RS	192	96	45	224	20
24	RS	192	96	38	224	30
25	LS	192	96	32	224	99
26	LS	192	96	30	224	59
27	RS	192	96	53	224	22

Figure 3.

Enhanced images with histograms obtained by different techniques for symmetrically skewed Boston image (a) Original Image (b) BBHE (c) DSIHE (d) MMBEBHE (e) RMSHE (f) RSIHE (g) BHEPL (h) ACEBSF (i) HGSHS.

Figure 4.

Enhanced images with histograms obtained by different techniques for left skewed Lady_liberty image (a) Original Image (b) BBHE (c) DSIHE (d) MMBEBHE (e) RMSHE (f) RSIHE (g) BHEPL (h) ACEBSF (i) HGSHS.

For performance comparison, the experimental results of the proposed HGSHS are compared with the state-of-the-art image enhancement techniques such as BBHE [6], DSIHE [7], MMBEBHE [8], RMSHE [9], RSIHE [10], BHEPL [11] and ACEBSF [12] for various differently skewed input images obtained from standard databases. Also to compare the performance of the proposed HGSHS technique with another recent BCCHS technique [21], the images from NASA database [30] have been enhanced using the proposed HGSHS and BCCHS techniques.

3.1 Qualitative assessment

The qualitative comparison of the images enhanced by different CE methods is presented in this section. To demonstrate the performance, the enhanced images of three differently skewed input images are chosen. The variation in performance are primarily assessed by subjective spectator perception to evaluate the levels of preservation of details, enhancement of contrast and appearance of sharp edges around the objects. The symmetrically skewed original Boston image, its enhanced images and corresponding histograms are shown in Fig. 3. Though the images enhanced using MMBEBHE and BHEPL techniques appears subjectively good, the details such as building and reflections in door glasses are lost in the encircled regions due to over enhancement and intensity saturation. The images processed using BBHE, DSIHE, RMSHE, RSIHE and ACEBSF techniques are found to be poorly enhanced and most of the details are lost due to brightness degradation. Though the existing methods result in marginal contrast improvement, the proposed HGSHS technique produces enhanced image with higher contrast improvement together with preservation of details in the encircled regions of the image.

In addition, the proposed HGSHS sharpens the edges around the objects, which makes the boundary of each object clearly visible. The Left skewed original Lady_liberty image, its enhanced images and corresponding histograms are shown in Fig. 4. It is observed that during enhancement all the existing methods produce brightness degradation in sky, face and tabula ansata as shown in the encircled regions. However, the proposed HGSHS technique enhances the image with preservation of details as observed in the encircled regions.

Figure 5.

Enhanced images with histograms obtained by different techniques for right skewed Couple image (a) Original Image (b) BBHE (c) DSIHE (d) MMBEBHE (e) RMSHE (f) RSIHE (g) BHEPL (h) ACEBSF (i) HGSHS.

Figure 6.

Sample images from NASA database [30] enhanced by BCCHS and HGSHS (a) Original (Image No. 5), BCCHS (k1 $=$ 2; k2 $=$ 2), HGSHS (BGS $=$ 192 $\sigma_{{L}}=$ 43; $\sigma_{{U}}=$ 24) (b) Original (Image No. 15), BCCHS (k1 $=$ 4; k2 $=$ 6), HGSHS (BGS $=$ 192 $\sigma_{{L}}=$ 35; $\sigma_{{U}}=$ 40) (c) Original (Image No. 18), BCCHS (k1 $=$ 4; k2 $=$ 6), HGSHS (BGS $=$ 192 $\sigma_{{L}}=$ 40; $\sigma_{{U}}=$ 30) (d) Original (Image No. 19), BCCHS (k1 $=$ 4; k2 $=$ 6), HGSHS (BGS $=$ 192 $\sigma_{{L}}=$ 40; $\sigma_{{U}}=$ 80) (e) Original (Image No. 25), BCCHS (k1 $=$ 2; k2 $=$ 2), HGSHS (BGS $=$ 192 $\sigma_{{L}}=$ 32; $\sigma_{{U}}=$ 99) (f) Original (Image No. 26), BCCHS (k1 $=$ 2; k2 $=$ 2), HGSHS (BGS $=$ 192 $\sigma_{{L}}=$ 30; $\sigma_{{U}}=$ 59).

The Right skewed original Couple image, its enhanced images and corresponding histograms are shown in Fig. 5. It is observed that the existing techniques poorly enhanced the images with loss of details due to intensity saturation as shown in the encircled regions. But the proposed HGSHS technique effectively enhances the image with improved contrast and the details in dark regions are also made visible such as the edges of the man’s coat and legs of the furniture behind the couple as observed in the encircled regions.

For qualitative comparison, few sample images enhanced using the proposed HGSHS and BCCHS are shown in Fig. 6. In some of the images enhanced by BCCHS technique, the occurrence of brightness degradation and over enhancement are clearly observed in the encircled regions as shown in Fig. 6. Whereas, in the images enhanced by the proposed HGSHS technique the enhancement of visibility of objects in dark regions with sharper edges around the objects are observed in the encircled regions.

3.2 Quantitative assessment

To evaluate the performance of the CE techniques quantitatively, the contrast, DIE and gradient values produced by these techniques are calculated for all the differently skewed input images and are given in Tables 3–5.

Table 3
Contrast of images enhanced by various techniques

Image name	Histogram	Original	BBHE	DSIHE	MMBEBHE	RMSHE	RSIHE	BHEPL	ACEBSF	HGSHS
Pollen grain	S	40.6608	40.9152	40.9152	40.9319	40.8821	40.7254	40.9875	41.1057	44.0538
Boston	S	42.0439	42.1201	42.2619	42.5417	42.2392	42.1205	43.0540	42.2139	44.0348
Roadside	S	41.8966	42.4476	42.5299	41.9980	42.4564	42.1907	42.3826	41.8364	44.0458
Child	S	41.4938	41.4736	41.6629	41.8715	41.5673	41.5346	42.3332	41.8138	44.0409
Foxy	S	40.6739	40.7456	40.7944	40.8416	40.7181	40.6740	41.1274	41.1676	44.0388
Plane	LS	45.7186	44.5540	44.1832	45.5816	44.5951	45.0396	45.2863	45.2018	45.5691
Aerial	LS	45.0989	44.6832	44.3087	45.1332	44.7275	44.8397	44.8083	43.2101	45.1913
F16	LS	44.9741	44.7424	44.2800	45.0212	44.7109	44.7276	44.8400	44.4054	45.1131
Aerial1	LS	45.8650	45.0436	44.6857	45.5416	45.0533	45.3239	45.2615	43.7679	45.4313
Lady_liberty	LS	46.5532	45.5028	45.4887	46.3450	45.4074	46.1007	44.9886	45.5473	46.5265
Seashore	RS	29.3463	30.9256	36.4789	31.4600	30.7591	31.9087	33.0790	34.7395	37.6644
U2	RS	29.2259	31.8006	36.7209	31.3875	31.9498	32.5997	32.2716	34.6856	36.4461
Plant	RS	27.7381	34.4745	37.4783	33.3814	34.4647	33.0091	34.6401	35.3168	39.7271
Couple	RS	29.3659	35.9356	37.6117	33.3313	35.9933	33.9301	36.4797	37.3137	39.6040
Cat	RS	34.9112	36.8392	37.5134	36.6743	36.6249	35.0407	37.7784	38.2584	39.1146

Table 4

DIE of images enhanced by various techniques

Image name	Histogram	Original entropy	BBHE	DSIHE	MMBEBHE	RMSHE	RSIHE	BHEPL	ACEBSF	HGSHS
Pollen grain	S	5.2257	0.2126	0.0007	0.2087	0.00810	0.2371	0.2157	1.4928	0.0000
Boston	S	4.4782	0.1690	0.0138	0.2644	0.05250	0.2406	0.2604	1.4971	0.0025
Roadside	S	6.7560	0.1411	0.0931	0.1495	0.39480	0.1734	0.1615	0.9003	0.0170
Child	S	4.8476	0.2025	0.0176	0.2097	0.08350	0.2688	0.2621	1.5283	0.0000
Foxy	S	5.8592	0.1404	0.0000	0.1608	0.00000	0.1486	0.1573	1.4476	0.0000
Plane	LS	6.4592	0.1815	0.1653	0.1754	0.26920	0.1799	0.1261	0.5961	0.1553
Aerial	LS	6.9940	0.2254	0.1923	0.2419	1.07930	0.2181	0.1754	0.8956	0.1249
F16	LS	6.7135	0.1446	0.1203	0.1524	0.47560	0.1675	0.2094	0.8360	0.0619
Aerial1	LS	7.0155	0.2236	0.2233	0.2497	1.62930	0.2254	0.1310	0.8102	0.1929
Lady_liberty	LS	6.2935	0.2565	0.2810	0.2909	2.19610	0.3313	0.2292	0.6372	0.2011
Seashore	RS	5.8856	0.2300	0.2306	0.2685	2.27810	0.2570	0.1648	1.1341	0.1875
U2	RS	5.4652	0.1414	0.1473	0.2431	0.45730	0.1393	0.1764	1.1072	0.2071
Plant	RS	5.9937	0.2605	0.3406	0.1970	1.03190	0.2467	0.1431	1.1219	0.1797
Couple	RS	6.4003	0.2434	0.2337	0.2041	1.59620	0.2065	0.1677	1.0822	0.1383
Cat	RS	6.7804	0.3400	0.3603	0.3554	2.47600	0.3510	0.1941	0.5544	0.3886

Table 5

Gradient of images enhanced by various techniques

Image name	Histogram	Original	BBHE	DSIHE	MMBEBHE	RMSHE	RSIHE	BHEPL	ACEBSF	HGSHS
Pollen grain	S	1.1984	1.4761	1.4827	4.9660	1.4087	5.3572	1.4606	3.7861	2.6727
Boston	S	1.2957	2.3979	6.7792	2.3133	6.4432	2.2939	2.0523	3.7870	6.0282
Roadside	S	3.7009	5.3037	6.7319	5.3258	6.7949	5.3111	4.7858	7.4299	4.4648
Child	S	2.0711	3.4407	7.9988	3.4421	7.5280	3.4768	2.7767	5.4092	4.6853
Foxy	S	3.6612	3.8544	7.6187	3.8794	7.6755	3.8652	3.7255	7.1054	4.8726
Plane	LS	1.2891	1.9976	1.9278	2.1431	2.1998	1.9653	1.8345	3.1335	1.9121
Aerial	LS	5.6964	6.9236	6.5983	7.0547	6.5765	6.8853	6.4462	7.7822	6.5146
F16	LS	3.3323	4.0131	4.8292	4.4094	4.7954	4.0237	4.0595	6.0519	4.3614
Aerial1	LS	5.7463	6.5368	6.1413	6.7251	6.2709	6.5123	6.1473	7.7733	6.1116
Lady_liberty	LS	2.0807	3.6032	2.2905	3.4275	3.8893	3.4556	2.5871	4.3457	2.6907
Seashore	RS	2.3436	2.7714	2.7733	3.9887	2.9011	2.7215	3.0618	4.5013	4.9702
U2	RS	3.0700	4.5300	5.3000	6.2900	5.2900	4.6000	4.5200	6.9900	7.1800
Plant	RS	2.4007	3.4074	3.3536	4.1480	3.5993	3.3950	3.2944	4.7858	4.0188
Couple	RS	2.1550	3.2987	2.4475	3.7645	3.3275	3.3374	3.0061	4.4337	2.3922
Cat	RS	3.0548	3.2408	3.2159	3.3822	3.0251	3.2210	3.1357	4.9863	3.2454

Table 6

Contrast of images enhanced by BCCHS and HGSHS techniques on NASA database [30]

Image no.	Histogram	Original	BCCHS	HGSHS
1	RS	38.8493	42.4607	41.7122
2	RS	37.3599	41.4678	40.1697
3	RS	37.2629	40.3615	40.4938
4	RS	37.6222	40.2195	40.3380
5	RS	39.0306	38.1887	40.2496
6	RS	38.7986	40.5627	40.9322
7	RS	35.5551	41.8960	39.8191
8	RS	36.4208	41.3707	39.7471
9	RS	31.8992	40.6655	40.3929
10	RS	38.2861	40.1932	40.8008
11	RS	39.7119	41.5255	40.7435
12	RS	37.4054	39.3169	40.5427
13	RS	37.9818	39.6240	40.3100
14	RS	39.3622	43.2059	40.5848
15	RS	33.9483	41.9128	39.8905
16	RS	35.9232	42.0568	40.8921
17	RS	36.3562	42.2805	40.8473
18	RS	34.6425	39.7370	39.6244
19	RS	41.2280	44.3980	41.3668
20	RS	37.0323	42.1626	40.0168
21	RS	6.05360	26.4107	39.6477
22	RS	34.8294	42.0428	40.0437
23	RS	34.9785	42.0305	40.5554
24	RS	32.1188	41.0652	39.9138
25	LS	43.9857	35.7245	39.5441
26	LS	42.6843	28.4584	39.5389
27	RS	35.4354	40.9968	40.2237

Table 7

DIE of images enhanced by BCCHS and HGSHS techniques on NASA database [30]

Image no.	Histogram	Original	BCCHS	HGSHS
		Entropy	DIE	DIE
1	RS	6.0864	0.3031	0.1267
2	RS	7.3262	0.4828	0.2020
3	RS	7.4406	0.3983	0.3107
4	RS	7.4202	0.3369	0.3765
5	RS	7.3740	0.4484	0.0904
6	RS	7.4780	0.3055	0.2416
7	RS	7.1012	0.2389	0.2287
8	RS	7.0851	0.2465	0.3781
9	RS	6.1994	0.3189	0.2100
10	RS	7.3116	0.3999	0.1292
11	RS	7.4152	0.5005	0.1735
12	RS	7.2366	0.4178	0.1718
13	RS	7.3972	0.3711	0.3458
14	RS	7.4837	0.6476	0.1856
15	RS	6.7467	0.2370	0.1265
16	RS	7.1346	0.4023	0.2849
17	RS	7.0935	0.6430	0.2605
18	RS	6.8250	0.1770	0.1161
19	RS	7.3159	1.2821	0.0589
20	RS	7.3856	0.4281	0.2008
21	RS	3.3253	0.5036	0.0393
22	RS	6.6126	0.2254	0.1136
23	RS	7.0120	0.3191	0.2044
24	RS	6.5746	0.2147	0.0673
25	LS	5.0570	0.1063	0.0044
26	LS	5.5800	0.3782	0.0465
27	RS	7.1449	0.7084	0.3127

Table 8

Gradient of images enhanced by BCCHS and HGSHS techniques on NASA database [30]

Image no.	Histogram	Original	BCCHS	HGSHS
1	RS	1.1748	3.2541	2.2568
2	RS	2.1537	4.6588	2.5856
3	RS	1.7475	3.4029	2.2388
4	RS	1.9810	1.5569	2.4264
5	RS	1.8444	2.9274	2.1355
6	RS	2.1270	3.4397	2.4186
7	RS	1.2519	5.0674	1.3665
8	RS	1.2926	3.0754	1.3332
9	RS	1.1349	4.5086	3.0641
10	RS	2.3322	2.8133	2.8277
11	RS	3.1176	3.3534	3.7672
12	RS	2.4349	4.2665	3.1625
13	RS	1.2654	0.5527	1.4427
14	RS	1.7367	3.4408	2.1079
15	RS	1.4723	4.7569	2.2586
16	RS	2.2563	2.8497	3.3197
17	RS	1.2119	2.9043	2.3096
18	RS	2.6144	1.5961	3.6730
19	RS	1.6292	5.0698	1.9106
20	RS	2.5347	3.6291	2.7594
21	RS	0.5215	2.2799	0.8843
22	RS	1.4527	2.2403	2.5610
23	RS	2.5333	1.9194	3.8971
24	RS	1.2336	2.7003	1.9987
25	LS	0.7953	2.2965	3.2769
26	LS	1.0449	2.4929	2.6999
27	RS	3.8620	3.9341	4.4380

From Table 3, it is observed for all the types of skewness, the contrast values obtained by the proposed HGSHS technique are higher than that of other existing techniques. It is evident that because of the higher contrast obtained the details in the encircled regions of Figs 2–4 corresponding to HGSHS are more visible than that of the other existing techniques. From Table 4, it is observed that for symmetrically skewed images, the closeness of the entropy values of the images enhanced by the proposed HGSHS technique given as DIE values are found to be very less (close to zero) compared with that of the other techniques is an evidence of the preservation of details. Hence, it is very clear that the symmetrically skewed images are efficiently enhanced by the proposed HGSHS technique. For left and right skewed images, though the DIE values obtained by the proposed HGSHS is slightly worse than RSIHE technique, the details in dark regions of the image obtained by HGSHS technique is better visible than the RSIHE technique as the contrast obtained is significantly high. In addition, the DIE values obtained by the proposed HGSHS is found to be better than that of remaining existing techniques.

The values of gradient, the measure of sharpness obtained for the images enhanced by various techniques are shown in Table 5. The average increase in gradient with respect to original image for the proposed HGSHS technique is above 50%, however the details in dark regions are found to be better visible due to high contrast achieved by the proposed HGSHS when compared to ACEBSF, BHEPL and MMBEBHE as shown in Figs 2–4. In addition, the average increase in gradient obtained by the proposed HGSHS technique is found to be higher than that of BBHE, DSIHE, RMSHE and RSIHE.

The contrast, DIE and gradient values obtained for NASA database images enhanced using HGSHS and BCCHS techniques are shown in Tables 6–8. It is observed that the average contrast improvement obtained by the proposed HGSHS technique is 29.13%, which is higher than that of the BCCHS technique (21.75 %). Further, it is observed that the DIE values obtained by the proposed HGSHS technique are also better than that of BCCHS, due to which the details in the images enhanced by the proposed HGSHS technique are found to be highly preserved. It is observed that for all the NASA images, the gradient values obtained for images enhanced using HGSHS is higher than that of the original images. Whereas for BCCHS, the gradient values obtained for some of the images are lower than that of the original images which results in brightness degradation and annoying artifacts. Based on the results obtained and the analysis, it is evident that the Histogram shape based Gaussian Sub-Histogram Specification (HGSHS) technique is best suitable for enhancement of contrast of differently skewed images.

In the present work the search for optimum statistical parameters is limited for BGS, $\sigma_{{L}}$ and $\sigma_{{U}}$ considering the complexity in computation while handling high resolution images. In addition, there is extensive future scope for utilizing the results obtained during the vast experiments of the present work as resource for development of soft computing tools that can be used in conjunction with modern machine learning strategies.

4. Conclusion

In this paper, a new histogram shape based Gaussian sub-histogram specification technique for contrast enhancement is proposed. To enrich the visual quality of the enhanced image without annoying side effects, the Gaussian parameters of the proposed technique is determined relative to the shape of the histogram of the given image. To evaluate the performance of the proposed technique, images from standard databases and NASA database were enhanced and compared. The overall experimental results showed that the proposed HGSHS technique can give better results than the existing contrast enhancement techniques.

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Histogram shape based Gaussian sub-histogram specification for contrast enhancement

Abstract

Keywords

1. Introduction

2.1.1 Contrast

Table 1 Statistical parameters of input histogram and specified Gaussian sub-histograms

Table 3 Contrast of images enhanced by various techniques

References

Table 1
Statistical parameters of input histogram and specified Gaussian sub-histograms

Table 3
Contrast of images enhanced by various techniques