Journal of Computer and Communications, 2014, 2, 52-56
Published Online January 2014 (http://www.scirp.org/journal/jcc)
http://dx.doi.org/10.4236/jcc.2014.22010
OPEN ACCESS JCC
Enhancement Technique of Image Contrast using New
Histogram Transformation
Wanhyun Cho1, Seongchae Seo2, Jinho You3, Soonja Kang4
1Department of Statistics, Chonnam National University, Gwang-ju, Korea; 2Department School of Electronics & Computer Engi-
neering, Chonnam National University, Gwang-ju, Korea; 3Doul Infotech, Gwang-ju, Korea; 4Department of Mathematical Educa-
tion, Chonnam National University, Gwang-ju, Korea.
Email: whcho@chonnam.ac.kr; scseo@chonnam.ac.kr; loafers@daum.net; sjkang@chonnam.ac.kr
Received November 2013
ABSTRACT
This paper presents a preprocessing technique that can provide the improved quality of image robust to illumi-
nation changes. First, in order to enhance the image contrast, we proposed new adaptive histogram transforma-
tion combining histogram equalization and histogram specification. Here, by examining the characteristic of
histogram distribution shape, we determine the appropriate target distribution. Next, applying the histogram
equalization with an image histogram, we have obtained the uniform distribution of pixel values, and then we
have again carried out the histogram transformation using an inverse of target distribution function. Finally we
have conducted various experiments that can enhance the quality of image by applying our method with various
standard images. The experimental results show that the proposed method can achieve moderately good image
enhancement results.
KEYWORDS
Image Preprocessing Technique; Contrast Enhancement; Histogram Equalization and Specification;
Target Distribution Fun ct ion
1. Introduction
Image enhancement is the preprocessing of image to im-
prove the interpretability or perception of information in
images for human viewers and to provide a better input
for other automated image processing techniques. The
principal objective of image enhancement is to modify
attributes of an image to make it more suitable for a giv-
en task and a specific observer. During this process, one
or more attributes of an image are modified. The choice
of attributes and the way that they are modified are spe-
cific to a given task. Moreover, observer-specific factors,
such as the human visual system and the observer’s ex-
perience, will introduce a great deal of subjectively into
the choice of image enhancement methods [1,2].
Image enhancement is generally used in the following
three cases: noise reduction from image, contrast en-
hancement of the very dark and bright image, and high-
light the edges of the objects in a blurring image. Noise
reduction is the process of removing noise form a signal
or an image. In general, images taken with both digital
camera and conventional film cameras will pick up noise
from a variety of sources. Therefore, it is required that
the noise is removed for many further uses of these im-
ages. Contrast enhancement is acquiring clear image
through brightness intensity value redistribution. That is,
this is enhancing features as stretching interval between
dark and brightness area. De-blurring process is to re-
store the sharp images via image de-convolution such as
Wiener de-convolution.
Here, we are mainly interested in the contrast en-
hancement methods. Several methods have been pro-
posed to achieve contrast enhancement invariant to illu-
mination variations [3-7]. There are called as Gray level
transformations, Gamma correction, Contrast stretching,
Histogram equalization, Histogram matching and so on.
A very popular one among contrast enhancement tech-
niques is histogram equalization. This technique is per-
formed by remapping the gray levels of the image based
on the probability distribution of the input gray image
levels. It flattens and stretches the dynamic range of the
image’s histogram and resulting in overall contrast en-
hancement. But, in spite of its popularity and simplicity,
histogram equalization is not very suitable to be imple-
Enhancement Technique of Image Contrast using New Histogram Transformation
OPEN ACCESS JCC
53
mented in consumer electronics, such as digital TV, be-
cause the method tends to produce undesirable artifacts.
Hence, many improved methods have been proposed to
overcome these drawbacks. They are brightness preserv-
ing bi-histogram equalization (BBHE), dualistic sub-
image histogram equalization (DSIHE), minimum mean
brightness error bi-histogram equalization (MMBEBHE),
recursive mean-separate histogram equalization (RMSHE),
recursive sub-image histogram equalization (RSIHE),
mul ti -peak histogram equalization with brightness pre-
serving (MPHEBP), and dynamic histogram equalization
(DHE). On the other hand, another popular contrast en-
hancement scheme is histogram specification. This tech-
nique enables us to match the histogram of input image
close to the histogram of target image. However, speci-
fying the output histogram is not a smooth task as it va-
ries from image to image. Hence, several researches have
been proposed on improvement of histogram specifica-
tion. They are dynamic histogram specification (DHS),
Histogram specification with Gamma distribution (HSGD),
image fusion histogram specification (IFHS), and auto-
matic exact histogram specification (AEHS).
However, there are some problems when we have used
the histogram equalization (HE) to improve the contrast
of the image. First, the HE method does not take the
mean brightness of an image into account. Second, the
HE method may result in over enhancement and satura-
tion artifacts due to the stretching of the gray levels over
the full gray level range. Third, the HE method always
yields the middle gray level regardless of the input image,
and cause undesirable artifacts. Therefore, in order to
improve these problems, we have decided in advance the
target images and then we use the histogram specifica-
tion method to an input image to get an image similar
with target image. But, it is difficult that we determine in
advance the appropriate target image. Hence, it is re-
quired to a new contrast enhancement method robust to
illumination changes.
Hence, in order to solve these problems at the same
time, we try to propose a new image enhancement me-
thod that uses a new histogram transformation. In the
Section 2, in order to enhance the image contrast, we
have considered new adaptive histogram transformation
combining histogram equalization and histogram speci-
fication. In the Section 3, we presented experimental
results that is able to demonstrate the effectiveness of the
proposed method in comparison to a few existing me-
thods quantitatively. And in the Section 4, we mentioned
the conclusion of my paper.
2. Contrast Enhancement
2.1. CDF Transformation
Here we will propose a technique that can improve the
contrast of an image by using a combination of Histo-
gram Equalization (HE) and Histogram Specification
(HS). This technique can be thought as the transforma-
tion that converts the values in the ranges between 0 and
1 given by histogram equalization of input image into
pixel values of particular output image by using the spe-
cified cumulative distribution function (CDF) to achieve
a well illuminated image. In our case, we adaptively se-
lect the CDF so that the contrast of image can automati-
cally achieve an optimal level.
First, we assume to have an input image I(x,y) with N
pixels and a total number of L gray levels, e.g., 256 gray
levels for an 8-bit image. We transform the distribution
of the pixel intensity values in the image I(x,y) into a
uniform distribution on interval [0,1] by using the histo-
gram equalization defined as the following formula. For
a grey level of k, k = 0, 1, , L-1, a new transformed one
uk is defined by
0
,[0, ,L 1]
ki
ki
n
uk
N
=
= ∈−
. (1)
where ni denotes the number of pixels in I(x,y) with the
grey level value i. Equation (1) defines a mapping of the
pixel’ intensity values from their original range [0,,L-1]
to the domain of [0,1].
Second, if the distribution of desired target image ITA
is specified, we define its probability density function
(PDF) and CDF as follows:
0
G(z)(v)dv,z[0,L 1]
z
z
p= ∈−
. (2)
Third, we try to find a new value knew corresponding
with uk such that
0
uG(k )(v)dv
new
k
k newz
p= =
. (3)
But, since a new value knew is continuous value scaled
on an interval [0, L-1], we should take a Gauss bracket
integer [knew + 0.5].
Here, the procedure that we have considered so far
would be expressed as the following example picture.
Figure 1 shows the density histogram of a given image,
its equalized histogram & specified CDF, and the density
histogram of output image.
Furthermore, we consider the three types of density
histogram structures in order to determine adaptively a
proper CDF form in our CDF transformation.
2.2. Skew Histogram to the Right
When it is given a dark image like as the following ex-
ample image in Figure 2, its density histogram has a
form skewed to the right.
In this case, the average of the gray values of a given
image is smaller than the average value (N + 1)/2 of
symmetrical distribution. Furthermore, in order to im-
Enhancement Technique of Image Contrast using New Histogram Transformation
OPEN ACCESS JCC
54
(a) (b)
(c)
Figure 1. Graphical Representation of our procedure. (a)
Histogram of synthetic image; (b) Its equalized histogram
& specified CDF; (c) Histogram transformation.
Figure 2. Dark sample image and its histogram.
prove the contrast of a given image, it is required with
brighter image. Therefore, we have to consider a skew
distribution to the left such as the Gompertz distribution
with the opposite structure about a given histogram. Here,
the expressions for its PDF, CDF and Inverse CDF are
given respectively by
( )
( )
( )
( )
( )
ηexp ,η,b 0
G z1expη1
bz bz
z
bz
p zbeee
e
η
η
= −>
=−− −
(4)
and
. Finally, when ap-
plying our method with CDF being Gompertz distribu-
tion to a given image, we have to select two parameters,
η and b. Here, we used η = 0.018 and b = 2.322. Figure 3
shows the contrast improved image and its histogram
obtained by using our method.
2.3. Skew Histogram to the Left
As opposed to above, suppose that we have a very bright
image like as the following example image in Figure 4.
Then, its density histogram has a form skewed to the left.
In such a case, the average of the gray values of a giv-
Figure 3. Contrast enhanced image and its histogram after
applying CDF transformation.
Figure 4. Bright sample image and its histogram.
en image is larger than the average value (N + 1)/2 of
symmetrical distribution. Hence, in order to improve the
contrast of a given image, it is required with darker im-
age. Therefore, we have to consider a skew distribution
to the right such as the log-normal distribution or the
Weill distribution with the opposite structure about a
given histogram. Here, the expressions for PDF, CDF,
and inverse CDF of the Weibull distribution are given
respectively by
( )
( )
1
1
z 0,λ
>0,k>0
λλ
Gz1 e
,
xp λ
k
z
k
kz
pz
z

= ≥




=−−





(5)
and
( )()
( )
1/
1
λln 1
k
Gu u
=−−
. Finally, when applying
our method with CDF being Weibull distribution to a
given image, we have to select two parameters, λ (scale)
and k (shape). Here, we used λ = 1.0 and k = 1.5. Figure
5 shows the contrast improved image and its histogram
obtained by using our method.
2.4. Symmetrical Histogram
Third, suppose that we have a usual image or equalized
image like as the following example image in Figure 6.
Its density histogram is generally given as the shape sim-
ilar to the histogram of a symmetric distribution.
In this case, the average of the gray values of a given
image is approximately equal to the average value (N +
1)/2 of symmetrical distribution. Hence, in order to im-
prove the contrast of a given image we have to consider a
symmetric distribution such as the Normal distribution,
the Student t distribution or the Logistic distribution.
Here, we used the Normal distribution and its PDF and
CDF are given respectively by
Enhancement Technique of Image Contrast using New Histogram Transformation
OPEN ACCESS JCC
55
Figure 5. Contrast enhanced image and its histogram after
applying CDF transformation.
Figure 6. Usual sample image and its histogram.
( )
2
11
exp,- <,0
2
2
z
z
pz
µµσ
σ
πσ


=−∞<∞ >





(6)
and
( )
2
0
11
G zexp2
2
z
udu
µ
σ
πσ


= −





Finally, when applying our method to a given image
with CDF being the Normal distribution, we have to se-
lect two parameters, μ (location) and σ (scale). Here, we
used μ = 127.5 and σ = 14. Figure 7 shows the contrast
improved image and its histogram obtained by using our
method.
2.5. Adaptive Histogram Transformation
Finally, we adaptively improve the contrast of input im-
age by applying the following procedure. This method is
summarized below.
1) Calculate the average for the gray values of the in-
put image.
2) Determine whether this value belongs something
among the three regions [0, μ-σ], - σ, μ + σ] and [μ + σ,
255], where μ and σ are selected by the mean and the
standard deviation of normal distribution. Here, we used
μ = 127.5 and σ = 42.
3) If this value belongs to the first region, we apply the
Gomertz CDF method for input image, else if this value
belongs to the second region, we apply the normal CDF
method for input image, and else if this value belongs to
the third region, we apply the Gumbel CDF method for
input image.
3. Experiments
In this section, we provide experimental results in order
to demonstrate the effectiveness of the proposed method
in comparison to a few existing methods quantitatively.
Here, we consider the performance of the proposed his-
togram transformation technique for global contrast en-
hancement of grayscale images. The performance of the
various contrast enhancement methods were tested on
standard images Camera man, Man, Barbara, Lena,
Elaine. All of images are with size of 512 × 512 pixels.
To compare their performances, the same images are
enhanced with Gamma correction (GC), Histogram
equalization (HE), Histogram specification (HS), and
proposed method (PM). For all these methods, the per-
formance is measure qualitatively in terms of human
visual perception and quantitatively by using the widely
used metric EME (a measure of enhancement) for mea-
suring contrast enhancement. This measure is defined as
follows:
21
;,
11
12 ;,
1
EME 20log
w
kk max k l
w
lk mink l
I
kk I
= =
=
∑∑
where an image I(x,y) is split into k1 k2 blocks Wk,l (x,y)
of sizes
12
ll×
, and
max; ,
wkl
I
and
min; ,
wkl
I
are respectively
maximum and minimum of the image I(x,y) inside the
block Wk,l (x,y). The EME values for different images
are given in Table 1. Here, Org, GC, HE, HS, and PM
denote respectively for original image, gamma correction,
histogram equalization, histogram specification, and pro-
pose method.
The enhanced images and histograms obtained by dif-
ferent methods for the Elaine image are shown in Figure
8. It is evident from the table and figure that the proposed
method provides better contrast enhancement than the
existing methods.
Figure 7. Contrast enhanced image and its histogram after
applying CDF transformation.
Table 1. EME values for different methods and images.
Came r a man Man Barb ara Lenna Elaine
Org 16.962 10.741 11.966 18.030 14.303
GC 19.548 19.083 25.106 18.241 16.198
HE 12.757 20.956 18.864 18.764 17.207
HS 8.626 26.035 12.870 19.178 18.229
PM 8.075 23.886 15.688 18.666 18.337
Enhancement Technique of Image Contrast using New Histogram Transformation
OPEN ACCESS JCC
56
Figure 8. Enhanced images and histograms given by differ-
ent methods.
4. Conclusion
In this paper, we propose a new image enhancement me-
thod that combines both the histogram transformation
and edge-preserving regularization. First, we proposed
new adaptive histogram transformation combining histo-
gram equalization and histogram specification in order to
enhance the image contrast. Second, we consider the
characters of a various regularization functions in the
energy functional that satisfies an edge-preserving noise
reduction.
From the experimental results, we note that the pro-
posed method can provide better contrast enhancement
than the existing methods. And we note that the total
variation method is considered as the best way to remove
noise than other methods.
Acknowledgemen ts
This work was supported in part by the Research Foun-
dation Grant by the Chonnam National University
(CNU-2012) and it also was the results of a study on the
Leades INdustry-university CooperationProject, sup-
ported by the Ministry of Education, Science & Tech-
nology (MEST).
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