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CHAPTER 3
CONTRAST STRETCHING RECURSIVELY SEPARATED
HISTOGRAM EQUALIZATION
3.1 INTRODUCTION
Histogram equalization is a technique commonly used for image
contrast enhancement. It works by redistributing the gray-levels of the input
image by using its probability distribution function (DeGroot et al 2002).
Despite its success, this technique has a well-known drawback: it does not
preserve the brightness of the input image in the output image. To overcome
such drawback, methods based on this technique have proposed to decompose
the original image into two sub-images, and then perform the histogram
equalization in each sub-image.
These methods decompose the original image by using statistical
properties, such as the mean gray-level value (Kim et al 1997), the equal-area
value (Wang et al (1999) or the level which yields the minimum brightness
error between the original and the enhanced images (Chen et al 2003).
Although these methods preserve the input brightness in the output image
with a significant contrast enhancement, they may produce images which do
not look as natural as the input ones. In order to enhance contrast, preserve
brightness and still produce natural looking images, this chapter presents a
improved technique called Contrast Stretching Recursively Separated
Histogram Equalization (CSRSHE) for brightness preservation and image
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contrast enhancement. This algorithm applies a two stage approach: 1) A new
intensity is assigned to each pixel according to an adaptive transfer function
that is designed on the basis of the global and local statistics of the input
image. 2) Performing recursive mean separate histogram equalization based
on a modified local contrast stretching manipulation.
Note that several histogram equalization methods proposed in the
literature are suitable for real-time applications, because they are quite simple.
The proposed CSRSHE methods are even more sophisticated in the
decomposition process of the original image than the others; remain fast and
thus suitable for real-time applications. The remainder of this chapter is
organized as follows. Section 3.2 describes some previous works in histogram
equalization which are closely related to our proposed methods. The proposed
Contrast Stretching Recursively Separated Histogram Equalization
(CSRSHE) methods are introduced in Section 3.3. Results and performance
analysis are made in section 3.4. Finally, conclusion is drawn in Section 3.5.
3.2 HISTOGRAM EQUALIZATION METHODS
This section describes some histogram equalization methods with
respect to brightness preserving. Classical histogram equalization (CHE)
method and other methods which are extensions of the CHE, namely BBHE
proposed by Kim (1997), DSIHE proposed by Wang (1999), MMBEBHE
proposed by Chen (2003) and Recursive Mean Separate Histogram
Equalization (RMSHE) proposed by Chen and Ramli (2003) are explained in
detail. These four extensions of the CHE method have one main point in
common: they decompose the original image into two or more sub-images,
and then equalize the histograms of these sub-images independently.
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3.2.1 Classical Histogram Equalization Method (CHE)
The classical histogram equalization (CHE) method (Wang et al
1999) for monochromatic images (e.g., gray-level ones) is the core of the
methods presented in this chapter.
The high performance of the histogram equalization in enhancing
the contrast of an image is a consequence of the dynamic range expansion of
the gray-level image domain. That is, theoretically, the output image
enhanced by a histogram equalization method uses all the gray-levels in the
image domain. Besides, the CHE tries to produce an output image with a flat
histogram, i.e., a uniform distribution. The entropy of a message source will
get the maximum value when the message has uniform distribution (Wang et
al 1999). This means that an enhanced image by the CHE method has the
maximum information (i.e., entropy) with respect to its original one.
However, the CHE method barely satisfies the uniform distribution property
in images with discrete gray-level domains.
Despite the advantages offered by the CHE method, it can
introduce a significant change in image brightness, i.e., its mean gray-level.
That is, due to the uniform distribution specification of the output histogram,
the CHE method shifts the brightness of the output image to the median gray-
level. This change in brightness is not desirable when applying the CHE
scheme into consumer electronics devices, for instance, TV, camcorders,
digital cameras and video surveillance. This is because; it may introduce
unnecessary visual deterioration to the output image.
3.2.2 Brightness Bi-Histogram Equalization Method (BBHE)
In order to overcome the drawback introduced by the CHE method
described in the previous subsection, a brightness preserving bi-histogram
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equalization (BBHE) method was proposed by Kim (1997). The essence of
the BBHE method is to decompose the original image into two sub-images,
by using the image mean gray-level, and then apply the CHE method over
each of the sub- images.
The BBHE method produces an output image with the value of the
brightness (the mean gray-level) located in the middle of the mean of the
input image and the median gray-level. The output mean brightness of the
BBHE method is a function of the input mean brightness. This fact clearly
indicates that the BBHE preserves the brightness of the image when
compared to the case of classical histogram equalization, where the output
brightness always tends to the median gray-level.
3.2.3 Dualistic Sub-Image Histogram Equalization Method (DSIHE)
After these definitions, following the same basic ideas used by the
BBHE method of decomposing the original image into two sub-images and
then equalizing the histograms of the sub-images separately in this thesis, it is
proposed and named as equal area dualistic sub-image histogram equalization
(DSIHE) method (Wang et al 1999). Instead of decomposing the image based
on its mean gray-level, the DSIHE method decomposes the images aiming at
the maximization of the Shannon’s entropy of the output image. The method
uses the Shannon’s entropy because the condition to maximize the average
information content (i.e., the entropy) of the processed image can seldom be
held for discrete images. For such aim, the input image is decomposed into
two sub-images, being one dark and one bright image, respecting the equal
area property. Then the two-sub images have their histogram equalized
independently and the composition of the resulting processed sublimates
constitutes the output image of the DSIHE method.
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Wang et al (1999) showed that the brightness of the output image
produced by the DSIHE method is the average of the equal-area level of the
image and the median gray-level of the image.
The authors claim that the brightness of the output image generated
by the DSIHE method does not present a significant shift in relation to the
brightness of the input image, especially for the large area of the image with
the same gray-levels (represented by small areas in histograms with great
concentration of gray-levels), e.g., images with small objects regarding the
great darker or brighter backgrounds.
3.2.4 Minimum Mean Brightness Error Bi-Histogram Equalization
Method (MMBEBHE)
Following the basic principle of the BBHE and DSIHE methods of
decomposing an image before applying the CHE method to equalize the
resulting sub-images independently, Chen et al (2003) proposed the minimum
mean brightness error bi-histogram equalization (MMBEBHE) method. The
main difference between the BBHE and the DSIHE methods and the
MMBEBHE one is that the latter searches for a threshold level that
decomposes the image into two sub-images such that the minimum brightness
difference between the input and output images is achieved, whereas the
former methods consider only the input image to perform the decomposition.
3.2.5 Recursive Mean-Separate Histogram Equalization Method
(RMSHE)
The extensions of the CHE method described were characterized by
decomposing the original image into two new sub-images. However, in the
extended version of the BBHE method, introduced by Chen et al (2003), and
named Recursive Mean-Separate Histogram Equalization (RMSHE), instead
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of decomposing the image only once the RMSHE method proposed
to perform image decomposition recursively up to a scale r, generating 2r sub-
images.
Note that, as far as time complexity is concerned, this method
presents a drawback: the number of decomposed sub-histograms increases in
a power of two.
3.3 THE PROPOSED METHODS
In this section the details of the proposed image enhancement
algorithm namely Contrast Stretching Recursively Separated Histogram
Equalization (CSRHE) are described which uses a local modified contrast
stretching manipulation of the intensity range within the subblocks. CSRSHE
consists of three modules:
1. Contrast stretching.
2. Histogram segmentation.
3. Histogram equalization.
The details of each module are described in the following
subsections.
3.3.1 Contrast Stretching
The proposed CSRSHE enhancement method performs histogram
equalization based on a local modified contrast-stretching manipulation and
replaces each original intensity value of the input image. The new intensity is
assigned to each pixel according to an adaptive transfer function that is
designed on the basis of the statistics of the input images. The details of this
algorithm are given below.
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First assumed that the input image is I, the output image is X and
the size is as same as the size of input image the intensity range of the input
image is defined as ‘Range’ which can be calculated as (3.1).
Range = Imax − Imin (3.1)
where Imax and Imin are the maximum and minimum intensity values of the
input image. The new intensity is assigned to each pixel according to equation
(3.2) ie.,
min
max
,
,
,
k k k
k k k k
k
I if I I
X I if I I
f else
σ
σ
− =��
= + =���
(3.2)
where, min
min
max min
kk I I
k
rf I
I I
−= +
−, (3.3)
kσ is the standard deviation of the input image.
and ( )2
kr w range w= − − (3.4)
‘w’ lies between 0.01 to 0.02. (Guodong Zhang et al 2008)
Using the above formulae, each pixel value is replaced. By this
way, the image noise can be suppressed while enhancing image features.
3.3.2 Histogram Segmentation
After completion of stretching process, the stretched histogram is
segmented based on its mean or median values.
If the input histogram is splitted into two or more sub histograms
recursively based on the mean, then it is called as CSRSHE-A. If the
36
histogram is splitted into two or more sub histograms recursively based on the
median of the image, this is called as CSRSHE-B.
3.3.3 Histogram Equalization Module
The task of the histogram equalization module is to separately
equalize each sub histograms. ie., The output image of the histogram
equalization, Y = {Y(i, j)}, can be expressed as
Y = f(X)
= {f (X(i, j) | ( , ) }X i j X∀ ∈ (3.5)
where
Transform function 0 1 0
( ) ( ) ( )L
f x X X X c x−
= + − (3.6)
The cumulative density function 0
( ) ( )k
jj
c x p X=
�= (3.7)
p(Xj) is associated with the histogram of the input image which represents the
number of pixels which have a specific intensity Xk and is given by
( ) k
k
np X
n= (3.8)
where Xk = x, for k = 0, 1, …, L – 1 ;
nk represents the number of times that the level Xk appears in the
input image X and ‘n’ is the total number of samples in the input image. In
fact, a plot of nk Vs Xk is known as histogram of X.
The high performance of the histogram equalization in enhancing
the contrast of an image as a consequence of the dynamic range expansion
besides, histogram equalization also flattens a histogram. Based on
information theory, entropy of message source will get the maximum value
37
when the message has uniform distribution property. The combination of all
resultant sub images now becomes the final output image.
3.4 RESULTS AND DISCUSSION
The performance of the proposed CSRSHE method was tested on
numerous images. The images like Einstein, girl, House, couple, copter, F16,
and jet are taken from data base (http://decsai.ugr.es/cvg/dbimagenes/) and
CT chest, CT brain, CT abdomen, MRI brain, MRI heart and MRI spine
images were obtained from Kanyakumari Government medical college,
Asaripallam, TamilNadu, India with the help of Dr.J.Ravindran. In this work
the sampling images of size 256x256 pixels namely CT chest, CT brain, CT
abdomen, MRI brain, MRI heart and MRI spine are selected to evaluate the
capability of the proposed methods. The proposed method was implemented
using VHDL coding and the performance analysis was done by MATLAB
coding. The proposed CSRSHE method was qualitatively and quantitatively
analyzed.
3.4.1 Qualitative Analysis
The qualitative analysis involves performance comparison with
existing brightness preserving methods, namely HE, BBHE, DSIHE,
RMSHE, RSIHE, CSRSHE-A and CSRSHE-B. Figures 3.1 to 3.6 shows, for
the CT chest, CT abdomen, CT brain, MRI brain, MRI heart and MRI spine
image, the output images produced by these histogram equalization methods
respectively.
38
(a) Original (e) RMSHE
(b) HE (f) RSIHE
(c) BBHE (g) CSRSHE-
(d) DSIHE (h) CSRSHE-B
Figure 3.1 Results for CT Chest image
39
(a) Original (e) RMSHE
(b) HE (f) RSIHE
(c) BBHE (g) CSRSHE-A
(d) DSIHE (h) CSRSHE-B
Figure 3.2 Results for CT abdomen image
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(a) Original (e)RMSHE
(b) HE (f) RSIHE
(c) BBHE (g) CSRSHE-A
(d) DSIHE (h) CSRSHE-B
Figure 3.3 Results for CT Brain image
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(a) Original (e) RMSHE
(b) HE (f) RSIHE
(c) BBHE (g)CSRSHE-A
(d) DSIHE (h) CSRSHE-B
Figure 3.4 Results for MRI Brain image
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(a) Original (e) RMSHE
(b) HE (f) RSIHE
(c) BBHE (g)CSRSHE-A
(d) DSIHE (h) CSRSHE-B
Figure 3.5 Results for MRI Heart image
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(a) Original (e) RMSHE
(b) HE (f) RSIHE
(c) BBHE (g) CSRSHE-A
(d) DSIHE (h) CSRSHE-B
Figure 3.6 Results for MRI Spine image
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Figures 3.1(b) to (h), 3.2(b) to (h), 3.3 (b) to (h), 3.4(b) to (h),
3.5(b) to (h) and 3.6(b) to (h), show the output images produced by existing
Histogram equalization methods (HE, BBHE, DSIHE, RMSHE RSIHE) and
proposed methods (CSRSHE-A and CSRSHE-B) for CT chest, CT abdomen,
CT brain, MRI brain, MRI heart and MRI spine image . Based on figures
3.1(b), 3.2 (b), 3.3(b), 3.4(b), 3.5(b) and 3.6(b), it is clear that the histogram
equalization method enhances the images but it produces some blocking
artifacts in the images. Hence this effects are reduced in the figures 3.1(c) to
(f), 3.2 (c) to (f), 3.3 (c) to (f), 3.4 (c) to (f), 3.5 (c) to (f) and 3.6(c) to (f).
Even these methods improve the contrast of the image when the ‘r’ value is
increased highly means the output which will be same as the input results un
enhancement of image. From figures 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6 (g and h),
CSRSHE-A & CSRSHE-B methods are produced acceptable and natural
enhanced images compared to other existing methods. The related samples
are detailed in Appendix 1.
3.4.2 Quantitative Analysis
The performance measures of proposed CSRSHE methods and
different histogram equalization based techniques are calculated and tabulated
in tables 3.1 to 3.3.
Three different Performance metrics chosen here is absolute mean
brightness error (AMBE), Standard deviation (STD) and Peak signal to noise
ratio (PSNR).
3.4.2.1 Absolute Mean Brightness Error (AMBE)
In order to investigate whether the proposed method successfully
maintains the input mean brightness, the absolute mean brightness error
(AMBE) has been used. This is defined as
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AMBE = { Xm-Ym) (3.9)
where, Xm = Mean of the input image
Ym = Mean of the output image
Table 3.1 Absolute Mean Brightness Error (AMBE)
Images HE BBHE DSIHE MMBEBHE RMSHE
(r=2) CSRSHE-A CSRSHE-B
Einstein 17.17 19.27 12.07 14.27 10.17 2.14 3.08
girl 5.29 23.51 4.46 3.04 0.45 0.05 1.4
House 58.81 25.09 31.92 25.06 8.07 2.68 3.91
couple 96.42 33.17 43.81 18.45 10.28 1.95 2.65
copter 62.72 17.21 26.91 32.14 3.08 0.24 2.07
F16 49.72 1.09 13.5 15.31 1.24 2.52 0.19
jet 71.76 4.91 26.84 2.07 0.64 0.29 0.31
CT chest 53.19 24.05 19.23 16.71 4.19 0.71 2.08
CT Brain 62.08 34.21 29.71 19.31 5.84 1.73 3.65
CT
abdomen 59.34 24.73 31.35 13.08 3.71 1.05 2.56
MRI
brain 47.17 28.63 29.53 18.91 7.73 2.58 3.79
MRI
heart 51.26 24.82 21.83 16.52 6.49 1.95 2.73
MRI
spine 58.63 27.89 17.53 17.21 5.24 1.68 2.52
Average 53.35 22.19 23.74 16.31 5.16 1.50 2.38
The minimum value of AMBE results that the mean brightness of
the input is successfully maintained in the output image. Table 3.1 and Figure
3.7 shows the AMBE measure obtained for the sample images.
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Figure 3.7 Comparison of AMBE values for different enhancement
methods
The AMBE values calculated for the existing methods (HE, BBHE,
DSIHE, MMBEBHE and RMSHE) by Mary Kim et al (2008) are compared
with the AMBE value of proposed CSRSHE methods. For all sample images,
the AMBE values of proposed CSRSHE method are less compared with the
existing methods and hence the brightness preservation is more for proposed
CSRSHE method. In average, CSRSHE-A has 71.3 % less value and
CSRSHE-B has 54.1 % less value compared with the RMSHE method which
has least AMBE value among all existing methods.
3.4.2.2 Standard Deviation (STD)
By measuring the standard deviation, the contrast of the image can
be studied.
Standard Deviation is given by
( )1
0
( )L
l
l p lσ µ−
=
�= − × (3.10)
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Where Mean, 1
0
( )L
l
l p lµ−
=
�= × (3.11)
‘l’ represents the pixel value in the image.
Table 3.2 Standard Deviation (STD)
Images HE BBHE DSIHE MMBEBHE RMSHE
(r=2) CSRSHE-A CSRSHE-B
Einstein 73.59 73.81 73.94 62.31 57.95 39.28 43.65
girl 75.41 70.12 75.49 68.73 37.85 29.34 32.78
House 73.65 75.13 75.51 55.43 56.79 42.65 51.2
couple 71.86 74.15 79.61 48.41 53.29 35.38 39.17
copter 73.17 72.73 76.72 52.59 52.07 46.51 49.23
F16 74.56 67.61 77.41 68.71 61.05 43.27 50.13
jet 74.32 64.72 78.31 54.31 56.74 31.27 40.25
CT chest 85.12 74.19 81.29 56.23 49.16 35.19 42.35
CT brain 80.24 70.27 76.34 62.16 57.34 39.54 48.97
CT
abdomen 82.34 76.35 79.56 69.13 50.37 32.19 39.37
MRI
brain 85.29 79.16 76.54 64.15 52.39 35.71 37.93
MRI
heart 81.64 74.37 69.28 61.75 49.37 32.48 34.18
MRI
spine 83.15 76.34 71.37 63.69 51.64 33.59 35.34
Average 78.02 72.99 76.25 60.58 52.77 36.64 41.88
From the Table 3.2 and Figure 3.8, the standard deviation value
obtained for the proposed CSRSHE methods is less compared to all the
existing enhancement methods for all the images. The STD values calculated
for the existing methods (HE, BBHE, DSIHE, MMBEBHE and RMSHE) by
David et al (2007) are compared with the STD value of proposed CSRSHE
methods. For all sample images, the CSRSHE method has less STD value
compared with the existing methods and hence the contrast of the image is
improved. In average CSRSHE-A has 29.6 % less value and CSRSHE-B has
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17.9 % less value compared with the RMSHE method which has least STD
value among all existing methods.
Figure 3.8 Comparison of STD values for different enhancement methods
3.4.2.3 PSNR
Based on mean squared errors (MSE), PSNR is defined as
PSNR = 10 log10 (L-1)2 / MSE (3.12)
Where ( ) ( )
2
, ,i j
X i j Y i j
MSEN
�� −
= (3.13)
X(i,j) and Y(i,j) are the input and output images respectively.
‘N’ is the total number of pixels in the input or output images
‘L’ is the number of intensity values.
The PSNR values of various enhancement methods for different
images are tabulated in table 3.3 and given in Figure 3.9.
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Table 3.3 Peak Signal to Noise Ratio (PSNR)
Images HE BBHE DSIHE MMBEBHE RMSHE
(r=2) CSRSHE-A CSRSHE-B
Einstein 15.27 15.19 15.53 18.97 19.52 31.47 29.63
girl 13.05 13.3 13.04 14.25 27.98 35.34 32.19
House 10.81 14.26 13.92 21.45 21.32 29.65 28.95
couple 7.56 13.16 11.64 19.56 19.64 39.25 32.73
copter 10.62 15.96 14.25 25.43 25.67 33.38 29.67
F16 11.94 20.67 16.05 20.37 22.78 40.31 35.13
jet 9.52 22.53 14.38 30.72 27.82 29.37 23.71
CT chest 14.35 19.53 15.37 29.73 33.46 35.19 26.82
CT brain 17.35 24.61 19.73 25.37 34.61 39.45 35.46
CT
abdomen 16.54 23.25 18.16 23.45 31.23 35.64 33.17
MRI
brain 18.25 25.37 20.61 24.35 30.27 36.29 33.28
MRI heart 21.37 27.56 23.97 27.15 33.19 39.37 36.34
MRI
spine 19.95 26.31 21.22 25.94 31.29 37.19 35.21
Average 14.35 20.13 16.75 23.59 27.59 35.53 31.71
Figure 3.9 Comparison of PSNR values for different enhancement
methods
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From Table 3.3 and Figure 3.9, the PSNR values of proposed
methods CSRSHE-A and CSRSHE-B are ranked the first and second highest
values respectively.
From this table, it can be observed that the images processed by
proposed CSRSHE methods produce the best PSNR values as they are within
the range [28 dB to 40 dB] whereas the existing RMSHE method (David et al
2007) has the range [20 dB to 35 dB]. From these values it can be concluded
that the proposed method performs better image contrast enhancement
compared to the existing methods.
3.5 CONCLUSION
In this chapter, a modified histogram equalization method named as
CSRSHE (Contrast Stretching Recursively Separated Histogram
Equalization) was proposed. In fact, CSRSHE is designed to achieve two
goals: Preserve the image brightness and enhance the image contrast as well.
CSRSHE consists of three modules: Contrast stretching module, Histogram
segmentation module and Histogram equalization module. The contrast
stretching module performs histogram equalization based on a local modified
contrast-stretching manipulation and replaces each original intensity value.
The new intensity is assigned to each pixel according to an adaptive transfer
function that is designed on the basis of the statistics of the input images. The
histogram segmentation module split the histogram into two or more sub
histograms recursively based on the mean (CSRSHE-A) or median
(CSRSHE-B). Lastly histogram equalization module equalizes the sub
histogram independently.
The measured AMBE, STD, and PSNR values show that CSRSHE
preserves the image brightness more accurately than other existing histogram
equalization based methods and produces images with better contrast
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enhancement. Specifically, as CSRSHE-A has highest PSNR value, lowest
STD and AMBE value, it can be concluded that CSRSHE-A is the best
method for brightness preservation and contrast enhancement and CSRSHE-B
is the second best method.
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