29

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

30

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.

31

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

32

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.

33

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

34

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.

35

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

40

(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

41

(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

42

(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

43

(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

44

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

45

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.

46

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)

47

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

48

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

50

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

51

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.