An analysis of Histogram equalization method for...

1 Gourav Garg, Poonam Sharma

International Journal of Innovations & Advancement in Computer Science

IJIACS

ISSN 2347 – 8616

Volume 3, Issue 4

July 2014

An analysis of Histogram equalization method for Brightness

Preserving and Contrast Enhancement

Gourav Garg1 , Poonam Sharma2 Department of C.S.E. & I.T

Madhav Institute of Technology and Science

Gwalior, India

ABSTRACT: The contrast of an image is a feature which determines how image looks better

visually. The Contrast enhancement is considered as one of the most important issues in image

processing. Histogram equalization (HE) is one of the common methods used for improving contrast

in digital images. This technique is usually used for image enhancement because of its simplicity,

practical and comparatively better performance on almost all types of images. One drawback of HE

can be found that it is tends to introduce some annoying artifacts and unnecessary enhancement. In

this paper some brightness preserving techniques are used as a result overcome drawbacks of HE.

For performance assessment we have used Peak Signal to Noise Ratio (PSNR), absolute mean

brightness error (AMBE), and entropy. From experimental result, it is observed that NMSE and

BPDFHE have better image enhancement capability.

Keywords: Contrast enhancement, HE, BBHE, NMHE, BPDFHE

1. INTRODUCTION:

Image enhancement is a process in which changed the pixels’ intensity of the input image;

make the output image looks better. The aim of image enhancement is to recover the interpretability or perception of information

contained in the image for human viewers, or to deliver a “better” output for other automated

image processing systems. Many image enhancement techniques have been proposed such as aim, out of which histogram

equalization (HE) is one of technique for image enhancement. This technique is commonly

working for image enhancement because of its simplicity and comparatively. Histogram equalization achieves a uniform distributed

histogram by using the Cumulative density functions of the input image. Contrast

enhancement plays an important role in image processing applications, such as medical image processing, digital photography, satellite

imaging, and LCD display processing.

Normally, histogram equalization can be

categorized into two main processes: global

histogram equalization (GHE) and local

histogram equalization (LHE). In GHE, the

histogram of the whole input image is used to

calculate a histogram transformation function.

As a result, the dynamic range of the image

histogram is compressed and stretched, by

which the overall contrast is improved [1]. The

computational complexity of GHE is

comparatively low. The major drawbacks of

GHE are that it cannot adjust the local

information of the image and preserve the

brightness of the original image. Where LHE

uses a sliding window method, in this local

histograms are calculated from the windowed

neighbourhood to produce a local intensities

remapping for each pixel. The intensity of the

pixel at the centre of the neighbourhood is



IJIACS

ISSN 2347 – 8616

Volume 3, Issue 4

July 2014

improved according to the local intensity

remapping for that pixel. LHE is capable of

producing good contrast results but is

sometimes held to over-enhance images. It also

requires more computation than other methods

because a local histogram must be made and

deal with for every image pixel. Some extension

methods of GHE have been developed for

preserving brightness: Contrast-Limited

Adaptive Histogram Equalization(CLAHE) [2],

brightness preserving bi-histogram equalization

(BBHE) [3], dualistic sub- image histogram

equalization (DSIHE) [4], minimum mean

brightness error bi-histogram equalization

(MMBEBHE) [5], recursive mean separate

histogram equalization (RMSHE) [6], recursive

sub- image histogram equalization (RSIHE) [7],

Recursively Separated and Weighted Histogram

Equalization for Brightness Preservation and

Contrast Enhancement(RSWHE)[8].Non-

parametric modified histogram equalisation for

contrast enhancement (NMHE) [9], Brightness

Preserving Dynamic Fuzzy Histogram

Equalization [10].

Rest of the paper is organized as follows:

Section 2 presents Histogram equalization (HE).

In section 3, various HE techniques are

reviewed. Section 4 presents experimental

analysis of various HE Approaches. Section 5

concludes the paper.

2. Histogram equalization (HE):

Histogram equalization technique is commonly

working for image enhancement because of its

practical and comparatively better performance

on almost all types of images [1]. Histogram

equalization achieves a uniform distributed

histogram by using the Cumulative density

functions of the input image.

For a given image X, the probability density

function p ( ) is defined as:

(1)

Where is no. of times that the level

appears in input image X and n is total no. of

pixel in the image.

Its cumulative distribution function (CDF) is

defined as:

(2)

Where k=O, 1…L-1, and it is obvious

that . Let define transform function

f(x) by using the cumulative density function

(CDF), graphical representation of histogram

equalization plots an input gray level into an

output gray level f( ). Where f( ) is

commonly called a level transformation

function, which is defined as:

(3)

3. Some techniques of histogram

equalization:

3.1. Contrast limited adaptive histogram

equalization (CLAHE)

S.M. Pizer et al. (1990) has proposed Contrast

Limited Adaptive Histogram Equalization

(CLAHE) [2]. This method is depend on local

histogram equalization (LHE) such that CLAHE

operates on small regions in the image, is

known as tiles, rather than the entire image.

Each tile contrast is enhanced, to match the

histogram of the output region approximately

with the histogram specified by the distribution

parameter. Then combined the neighboring tiles

using bilinear interpolation to eliminate

artificially induced boundaries.

CLAHE ALGORITHM:

Step 1: Obtain all the inputs Image: In this step

find out the Number of regions in row and

column directions, Number of bins of the

histograms used in building image transform



IJIACS

ISSN 2347 – 8616

Volume 3, Issue 4

July 2014

function. Clip histogram is normalized from 0

to 1.

Step2: Pre-process the inputs: pad the image

before splitting it into regions. Normalize value

is determine the real clip limit.

Step3: Determine gray level value by process of

each contextual region (tile): Firstly citation a

single image region and determine histogram of

it by using the specified number of bins, after

that clip the histogram using clip limit, finally

create a transformation function for this region.

Step4: Interpolate gray level mappings in order

to assemble final CLAHE image: Extract cluster

of four neighboring mapping functions, process

image region partly overlapping each of the

mapping tiles, extract a single pixel, apply four

mappings to that pixel, and interpolate between

the results to obtain the output pixel; repeat over

the entire image.

3.2. Preserving Bi-Histogram Equalization

(BBHE) YEONG TAEG KIM [3] (1996) has

proposed Preserving Bi-Histogram Equalization

(BBHE) [3]. Histogram equalization (HE) is a

method of image enhancement has one

drawback; intensity value of an image can be

changed after the HE. This method divides the

image histogram into two parts as shown in

Figure 1. In this method, the separation

intensity is used for separation of

histogram. The intensity value ( ) is

calculated by the mean brightness of input

image. And then these two histograms are

independently equalized. The mean brightness

of the resultant image will lie between the

input mean and the middle gray level.

The histogram with range from 0 to L-1 is

divided into two parts with separating intensity

( ). This separation produces two histograms.

The first histogram has the range of 0 to

while the second histogram has the range of

to L-1.

Figure 1.bi-histogram equalization

The BBHE algorithm is given below: 1. Input the image, F (i, j) with a total number of ‘n’ pixels in the gray level range [ ].

2. Make the histogram of image.

3. Segment F (i, j) into lower sub- images and upper sub-image based on

its mean ‘ ’. 4. Equalize each partition independently using

PDF and CDF.

3.3. Dualistic sub image histogram

qualization (DSIHE)

YU WANG et al. (1999) has proposed Dualistic

sub image histogram equalization (DSIHE) [4],

one drawback of histogram equalization (HE) is

discuss the above (BBHE), intensity value of an

image may be changed suddenly it never be

utilized in video system in past. Following the

same basic ideas used by the BBHE method of

decomposing the original image into two sub-

images and then equalizes the histograms of the

sub- images separately. Dualistic sub- image HE

(DSIHE) method is used median value of image

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. For such aim, the input image is

decomposed into two sub- images, being one

dark and one bright.

The DSIHE algorithm is given below:

1. Input the image, F (i, j) with a total number

of ‘n’ pixels in the gray level range [ ].



IJIACS

ISSN 2347 – 8616

Volume 3, Issue 4

July 2014

2. Make the histogram of image.

3. Segment F (i, j) into lower sub- images

and upper sub-image based on

its median ‘ ’.

4. Equalize each partition independently using

PDF and CDF.

3.4. Minimum mean brightness error Bi -

histogram equalization (MMBEBHE)

CHEN & RAMLI (2003) has proposed

Minimum mean brightness error bi-histogram

equalization (MMBEBHE) method [5]. BBHE

and DSIHE could preserve the mean brightness

but these are not preserving optimally. To avoid

annoying artifacts, these images require higher

degree of brightness preservation. The main

difference between MMBEBHE and other is

that the minimum absolute mean brightness

error (AMBE) between the input image and the

output image is select as threshold. The ultimate

goal of the MMBEBHE is to allow maximum

level of brightness preservation in Bi-

Histogram Equalization and it avoids unpleasant

artifacts and unnatural enhancement due to

excessive equalization.

3.5. Recursive Mean-Separate Histogram

Equalization (RMSHE)

Chen and Ramli ( 2003) has proposed Recursive

Mean-Separate Histogram Equalization

(RMSHE)[6].This method is not only better but

also scable brightness preserving before

equalizing them independently, BBHE separates

the input image's histogram into two by using

mean histogram. However, an extended version

of the BBHE method named recursive mean

separate HE (RMSHE) proposes. In the BBHE

decomposing the image only once, the RMSHE

method proposes to perform image

decomposition recursively. Note that the

RMSHE method is equivalent to the CHE when

r = 0 (no sub- images are generated) and is

equivalent BBHE methods when r = 1 as shown

in Figure 2(a) and 2(b). The mathematically

showed that the brightness of the output image

is better preserved as r increases.

3.6 Non-parametric modified histogram

equalization for contrast enhancement

S. Poddar et al. (2013) has proposed Non-

parametric modified histogram equalization for

contrast enhancement [9].The proposed non-

parametric modified HE (NMHE)

Figure 2(a) RMSHE r=1 and Figure 2(b)

RMSHE r=2

Enhancement method performs HE on a

modified histogram which is explained in this

section. Let us consider an input image I, with

dynamic range [0-255], where I(i, j)∈[0, 255].

Step1: Compute histogram ( ) for input image

In order to proceed with NMHE, first read

image in data base and then calculate its

histogram.

Step2: Compute clipped histogram ( )

Consider the original histogram (hi) of any

generic image as shown in Figure 3(a). This

histogram is normalized and clipped to a value

of (1/L) as shown in Figure 3(b) defined by (4).

It is then subtracted from a perfectly uniform



IJIACS

ISSN 2347 – 8616

Volume 3, Issue 4

July 2014

probability density function (u) which is given

as

u=ones (L, 1)/L (4)

Figure 3(a). Histogram of image,

3(b).Clipped histogram at maximum level

of (1/L), where L is total no of gray level

Clipped histogram obtained from is given as

(K)=

(5)

if

Step3: Find ( ) using uniform histogram (u)

and clipped histogram ( )

Measure of un-equalization (Mu) is now

calculated by the following equation

(6)

Step 4: Calculate spike free histogram ( )

First the spikes are removed from the original

histogram. To compute the modified histogram

(hmod), Arici et al. proposed a method in which

they consider only those pixels which have

dissimilarity with their neighbour’s thus

removing spike from the histogram.

(i)=p[i|C] (7)

Where p[i|C] is the probability of occurrence of

grey- level given the event C, where C

denotes a horizontal contrast variation. C has

been assigned a default value of six empirically

and works fine with all sorts of image. The

modified histogram is then normalized by the

total no. of pixels considered in the above

process to keep the value in between ‘0’ and

‘1’.

Step 5: Use to obtain modified histogram

A unique parameter is calculated, which is used

in (8) to weight the uniform distribution and the

modified histogram ( ). This factor is

defined as measure of un-equalization (Mu) and

is calculated from the original histogram (hi) as

follows

+ (1-w) u (8)

The optimization function for a weighted

histogram is given by

(9)

Where W (i.j) is an average local variance of

pixels with the gray level I

Step6: Obtain modified HE image ( )

The output image produced NMHE

can be

expressed as

∈

(10)

Step7: using the altered histogram

This value of Mu indicates the degree to which

the histogram of any given image does not

follow a uniform distribution. It is then used as

weighing factor in (6) to obtain the modified

PDF given as

(11)

The CDF of the image is then obtained from

the eventually redesigned histogram ( ) as

(12)

The transformation function ( ) obtained by

using is given by

(13)



IJIACS

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July 2014

3.7. Brightness preserving dynamic fuzzy

histogram equalization

S. Sheet et al.(2010) has proposed brightness

preserving dynamic fuzzy histogram

equalization[10].The BPDFHE technique

operates the image histogram in such a way that

distribution of gray value in histogram is

equalize. It clearly depicts that no remapping of

the histogram peaks takes place, while only

redistribution of the gray-level values in the

valley portions between two consecutive peaks

takes place. The BPDFHE technique consists of

following operational stages:

Step1. Fuzzy Histogram Computation

Fuzzy histogram is a sequence of real numbers

h(i),I ∈

Where h(i) is the frequency of occurrence of

gray levels that are “around i”. By considering

the gray value I(x, y) as fuzzy number

the fuzzy histogram is computed as:

∈ (14)

Where is the triangular fuzzy

membership function defined as

(15)

And [a, b] is the support of the membership

function

Step2. Partitioning of the Histogram

The local maxima based partitioning of the

histogram, to obtain multiple sub-histograms, is

performed in this step. This way every valley

portion between two consecutive local maxima

forms a partition. When the dynamic

equalization of these partitions is performed, the

peaks of the histogram do not get remapped and

this results in better preservation of the mean

image-brightness while increasing the contrast.

(1)Detection of Local Maxima: The local

maxima in the Fuzzy Histogram are defined

using the first and second Derivative of the

Fuzzy histogram. Since the histogram is a

discrete data sequence, we use the central

difference operator for approximating a discrete

derivative

(2) Creating Partitions: The local maxima points

in the fuzzy histogram can now be used to form

the partitions. Let (n+1) intensity level

correspond to the local maxima, detected in the

previous stage of operation, i.e denoted by

{ }.Assume the original fuzzy

histogram is spread in the range of [ ],

then the (n+1) sub-histograms obtained after

partitioning are {[ ], [

],….[ ]}.

Step3. Dynamic Histogram Equalization of the

Partitions: The DHE [5] technique is used to

equalize the sub-histogram. This method uses a

spanning function based on total number of

pixels in the partition to perform equalization. It

involves two stages of operation, namely,

mapping partitions to a dynamic range and

histogram equalization.

Step4. Normalization of the image brightness

The image obtained from the dynamic

histogram equalization of each sub histogram

has the mean brightness that is slightly different

from the input image. To eliminate this

difference the normalization process is applied

on the output image. Let and be the

mean brightness levels of the input image and

the image (f) obtained after dynamic histogram

equalization stage. If g is the output image of

BPDFHE technique then the gray level value at

the pixel location (x, y) for the image g is given

as

(16)



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Volume 3, Issue 4

July 2014

This brightness preserving procedure ensures

that the mean intensity of the image obtained

after process is the same as the input.

4. Experiment Result:

Visual results have been displayed and

quantitative comparison has been done on the

basis of peak signal-to-noise ratio (PSNR),

Absolute mean brightness error (AMBE) and

Entropy.

4.1Peak signal to noise ratio (PSNR)

The value of PSNR is shows the ratio between

output image and input image, According to

definition of PSNR the output image quality is

better if that image has maximum PSNR.

Assume that N is the total number of pixels in

the input or output image, MSE (Mean Squared

Error) is calculated through (17). By the help of

MSE, we calculated value of PSNR. This is

defined by equation (18).

(17)

(18)

4.2. Absolute mean brightness error (AMBE)

The value of AMBE is shows the mean

brightness error between input image and output

image. If the value of AMBE is decreasing then

quality of image is decrease. Suppose is the

mean of the input image X = { } and is

the mean of the output image Y = { }. Then

AMBE is calculated by (19)

AMBE(X, Y) = | - | (19)

4.3. Entropy

The entropy is a valuable tool to measure of randomness that can be used to characterize the texture of i/p image. For a given PDF p, entropy

Ent[p] is computed by (20).

(20)

So AMBE is used to assess the degree of brightness preservation, while both PSNR and

entropy are employed to quantitatively assess the degree of contrast enhancement.

Figure 4: PSNR bar graph of image

enhancement of various techniques

Figure 5: AMBE bar graph of image

enhancement of various techniques

http://edutwin.com/s/absolute-mean-brightness-error-ambe-matlab-code

http://edutwin.com/s/absolute-mean-brightness-error-ambe-matlab-code



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Volume 3, Issue 4

July 2014

Figure 6: Entropy bar graph of image enhancement of various technique

Table 1: PSNR of various images

IMAGE HE CLAHE BBHE DSIHE BPDFHE NMHE

LENA 19.1347 18.8714 19.2751 19.3903 32.8156 26.0387

EINSTEIN 15.2397 17.8643 15.9589 16.2079 27.8884 21.3150

PEPPERS 20.5420 19.1508 20.9146 20.9014 36.9956 32.0912

HOUSE 17.6060 22.0949 17.3144 17.5636 28.2461 23.6592

Table 2: AMBE of various images


LENA 3.4437 7.1813 7.4376 4.3187 0.0297 11.5382

EINSTEIN 24.5969 17.8643 17.1839 14.1017 0.0217 11.8252

PEPPERS 4.4654 8.0643 2.2191 2.1136 0.0135 4.0654

HOUSE 10.6310 7.6559 13.1068 9.5043 0.0667 4.7692

Table 3: Entropy of various images


LENA 5.9690 7.8669 7.3478 7.3481 0.0058 7.2584

EINSTEIN 5.9664 7.7637 6.92 6.9141 0.0091 7.0311

PEPPERS 5.9778 7.8828 7.3554 7.3706 0.0 7.4060

HOUSE 5.4584 7.4624 6.25 6.2406 0.0072 6.1857



IJIACS

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Volume 3, Issue 4

July 2014

Table 1 contain the PSNR of various test images

after being enhanced by HE, CLAHE, BBHE,

DSIHE, BPDFHE and NMHE. After analysis of

table 1 we can show that the PSNR value of

BPDFHE is higher than other method, the

graphical representation of Table 1 is shown in

Figure 4. Table 2 represent various techniques

on the same image in term of AMBE. For all the

images value of BPDFHE is less than other

method in Table 2. The graphical represent of

Table 2 is shown in Figure 5. And same result

are shown in Table 3, entropy of the BPDFHE is

less than other method. The graphical represent

of Table 3 is shown in Figure 6.

Original

Image

1(a)

1(b)

1(c)

1(d)

HE

2(a)

2(b)

2(c)

2(d)

CLAHE

3(a)

3(b)

3(c)

3(d)

BBHE

4(a)

4(b)

4(c)

4(d)

DSIHE

5(a)

5(b)

5(c)

5(d)



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Volume 3, Issue 4

July 2014

BPDFHE

6(a)

6(b)

6(c)

6(d)

NMHE

7(a)

7(b)

7(c)

7(d)

Fig. 5: 1(a-d) represent original test images of Lena, Einstein, peppers and house respectively , 2(a-d)

represent enhance by HE, 3(a-d) represent enhance by CLAHE, 4(a-d) represent enhance by BBHE,

5(a-d) represent enhance by DSIHE, 6(a-d) represent enhance by BPDFHE , 7(a-d) represent

enhance by NMHE

It is analysis from the visual comparison that

BBHE exhibits better performance than HE due

to its partition-based enhancement. On the basic

of above result BPDFHE is best visual

performance compare than BBHE, DSIHE and

NMHE. For the AMBE quantitative test,

obviously the HE, BBHE and DSIHE methods

fail to preserve the original mean brightness.

Further these three methods tend to produce

intensity saturation and information loss.

Minimum AMBE is so that degree of brightness

preservation of BPDFHE, while both PSNR and

entropy of BPDFHE are employed to

quantitatively assess the degree of contrast

enhancement. The comparative study of

Histogram Equalization based methods shows

that the cases which require higher brightness

preservation and are not handled well by HE,

BBHE, DSIHE and NMHE have been properly

enhanced by BPDFHE, which are the extension

of HE method that provides maximal brightness

preservation. Though these methods can perform

good contrast enhancement hence it is observed

that NMHE and BPDFHE are better method for

enhancing the contrast and brightness

preserving.

5. Conclusion:

Histogram equalization (HE) is unable to

handle mean shift problem which is resolved

by BBHE and DSIHE. NMHE and BPDFHE

show better result visually. PSNR value of

NMHE and BPDFHE is better in comparison

to BBHE and DSIHE. BPDFHE outperforms

other methods on the basis of AMBE. NMHE

and BPDFHE achieve the best quality through

qualitative visual inspection and quantitative

accuracies of Peak Signal-to- Noise Ratio

(PSNR) and Absolute Mean Brightness Error

(AMBE) compared to other state-of-the-art

method.

References:

[1]. Rafael C. Gonzalez, and Richard E.

Woods “Digital Image Processing” Third

Edition Prentice Hall.

[2]. S.M. Pizer, R. E. Johnston, “Contrast-

Limited Adaptive Histogram Equalization:



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July 2014

Speed and Effectiveness”, IEEE Transactions

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[3]. yeong-Theg –kim,”contrast enhancement

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[4].Yu wang, quin chen Baomin zhang.

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[5]. S. Chen and A. R. Ramli, “Minimum

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[6]. S. D. Chen, and A. R. Ramli, “Contrast

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[7] K. S. Sim, C. P. Tso, and Y. Y. Tan,

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[8] M. Kim, and M. G. Chung, “Recursively

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[9] S.Poddar, S.Tewary, “Non-parametric

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