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COMPARISON AND ANALYSIS OF VARIOUS HISTOGRAM EQUALIZATION TECHNIQUES

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COMPARISON AND ANALYSIS OF

VARIOUS HISTOGRAM

EQUALIZATION TECHNIQUES

RUBINA KHAN*

Flat 7 Parijat Complex,158 Railway lines, Solapur,Maharashtra,India

rubynak@gm MADKI.M.R W.I.T,Ashok Chowk, Solapur, ,Maharashtra,India

mrrmadki@yahoo.com

Abstract— The intensity histogram gives information which can be used for contrast enhancement. The histogram equalization could be flat for levels less than the total number of levels. This could deteriorate the image. This problem can be overcome various techniques. This paper gives a comparative of the Bi-Histogram Equalization, Recursive Mean Seperated Histogram Equalization, Multipeak Histogram Equalization and Brightness Preserving Dynamic Histogram Equalization techniques by using these techniques to test few standard images. The method of bi-histogram uses independent histogram over two separate subimages. The method of recursive uses several subimages. Multipeak Histogram Equalization detects the peaks in the histogram and the subimages are formed based on the number detected. The Brightness Preserving Dynamic Histogram Equalization improves contrast while it maintains the brightness of the image. We shall compare the results through the metric parameters of absolute mean Brightness error and peak signal to noise ratio.

Index Terms— Bi-Histogram Equalization ,Multipeak Histogram Equalization,Metric Parameters,Recursive Histogram Equalization, subimages .

I. INTRODUCTION

The information extracted from image intensity histograms play a role in image processing areas such as enhancement, compression, and segmentation. The image enhancement involves changing the pixel’s intensity so that the final image looks better. A commonly used technique for enhancement is the histogram equalization (HE). The result of equalization is an image with increased dynamic range which will have a higher contrast.

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k

L L j

j

C x

p x

=

=

And;

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k

U U j

j m

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p

x

= +

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The following transform functions

0 0

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(

(

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L m L

f x

=

X

+

X

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1 1 1

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Equalize the two subimages over the two ranges X0…. Xm, and Xm+1 …. XL-1. Thus the entire range is covered.

In order to qualitatively see the effects of equalization the following test image was applied . The input image used for the various techniques and the corresponding histogram is

graph1 1

Fig1

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fig2 graph2

There can be seen a improvement in the mean brightness of the equalized image. The profile is more pronounced..

3. THE RECURSIVE MEAN SEPARATED HISTOGRAM TECHNIQUE AND ITS ANALYSIS

The recursive technique decomposes histogram using the mean value or the median.. The RMSHE, divides the input histogram H(X) recursively up to some specified recursion level r, thus generating 2r sub-histograms. It produces two segments based on the mean value .Consider one of the segmented histogram Ht(X) defined over gray level range [Xl, Xu] . The mean XM1. the sub-histogram Ht(X) is computed by using

XtM =

. ( ) /

( )

u u

k

k p K

k

p K

.

Based on the computed mean XtM , the histogram Ht(X) is then divided into two sub-histograms Ht+1 L(X)

and Ht+1 U(X) for the next recursion level t+1, where Ht+1 L(X) and Ht+1 U(X) are the two subsections of the segmented histogram. According to the specified recursion level r, the histogram generates subhistograms .Hence when r=2 we have four subsections of the histogram .Each subsection is normalized .as the probability density function gives a sum greater than one.The normalized subsections are then equalized. The equalized four subsections are then combined together to give the equalized image. The fig3 below shows the equalized image where the recursive level chosen is two.

In case of RMSHE we can see that the brightness of the equalized image is nearly similar to tha of the input image and at the same time there is an improvement in the contrast of the image.

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Fig4 graph4

In this equalized image we can see a improvement in the contrast .The profile lines are distinct. we can see the distinct shades in case of the hair of the figure. Also the brightness of the image is found not to be good.

5. THE BRIGHTNESS PRESERVING DYAMIC HISTOGRAM TECHNIQUE AND ITS ANALYSIS

The Brightness Preserving Dynamic Histogram Equalization is an extension to HE that can produce the output image with the mean intensity almost same as that of the input image .The method partitions the histogram based on the local maximum of the smoothed histogram. Before equalization the mapping of each partition to a new dynamic range is done. Then the normalization of output intensity is done so as to give the average intensity same as that of the input. The dynamic histogram equalization is done in five steps. First the histogram is smoothed using the averaging filter or the one dimensional Gaussian filter.

Smooth the histogram with Gaussian filter. The local maximums are found from the smoothed histogram. This is done by taking the derivative and the detecting the point where four successive –ve signs are followed by eight successive +ve signs. The number of sections formed will depend on the number of peaks detected .Each of the subsection is mapped to a new dynamic range. Each section is equalized separately. For equalization the transform function

Y=startrange1 +(endrange2 -- startrange1 )* cdf(value)

Normalization could shift the mean brightness of the output image., So to keep the average brightness of the output image same as that of the input image the transform equation

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Fig5 graph5

The equalized image has a brightness which is same as that of the input image.. The contrast is improved but not as much as compared to the other techniques seen till now.

6. COMPARISON OF THE EQUALIZATION TECHNIQUES

The performance of the histogram equalization techniques as described previously can be measured using the quantitative and qualitative parameters. The qualitative assessment is to judge if the output image is visually acceptable to human eyes and to find whether the output image has a natural appearance. Absolute Mean Brightness Error (AMBE), Peak Signal-to-Noise Ratio(PSNR), and entropy are the quantitative metrics .1)Absolute Mean Brightness Error is used to assess the degree of brightness preservation .It is calculated using the equation as

AMBE(X, Y) = |XM - YM|, where XM is the mean of the input image X = {X(i, j)} and YM is the mean of the output image Y = {Y(i, j).

A small value of AMBE indicates a better brightness preservation in the output image . Hence small AMBE is the requirement using the equalization techniques.

2) Peak Signal to Noise Ratio is used to quantitatively assess the degree of contrast enhancement. PSNR=10 log10 (L-1)2/MSE ,where MSE is the mean squared error. A large value of

PSNR indicates a good contrast enhancement in the output image.

3)Entropy also gives the quantitatively assessment of the degree of contrast enhancement. the entropy is a useful tool to measure the richness of the details in the output image.

Ent[ p]= Σ p(k)log2p(k).

Table1

Metric Parameter

BBHE RMSHE MPHE BPDHE

AMBE 7.6845 1.1363 0.5017 0

PSNR 19.2642 25.8629 28.8002 27.7283

ENTROP Y

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The BBHE is histogram equalization, which utilizes independent histogram equalizations over two subimages obtained by decomposing the input image based on its mean. The ultimate goal behind the BBHE is to preserve the mean brightness of a given image while enhancing the contrast of a given image The RMSHE equalizes subimages which are formed depending on the recursion level. Here we kept r=2. The MPHE equalizes the images independently. These subimagews are formed depending on the number of maximums. T

REFERENCE:

[1]S. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall, Englewood Cliffs, New Jersey, 1990.

[2]R. C. Gonzalez and P. Wints, Digital Image Processing,2nd Ed., Addison-Wesley Publishing Co.,Reading, Massachusetts, 1987.

[3]Yeong-Taeg Kim, “Method and circuit for video enhancement based on the quantized mean separate histogram equalization,” filed an a Korean patent, March 9, 1996,

[4]Y. Kim, “Contrast enhancement using brightness p reserving bihistogram equalization,” IEEE Transactions on Consumer Electronic vol. 43, no. 1, pp. 1-8, 1997.

[5]Y. Wan, Q. Chen, and B. Zhang, “Image enhancement based on equal area dualistic sub-image histogram equalization method,” IEEE Transactions on Consumer Electronics, vol. 45, no. 1, pp. 68-75, 1999.

[6]S. Chen and A. R. Ramli, “Minimum mean brightness error bi-histogram equalization in contrast enhancement,” IEEE Transactions on Consumer Electronics, vol. 49, no. 4, pp. 1310-1319, 2003.

[7]S. Chen and A. R. Ram--equalization for scalable brightness preservation,” IEEE Transactions on Consumer Electronics, vol. 49, no. 4, pp. 1301- 1309, 2003.

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