BI-HISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT

BY AYUSHI TEWARI

Histogram equalization is a simple method of image enhancement which improves digital image quality without knowledge about the source of degradation.

Histrogram equalization

Histogram of an image is a graph between grey level and number of pixel associated with it.

Histogram equalization is not suitable to be implemented in consumer electronic product such as TV, camera because it causes level saturation effect in small but visually important area.

Saturation effect not only degrades the appearance of image but also leads to information lost

To apply histogram equalization on an image a function where number of pixel on a grey level is divided by the total number is obtained for each gray level. This is called probability density function (P). From P, cumulative density function (CDF) is obtained using :

To find new grey level simply scan input image for each pixel and look at grey level and find corresponding level of cdf.

k

i

kiPCDF

0

Preserving mean brightness of image is essential to avoid annoying artifacts.

It also maintains the artistic value of image. Experimental results have also shown that

by preserving mean brightness of image saturation effect is also reduced and we are able to avoid unnecessary enhancement.

Importance of mean brightness in consumer

electronics

Over the years many mean brightness preserving histogram equalization methods have been introduced.

However many of these method are complicated to be implemented and require high computational time.

Furthermore many of these method require predefined parameter from user.

Why Bi-histogram equalization with plateau limit is needed?

Contd…… • Hence Bi-Histogram equalization with a Plateau Level (BHEPL) is one of the options for the system that require a short processing time image enhancement. • It does not require any parameter from user. • The proposed method also gives better enhancement result as compared with some multi-section mean brightness preserving histogram equalization method

BHEPL is a hybrid of two histogram equalization methods –

Bi-section mean brightness preserving histogram equalization.

Clipping histogram It combines the advantages of both methods and

overcomes their disadvantage hence it is a very powerful method. But we need to understand working of both these methods before we can understand BHEPL.

Introduction to BHEPL

Introduction to Bi-section mean preserving histogram

equalization

In bisection-MBHE the input histogram is divided into two section based on the value of average intensity.

Then two histogram sections are equalized independently.

Let Im be the mean of the image f and assume that Im €{0, L-1} where L is total number of gray level in image.Based on Im , the image is separated into two sub-images fi and fj

as f= fi U fj , Next, define the respective probability density

functions of sub-images fi and fj as: Pi(Ik)=(ni

k) / (ni) Pj(Ik)=(njk) / (nj)

Where ni

k and njk represent the respective values of Ik in

the two sub-images fi and fj . and ni and nj are the total values of fi and fj.

Implementation of BBHE

Contd…….. The respective CDF’s are then calculated as Pi=∑pi(Ik)

Pj=∑ pj(IK) Let us similarly define the following transformation functions

exploiting the CDFs Ti (Ik)=I0+(Im-I0) ·Pi (Ik) and Tj(Ik)=Im+1+(IL-1-Im+1) ·Pj (Ik) Then the resultant image of the histogram can be expressed as g(x,y)=T(f(x,y)), in which, T(I)= Io+(Im-Io).PI(IK) if Ik≤ Im And T(I)=Im+1+(Il-1-Im+1) Pj(Ik) else  

Bi-section MBHE can preserve the mean brightness to a certain extent.

Furthermore bisection MBHE can preserve the original mean brightness if and only if input histogram has quasi-symmetrical distribution

about its separating point. Most of input histogram do not have this property

hence this method can not be generalized

Clipping Histogram

histogram equalization pushes intensities towards left or right causing saturation effect.

To overcome this problem, clipping histogram restricts enhancement rate which is dependent on c(x)

Rate of enhancement is differential of c(x) and is equivalent to p(x).

Thus if enhancement rate is to be limited it can be done by limiting p(x).

Contd….. clipped histogram equalization modifies the

shape of the input histogram by reducing or increasing the value in the histogram’s bins based on a threshold limit before the equalization is taking place

This threshold limit is also known as the clipping limit, or the plateau level of the histogram. The histogram will be clipped based on this threshold value

There are two major problem associated with clipped histogram equalization

First, most of the methods need the user to set manually the plateau level of the histogram, which make these methods not suitable for automatic systems .

Secondly, some of the methods put weight to the modified histogram. The weight factor is also dependent to the user

shortcoming of clipping method

. First BHEPL divides input histogram in to two independent sub-histogram. This is done to maintain mean brightness.

Then these two histogram are clipped based on calculated plateau limit.

This is done to control enhancement rate

Working of BHEPL

First, similar to bi-section mean preserving equalization (BBHE), the average intensity of the input image, Xm, is calculated. Then, BHEPL decomposes the input image into two sub-images XL and XU based on Xm as given in to

X = XL ∪XU …………………………………(I) where XL = {X (i, j) | X (i, j) ≤ Xm,∀X (i, j)∈X}……….(II) and XU = {X (i, j) | X (i, j) > Xm,∀X (i, j)∈X}……….(III)

The sub-image XL is composed of {X0, X1, .., Xm},and the another sub-

image XU is composed of {Xm+1, Xm+2, ..,XL-1}. Actually, this condition separates the input histogram in to two sections.

The histogram created from XL is denoted as hL, and the histogram created from XU is denoted as hU. By using these histograms, BHEPL finds two plateau limits TL and TU, for XU

and XL, respectively.

 

Mathematically

The values for TL and TU are set automatically by using

  TL= (1/(Xm+1))∑ hL(k) ………………………..(IV)

TU=1/((L-1)-Xm) ∑hu(k) ……………………….(V)

  As given by (IV) TL is actually the average of hL. Similarly, from (V) TU is the

average of hU. Next, in order to control the enhancement rate of BHEPL, sub-histograms hL

and hU are clipped. The clipped histogram versions are denoted as hCL and hCU.

hcl(x)={ hL (x) if hL(x)≤TL …………………………..(VI)

TL elsewhere And hul(x)={ hu(x) if hu(x)≤TU ………………………….(VII)

TU elsewhere

Contd…..

Input imageGHEBHEBHEPL

BHEPL requires short processing time for image enhancement

BHEPL does not require any input parameter from the user

Experimental results have shown that BHEPL is able to preserve mean brightness better than other mean brightness preserving algorithm.

It is ideal method for consumer electronics where preserving mean brightness is very important.

Advantage of BHEPL

Currently many methods of image enhancement have been developed based on bi-histogram equalization like bi-histogram equalization method (BHEPL-D).

These methods are said to be an improvement on Bi-histogram equalization with plateau limits in terms of producing clearer enhanced image than any other proposed method.

Disadvantages Of BHEPL

Based on BHEPL a new method BHEPL-D has been developed.

In BHEPL-D histogram of input image is segmented into lower histogram, hL and upper histogram, hU .

BHEPL-D creates a plateau limit (Pl, Pu) for each sub-histogram.

Unlike in the BHEPL, the BHEPL-D sets the plateau limit as the median of the occupied intensity. The plateau limit PL and PU can be determined using

PU=median [hu(xk)]………………………….(A) PL=median[hL(xk)]………………………….(B) where k = m+1 , m+2 , m+3 ,…, L-1

Comparison of BHEPL with BHEPLD

EXPERIMENTAL RESULT

original BHEPLedBHEPLDed

BHEPL has been proposed as a hybrid between mean brightness preserving histogram equalization method with clipped histogram equalization method.

Experimental results show that this proposed method can enhance the images without producing unwanted artifacts. The method also is able to maintain the mean brightness better

Than some well known mean brightness preserving histogram

 

Summary and future scope

References •Soong-Der Chen and A.R.Ramli , ”Minimum mean brightness error bi histogram equalization in contrast enhancement”, IEEE Trans. Consumer electronics ,vol 49,no 4 ,pp1310-1319,November 2003 •Taekyung Kim and Joonki Paik, ”Adaptive contrast enhancement using gain controllable clipped histogram equalization”. ”, IEEE Trans. Consumer electronics ,vol 54,no 4 ,pp1803-1810,November 2008 •Nicholas Sia , Haidi Ibrahim, Chen Hee Ooi, and Derek, “Enhancement of microscopic images using modified self adaptive plateau histogram equalization”, submitted for publication in proceeding of 2009 International conference on Graphic and Image Processing,Malaysia, November 2009.Thank you