AMBE, Contrast Enhancement, Entropy, Histogram Equalization, PSNR, Segmentation. 1. INTROdUCTION. In the realm of digital image processing all the ...
International Journal of Computer Vision and Image Processing Volume 6 • Issue 1 • January-June 2016
Entropy based Range Optimized Brightness Preserved Histogram-Equalization for Image Contrast Enhancement Krishna Gopal Dhal, University of Calcutta, Kolkata, India Sankhadip Sen, Regent Education & Research Foundation, Kolkata, India Kaustav Sarkar, Regent Education & Research Foundation, Kolkata, India Sanjoy Das, University of Kalyani, Kalyani, India
ABSTRACT In this study the over-enhancement problem of traditional Histogram-Equalization (HE) has been removed to some extent by a variant of HE called Range Optimized Entropy based Bi-Histogram Equalization (ROEBHE). In ROEBHE image histogram has been thresholded into two sub-histograms i.e. histograms corresponding to background and foreground. The threshold is calculated by maximizing the sum of the entropy of these two sub-histograms. The range for equalization has been optimized by maximizing the Peak-Signal to Noise ratio (PSNR). The experimental results prove that ROEBHE has prevailed over existing methods and PSNR is a better range optimizer than Absolute Mean Brightness Error (AMBE). Keywords AMBE, Contrast Enhancement, Entropy, Histogram Equalization, PSNR, Segmentation
1. INTRODUCTION In the realm of digital image processing all the indigenous algorithms must be cognizant of the two main aspects viz. contrast enhancement and brightness preservation of the images experimented. The endeavour of the enhancement algorithms is to achieve an optimal condition using an objective function where the image attains a state of maximum clarity such that it can have a good visual analysis. Then only it can be differentiated from the original image having poor contrast and other technical anomalies. The first ever approach to achieve contrast enhancement was Histogram Equalization (HE) technique (Gonzalez & Woods, 2002). In HE method the pixels are well distributed over the full dynamic intensity range. Basically HE computes linear cumulative histogram of the original image and dispenses intensity values over its dynamic intensity range. HE based techniques have been used in medical image processing, satellite image processing etc. There are two types of HE methods: (a) Global HE method (b) Local HE method. Global HE method carries out modification of the pixels by the transformation function based on the gray-level content of an entire image. The distribution of the intensity levels are normalized DOI: 10.4018/IJCVIP.2016010105 Copyright © 2016, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
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International Journal of Computer Vision and Image Processing Volume 6 • Issue 1 • January-June 2016
by quantizing the Cumulative Density Function (CDF) obtained after calculating the Probability Density Function (the ratio of the pixels in a particular intensity level to the total no. of pixels in the image) so that the output image may have a linear distribution of intensity levels. This global aspect is appropriate for overall enhancement of the image, but there may be some cases in which it is necessary to enhance the details over local areas in an image. In those cases this very procedure fails to preserve the brightness and contrast features locally. In case of Local HE the neighbourhood pixels are considered for equalization by using their histogram intensity statistics. The original image is divided into various sub-blocks in the form of square or rectangular neighbourhood. At each location, the histogram of the points in the neighbourhood is computed and either a histogram equalization or histogram specification transformation function is obtained. Then after repeating these steps finally the resultant image is obtained by merging the sub-blocks which results in the creation of several unwanted artifacts all over the image known as checkerboard effect. The method of Traditional Histogram Equalization (Gonzalez & Woods, 2002) is described below where probability density function is defined as: PDF (X k ) =
nk W
for 0 ≤ k ≤ L − 1
(1)
where, nk is the total number of pixels with intensity level X k . The plot of X k vs. nk is called histogram of image f . W is the total no. of pixels in the image f. L is the number of discrete grey level. For an 8 bit image L = 256 . The cumulative density function is defined in (Gonzalez & Woods, 2002): k
CDF (X k ) = ∑PDF (X i )
(2)
i =0
Traditional HE maps the corresponding image into the total dynamic range X 0 , X L−1 with the help of the CDF . The mapping is given below: f (X ) = X 0 + (X L−1 − X 0 ) .CDF (X )
(3)
Basically HE procedure flattens the histogram of the original image. Theoretically the entire grey levels are distributed with uniform distribution. As a result of this it improves the contrast of the image, maximizes the image entropy. As the histogram of the output image is uniformly distributed the mean brightness is approximately changed to the middle of the grey level regardless of the mean of the input image (Chen & Ramli, 2004; Kim, 1997). The equation of mean or statistical expectation E (.) of the output image G is given below: 1 E (G ) = Gmean = (X 0 + X L−1 ) 2
(4)
where, Gmean is the mean of the output image in traditional HE procedure. Therefore, traditional HE procedure is not suitable for consumer electronics purpose. To overcome this problem several modifications has been done on traditional HE. The common two techniques among those methods were:
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