Entropy based Range Optimized Brightness Preserved Histogram-Equalization for Image Contrast Enhancement

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 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: for (1) where, is the total number of pixels with intensity level . The plot of vs. is called histogram of image W is the total no. of pixels in the image f. is the number of discrete grey level. For an 8 bit image . The cumulative density function is defined in (Gonzalez & Woods, 2002):

Traditional HE maps the corresponding image into the total dynamic range with the help of the. The mapping is given below: