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Top1. Introduction
The aim of Image enhancement is to process an image using some transformation function such that the resultant image is more suitable than the original one for some specific applications (Gonzalez & Woods, 2002). The choice of transformation function will vary depending upon the objective of image enhancement. Enhancement is taken as a pre-processing step in image processing field because many images, such as remote sensing images, medical images and also various real-life images suffer from poor contrast. Image enhancement can be applied for various image processing applications like contrast enhancement, noise reduction, edge enhancement and edge restoration (Gonzalez & Woods, 2002). The approaches for image enhancement are classified into two main categories: Spatial Domain methods where pixel values have been taken into consideration and Frequency Domain methods where Fourier transforms has been applied on the image (Gonzalez & Woods, 2002). Different spatial domain techniques are image negatives, log transformation, power-law transform, contrast stretching, gray-level slicing etc. (Gonzalez & Woods, 2002;Gorai, A., & Ghosh, A. 2009). Basically spatial domain image enhancement techniques are divided into two categories; a) global enhancement methods b) local enhancement methods (Gonzalez & Woods, 2002). Global enhancement methods like traditional histogram equalization (HE) (Gonzalez & Woods, 2002; Gorai, A., & Ghosh, A. 2011) only take global information of the image to enhance it. It does not use the local information to enhance the image. These methods take less time but over-enhancement is the main disadvantage (Gonzalez & Woods, 2002). Local enhancement methods like adaptive histogram equalization (AHE) produce good result than traditional HE but takes more time (Gonzalez & Woods, 2002;Gorai, A., & Ghosh, A. 2009). To overcome this problem a parameterized transfer function has been developed which consider global as well as local information to enhance the image (Gorai, A., & Ghosh, A. 2009;Munteanu, C., & Rosa, A. 2001). In this study this technique has been taken into consideration. Histogram equalization (HE) takes the cumulative histogram of the input image and dispenses the pixel values over the intensity range of the output image (Gonzalez & Woods, 2002; Cheng, H.D., & Shi, X. J 2004; Chen, S. D., Ramli, & A. R. 2004; Chen, S. D., Ramli, & A. R. 2003; Chen SD and Ramli A 2003). HE flattens the histogram of the image and as a result of that, the mean brightness of the enhanced image is around the middle of the gray scale regardless of input image mean (Chen, S. D., Ramli, & A. R. 2004). This fact is useful for face detection but does not suit for consumer electronics applications (Chen, S. D., Ramli, & A. R. 2004). Several modifications have been done on traditional HE to overcome this problem (Cheng, H.D., & Shi, X. J 2004; Chen, S. D., Ramli, & A. R. 2004; Chen, S. D., Ramli, & A. R. 2003; Chen SD and Ramli A 2003). Brightness Preserving Bi-Histogram Equalization (BBHE) is one of the simple variant of basic HE (Chen, S. D., Ramli, & A. R. 2004; Chen, S. D., Ramli, & A. R. 2003; Chen SD and Ramli A 2003). In BBHE histogram of the image separated around its mean and then the two divided parts equalized separately (Chen, S. D., Ramli, & A. R. 2004; Shanmugavadivu, P., Balasubramanian, K., & Muruganandam, A. 2014). It is proved that BBHE method preserved the original brightness to a certain level (Chen, S. D., Ramli, & A. R. 2004; Shanmugavadivu, P., Balasubramanian, K., & Muruganandam, A. 2014).Wan et. al. proposed another method known as Dualistic Sub-Image Histogram Equalization (DSIHE) (Chen, S. D., Ramli, & A. R. 2004; Shanmugavadivu, P., Balasubramanian, K., & Muruganandam, A. 2014) in which the histogram was separated by median instead of mean (Chen, S. D., Ramli, & A. R. 2004; Chen, S. D., Ramli, & A. R. 2003; Chen SD and Ramli A 2003; Shanmugavadivu, P., Balasubramanian, K., & Muruganandam, A. 2014). DSHIE method is suitable for only those kinds of images which have uniform intensity distribution. The potential of preserving the original brightness is not so good of DSIHE method. There is another variant of BBHE method which was known as Minimum Mean Brightness Error Bi-Histogram Equalization (MMBEBHE) proposed by Chen and Ramli (Chen, S. D., Ramli, & A. R. 2004; Chen, S. D., Ramli, & A. R. 2003). In MMBEBHE, at first the histogram has been separated using a specified threshold which preserves the minimum mean brightness error between input and output image. Then the two parts have been equalized independently. This technique is better than BBHE but it also suffers from deficiency of contrast and brightness (Shanmugavadivu, P., Balasubramanian, K., & Muruganandam, A. 2014). Recursive Mean Separate Histogram Equalization (RMSHE) was another HE based procedure proposed by Chen and Ramli, where the input image is separated recursively (Chen, S. D., Ramli, & A. R. 2004; Chen SD and Ramli A 2003; Shanmugavadivu, P., Balasubramanian, K., & Muruganandam, A. 2014). Each part was equalized independently and parts were combined then to give an enhanced image. It was proved that RMSHE method is better than BBHE (Chen, S. D., Ramli, & A. R. 2004) as RMSHE could preserve the brightness well and could give a natural enhancement (Chen, S. D., Ramli, & A. R. 2004). The disadvantages of RMSHE are its large time complexity and the finding of optimal recursion level. So to preserve the brightness, main concept is to divide the image into two parts namely background and foreground. After that equalized sub parts individually within a specific range. In this study separation has been done using CS and its variants by using inter class variance as objective function. Then the range for equalization has been found optimally by maximizing the objective function Peak-Signal to Noise Ratio (PSNR). That metric helps to preserve the original brightness and enhance the contrast.