Abstract:

As light is weakened when spreading in water so the images in the water and their clarity varies at every point so the objects in the underwater images are not clearly visible and due to low contrast and scattering of light and the large noise present in the environment the images provide no clarity. This paper represent a method called Contrast Limited Adaptive Histogram Equalization(CLAHE) this method is developed for underwater images enhancement. This method first apply (CLAHE) on RGB and HSI and then combine the results using Euclidean normalization. After this we convert it into RGB and apply (CLAHE) on it and the we convert it into HSV and apply (CLAHE) on it and after RGB and the again HSI and again convert it into RGB and gets our results
 

Introduction:

 
Digital Image processing is a processing of image using computer algorithm on digital images. An input can either be an image or series of images or a video and the output of image processing may be either image series of images or a video. Images on different areas got crupted through many ways e.g due to displacement of lens image become blur or during the process of transmission of image from one device to another many pixels got corrupted and images filled up with noise so in these cases and many other like these one , image processing is tool use to minimize these issues. Digital image processing was first developed in 1960s at the Jet propulsion lab, Massachusetts institute of technology, Bell laboratories, University of Maryland and few more institute. There are many techniques in image processing like image enhancement ( enhances the image making  information more visible ) Arithmetic operations( adding images or subtraction or other arithmetic’s operations) and noise filters (removing noise from images like impulse noise using filters like Gaussian filters), image analysis(extracting information from image for many purposes )and restoration( due to many reasons some parts of image got corrupted so in order to get information we use many techniques of restoration to restore image).Among many techniques we use image enhancement in our paper to enhance the quality of underwater images Image. Enhancement is a process of adjusting the image in order to get suitable results like removing noise or sharpen the image or brighten the image making it easy to understand. In enhancement there is a also many techniques for different kind of images as there can’t be only one method to enhance every kind of images. For underwater images there is a method called (CLAHE). This technique is used to increases the contrast of image and differ from original histogram equalizer, [4]as in histogram equalizer the range and the contrast of the image is modified by changing its histogram. By using cumulative function as mapping function we can achieve this. The peaks and the tough of the images are changed and equalized though out the image using histogram equalization, where as in the Contrast Limited Adaptive Histogram Equalization(CLAHE) histogram is divided into many parts using some threshold and then equalization is applied on it.It is an adaptive contrast histogram equalization so it adapts its self-according to the different situations and it applyclahe on little parts of image called tiles ,the contrast of the image is enhanced and the resulting neighbor tiles are then stitched back seamlessly using bili-near interpolation. The contrast in the homogeneous region can be limited so that noise amplification can be avoided. it is suitable for improving local contrast and enhancement.

Literature review:

 
 

Methodology:

 
No enhancement technique is good enough to be able to apply on every kind of image. Therefore various techniques are developed to handle various kind of images and the method discussed in this paper is focusing on underwater images. (CLAHE) one of the method which are used for under water images enhancement. This paper first convert image into HSI
 
 
The input image is first convert into HSI  where H represents Hue and S represents Saturation and I represents Intensity .The intensity component ranges between 0 and 1 in which 0 means black and 1 means white.
The separation of RGB determines the value of saturation as it is defining the spreading of color. if the RGB values are closer than the color will be close to grey and if they are far apart then the color will be quite intense. The range of saturation so from 0 to 1The Equation to do this is
 
\(S=\frac{V-\min\left(R,G,B\right)}{V}\)
While the hue is bit different from other. It defines the whether the color is red blue or green etc. at 0 degree the color is red while at 120 degree the color is green . In order to calculate Hue we must calculate R`, G`, B`
               
\(R`=\frac{V-R}{V-\min\left(R,G,B\right)}\) 
\(PSNR\ =\ 20\log\ \left(\frac{2^{\beta}-1}{\sqrt{\left(MSE\right)}}\right)\)
\(G`=\frac{V-G}{V-\min\left(R,G,B\right)}\)
\(PSNR\ =\ 20\log\ \left(\frac{2^{\beta}-1}{\sqrt{\left(MSE\right)}}\right)\)\(B`=\frac{V-B}{V-\min\left(R,G,B\right)}\)\(B`=\frac{V-B}{V-\min\left(R,G,B\right)}\)
 If S=0 then hue is undefined:
 H=
      \(5+B`\ \ \ \ \ R=\max\left(R,G,B\right)\ and\ G=\min\left(R,G,B\right)\)
            \(1-G`\ \ \ \ \ R=\max\left(R,G,B\right)\ and\ G\ !=\min\left(R,G,B\right)\)
            \(1-R`\ \ \ \ \ G=\max\left(R,G,B\right)\ and\ B=\min\left(R,G,B\right)\)
            \(3-B`\ \ \ \ \ G=\max\left(R,G,B\right)\ and\ B\ !=\min\left(R,G,B\right)\)
            \(3+G`\ \ \ \ \ B=\max\left(R,G,B\right)\ \)
\(5-R`\ \ \ \ \ otherwise\)            \(5-R`\ \ \ \ \ otherwise\)        
 
As at 360 there is discontinuity in hue and its quite difficult to perform arithmetic operations so we implement CLAHE on only Value and Saturation.
 
RGB define color in form of three colors Green blue and red and this methods combines these three basic colors and create other colors. Light is added to create form from out of darkness. RGB is the  sum of following functions:
\(PSNR\ =\ 20\log\ \left(\frac{2^{\beta}-1}{\sqrt{\left(MSE\right)}}\right)\)\(R=\int_{300}^{830}S\left(\gamma\right)\ R\left(\gamma\right)\ d\gamma\)
\(G=\int_{300}^{830}S\left(\gamma\right)\ G\left(\gamma\right)\ d\gamma\)
\(\)\(B=\int_{300}^{830}S\left(\gamma\right)\ B\left(\gamma\right)\ d\gamma\)
Where S(r) is light spectrum and R(r), G(r), B(r) are the functions for the R, G and B respectively. This paper implements clahe on all three components individually and then combine the three result to get future results.
 
 
The results obtained from both HSI and RGB provides undefined artifacts as well as much brightness so we introduce the combination of both of the results using Euclidean normalization. The reason to performing this is to increase the contrast of the image.This method normalizes the results obtained after applying CLAHE on RGB by using this formula:
 \(\left[Rc1\ \ Gc1\ \ Bc1\right]\ =\left[\frac{Rc}{Rc+Gc+Bc},\frac{Gc}{Rc+Gc+Bc},\frac{Bc}{Rc+Gc+Bc}\right]\) (1)
(Figure of clahe implement on RGB):
 
Whereas the result of HSI when clahe was implemented on it can be convert into RGB by finding chorma
 
\(C=S\ *\ V\)
AND
 
\(H`=\frac{H}{60^{\theta}}\)    
  
By using both c and H` we can find
 
\(X=C(1-|(H`\ mod\ 2)-1|)\)
 
Conversion of HSI to RGB can be done using this formula:
 ( Rc2 Gc2 Bc2 )=
                                    \(\left(0,0,0\right)\ if\ H\ is\ \ undefined\)
                                    \(\left(C,X,0\right)\ if\ 0\le H`\ <1\)
                                     \(\left(X,C,0\right)\ if\ 1\le H`<2\)
                                    \(\left(0,C,X\right)\ if\ 2\le H`<3\)
                                    \(\left(0,X,C\right)\ if\ 3\le H`<4\)
                                    \(\left(X,0,C\right)\ if\ 4\le H`<5\)
                                    \(\left(C,0,X\right)\ if\ 5\le H`<6\)        (2)
Finally by getting results from both eq 1 and eq 2 we can compute
Euclidean normal form:
 
 \(RGB=\left[\sqrt{R^2c1\ +R^2c2},\sqrt{G^2c1\ +G^2c2},\sqrt{B^2c1\ +B^2c2},\right]\)
 
(picture of clahe on his and rgb and after normalization)
 
 
After this we covert the image into HSV where H represents Hue and S represents Saturation and E represents Value The models was represented by Smith in 1978.In HSV when value is either max or min then saturation and Hue doesn’t make any difference. By taking the highest value of RGB the value of V can be calculated as HSV model Takes RGB in rages of 0 to 1. The computation of RGB can be described as:
\(V=\max(R,G,B)\)
The separation of RGB determines the value of saturation as it is defining the spreading of color. if the RGB values are closer than the color will be close to grey and if they are far apart then the color will be quite intense. The Equation to do this is
 
\(\)\(S=\frac{V-\min\left(R,G,B\right)}{V}\)
While the hue is bit different from other. It defines the whether the color is red blue or green etc. at 0 degree the color is red while at 120 degree the color is green . In order to calculate HUE we must calculate R`, G`, B`
 
\(R`=\frac{V-R}{V-\min\left(R,G,B\right)}\)
 \(PSNR\ =\ 20\log\ \left(\frac{2^{\beta}-1}{\sqrt{\left(MSE\right)}}\right)\)
\(G`=\frac{V-G}{V-\min\left(R,G,B\right)}\)
\(PSNR\ =\ 20\log\ \left(\frac{2^{\beta}-1}{\sqrt{\left(MSE\right)}}\right)\)\(B`=\frac{V-B}{V-\min\left(R,G,B\right)}\)\(B`=\frac{V-B}{V-\min\left(R,G,B\right)}\)
 If S=0 then hue is undefined:
 H=
\(\ \ \ \ \ \ \ \ \ 5+B`\ \ \ \ \ R=\max\left(R,G,B\right)\ and\ G=\min\left(R,G,B\right)\)
            \(1-G`\ \ \ \ \ R=\max\left(R,G,B\right)\ and\ G\ !=\min\left(R,G,B\right)\)
            \(1-R`\ \ \ \ \ G=\max\left(R,G,B\right)\ and\ B=\min\left(R,G,B\right)\)
            \(3-B`\ \ \ \ \ G=\max\left(R,G,B\right)\ and\ B\ !=\min\left(R,G,B\right)\)
            \(3+G`\ \ \ \ \ B=\max\left(R,G,B\right)\ \)
            \(5-R`\ otherwise\)    
 
As at 360 there is discontinuity in hue and its quite difficult to perform arithmetic operations so we implement CLAHE on only Value and Saturation.
After getting the results it was converted into RGB then HSI and again apply CLAHE on it and finally converted the results into RGB
(picture of our result and picture of previous paper)
 
 

The Mean square error\(MSE=\left[\frac{\Sigma\ M,N\ \left[I1\left(m,n\right)\ -\ I2\left(m,n\right)\right]^2}{M\cdot N}\right]\)

The Mean square error (represents cumulative squared error and peak signal noise ratio(peak error) are the two scales which re use to compare the quality of enhanced underwater images.
Higher value of both methods represents bad method and low value represents good method.
MSE can be calculated through:
 
\(MSE=\left[\frac{\Sigma\ M,N\ \left[I1\left(m,n\right)\ -\ I2\left(m,n\right)\right]^2}{M\cdot N}\right]\)\(MSE=\left[\frac{\Sigma\ M,N\ \left[I1\left(m,n\right)\ -\ I2\left(m,n\right)\right]^2}{M\cdot N}\right]\)
\(MSE=\left[\frac{\Sigma\ M,N\ \left[I1\left(m,n\right)\ -\ I2\left(m,n\right)\right]^2}{M\cdot N}\right]\)
 
Where l1 and I2 represents the original images and new image and he size must b same and denoted by M*N whereas PSE is represented by:
 
 \(PSNR\ =\ 20\log\ \left(\frac{2^{\beta}-1}{\sqrt{\left(MSE\right)}}\right)\)              
              
Where B represents bits per sample
 

Analysis:

 
When this method applied on the images it increases the contouring.
 

References:

 
[1] Muhammad Suzuri Hitam,Wan Nural Jawahir Hj Wan Yussof and Ezmahamrul Afreen Awalludin, Zainuddin Bachok proposed a paper named Mixture Contrast Limited Adaptive Histogram Equalization for Underwater Image Enhancement .
 
[2] Haocheng Wen and Yonghong Tian+, Tiejun Huang, Wen Gao also presented “Single Underwater Image Enhancement with a New Optical Model
 
[3] [Rajesh kumar Rai1, Puran Gour2, Balvant Singh represents Underwater Image Segmentation using CLAHE Enhancement and Thresholding.****
 
[4]  Neethu M. Sasi, V. K. Jayasree proposed Contrast Limited Adaptive Histogram Equalization for Qualitative Enhancement of Myocardial Perfusion Images