## 4 Experimentation  
### Performance Measures  
Evaluation measures, such as Root Mean Squared Error (RMSE), Peak Signal-to-Noise Ratio (PSNR), Normalization Coefficient (NC), Mean Squared Error (MSE), and Correlation Coefficient (CoC), are commonly used to assess the performance of contrast enhancement methods in image processing. These measures provide a quantitative evaluation to compare the quality of the enhanced image with the original image. This section shall explore each measure and its corresponding equation:  
**Peak Signal-to-Noise Ratio:** PSNR serves as a commonly employed metric for assessing the effectiveness of contrast-enhanced images [25]. It offers insight into the relationship between the highest attainable signal strength and the magnitude of noise present in the image. PSNR is calculated using the following equation:  
\[PSNR=10*log10\Big{(}MAX^{2}/MSE\Big{)} \tag{4}\]  
where _MAX_ is the maximum possible pixel value in the image (e.g., 255 for an 8-bit image) [26; 27].  
**Mean Squared Error:**_MSE_ quantifies the average squared disparity between the pixel values of the initial image and the enhanced image. A diminished MSE value reflects more favorable outcomes, indicating that the enhancement has successfully minimized the differences between the two images [27; 28]. _MSE_ is calculated using the following equation:  
\[MSE=\bigg{(}\frac{1}{X\times Y}\bigg{)}\times\sum\sum\Big{[}(I(r,s)-D(r,s))^{2 }\Big{]} \tag{5}\]  
where \(X\) and \(Y\) are the width and height of the image, \(I(r,s)\) represents the pixel value of the original image at coordinates \((r,s)\), and \(D(r,s)\) represents the pixel value of the denoised image at the same coordinates.  
**Root Mean Squared Error:** RMSE is the square root of the _MSE_ and provides a measure of the average difference between the original and enhanced image pixel values [29]. It is commonly used as an error metric in image processing.  
RMSE is calculated using the following equation:  
\[RMSE=sqrt(MSE) \tag{6}\]  
**Correlation Coefficient:** The _CoC_ measures the linear relationship between the pixel values of the original and enhanced images. It provides a measure of how well the denoised image matches the original image. The Correlation Coefficient is calculated using the following equation:  
\[CoC=cov(I,D)/(\sigma_{I}*\sigma_{D}) \tag{7}\]  
where _cov_(_I_, _D_) represents the covariance between the pixel values of the original and denoised images, and \(\sigma_{I}\) and \(\sigma_{D}\) represent the standard deviations of the original and denoised images, respectively.  
**Normalization Coefficient:** The _NC_ is a measure used to assess the similarity of contrast enhancement results between original and enhanced images. A higher value of NC indicates that contrast enhancements were achieved.  
The equation for calculating the Normalization Coefficient (_NC_) can vary depending on the general approach for calculating the _NC_ based on the concept of normalization.  
Here is a general equation for calculating the Normalization Coefficient (_NC_):  
\[NC=(CE_{A}-Org_{B})/(CE_{A}+Org_{B}) \tag{8}\]  
where _NC_ is the Normalization Coefficient and \(CE_{A}\) represents the contrast enhancement image, while the \(Org_{B}\) is the original image.  
These evaluation measures provide objective metrics to assess the performance of enhanced images. Lower RMSE and higher PSNR values indicate better quality, while a higher Correlation Coefficient signifies a stronger correlation between the original and enhanced images.