## 3 Methodology and Accuracy Assessment
### Accuracy Assessment
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quality** & **Description** & **Formula** & **What Value** \\
**Metric** & & & **to Look for** & **Reference** \\ \hline \multirow{3}{*}{RMSE} & Root Mean Square Error (RMSE) is used to & & \\  & calculate the variation in DN values for checking & & \\  & the difference between the Pan sharpened and & & \\  & reference image. & & \\ \hline \multirow{3}{*}{ERGAS} & Relative dimensionless global error synthesis & & \\  & (ERGAS) is used to calculate the accuracy of Pan & & \\  & sharpened image considering normalized & & \\  & average error of each band of the result image. & & \\ \hline \multirow{3}{*}{SAM} & Spectral Angle Mapper (SAM) represents the & & \\  & spectral similarity between the Pan sharpened & & \\  & and reference MS image using the average & & \\  & spectral angle & & \\ \hline \multirow{3}{*}{RASE} & Relative average spectral error (RASE) is an error & & \\  & index to calculate average performance of Pan & & \\  & sharpening algorithm into spectral bands. & & \\ \hline \multirow{3}{*}{PSNR} & Peak signal-to-noise ratio is widely used metric & & \\  & for comparison of distorted (Pan sharpened) & & \\  & original (reference) image. & & \\ \hline \multirow{3}{*}{QAVG} & The Average Quality index based on quality & & \\  & index is used to model the difference between & & \\  & reference and Pan sharpened images as a & & \\  & combination of three different factors: loss of & & \\  & correlation, luminance distortions and contrast & & \\  & distortion. As QI can only be applied to one & & \\  & band, the average value of three or more bands & & \\  & (QAVG) is used for calculating a global spectral & & \\  & quality index for multiband images. & & \\ \hline \multirow{3}{*}{SSIM} & Structural Similarity index (SSIM) is a method for & & \\  & measuring the structural similarity between & reference and Pan sharpened images. This & & \\  & method compares the local patterns (luminance, contrast and structure) using means and & & \\  & standard deviations of two images. & & \\ \hline \multirow{3}{*}{CC} & To assess the spatial quality of Pan sharpened & & \\  & images, the correlation coefficient between the & & \\  & Pan image and the intensity component of the & & \\  & Pan sharpened image is used. & & \\ \hline \multirow{3}{*}{ZHOU index} & Zhou’s spatial index uses a high frequency & & \\  & Laplacian filter for extracting high frequency & & \\  & information from both Pan and Pan sharpened & & \\  & images. Correlation coefficient is then calculated & & \\  & between filtered Pan image and each band of Pan & & \\  & sharpened image. The average of calculated cc is & & \\  & considered as spatial quality index. & & \\ \hline \multirow{3}{*}{SRMSE} & Sobel based RMSE (SRMSE) is an index for & & \\  & spatial accuracy assessment that uses absolute & & \\  & edge magnitude difference of Pan and Pan & & \\  & sharpened image. This index utilizes \(3\times 3\) & & \\  & vertical and horizontal Sobel filter kernels for & & \\  & calculating the gradient of edge intensities. & & \\  & RMSE then calculated between Pan and & & \\  & sharpened edge magnitude images. & & \\ \hline \multirow{3}{*}{Sp-ERGAS} & Spatial ERGAS (Sp-ERGAS) is an index for & & \\  & spatial quality assessment of Pan sharpened & & \\  & image, which uses spatial RMSE for assessment & & \\  & procedure & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The description of all accuracy indices (definition of terms provided in List A1).