# Normalized Weighting Schemes for Image Interpolation Algorithms
## 3 Results and Discussions
### Objective Image Interpolation Quality Assessment  
In this section, the main goal was to use IQA metrics capable of predicting the quality of an interpolated image accurately and automatically. However, in Figure 9, the computational efficiency was evaluated by measuring the elapsed time. As can be seen, in Figure 9, the TN remained the fastest of all algorithms, because, in each scaling ratio case, it used the smallest average time, among the other algorithms mentioned. The elapsed time by the TB was shorter than MD, HR, AT, and AC. The main reason for the slowness of new or non-traditional algorithms was increased computational efforts which required more MATLAB lines reading time. For example, TN is the fastest because it does not do any computations. It only uses the destination image coordinates to locate the corresponding coordinates in the source image and those that match, their pixel values are copied from the source image to the destination image. That is not the case with any other algorithms mentioned, because, for example, the TB used the weighted average of four pixels to calculate each pixel value in the destination image. This required taking into account simultaneously a group of four pixels and sliding those four pixels kernel over the entire image, which understandably would take more time than a \"copy-paste\" like operation on which the TN was based. It is important to note that the software built-in interpolation functions of the traditional TN, TB, and TC normally perform better than the manually implemented functions. Now focusing on IQA metrics to predict automatically and/or accurately the image interpolation quality--Figure 10 presents the average scores that each interpolation algorithm produced or achieved in terms of the MSE. As can be seen, when the scaling ratio was 2 and 4, the TC achieved the best SME scores among traditional and non-traditional image interpolation algorithms. Focusing on non-traditional image interpolation algorithms alone (i.e., MD, HR, AT, and AC), it can be seen that the AC-based algorithm achieved the best MSE scores in both cases involving the scaling ratios equal to 2 and 4. Here, it is important to note that the lower MSE value (closest to zero) theoretically means the better image interpolation quality. Figure 11 presents the average scores, each interpolation algorithm produced or achieved in terms of the SSIM. As can be seen, for the cases involving all image interpolation algorithms as well as the scaling ratio equal to 2 and 4, TC achieved the best SSIM scores among all image interpolation algorithms mentioned. Focusing on image interpolationalgorithms based on new weighting schemes alone, when the scaling ratio was 2, the HR-based algorithm achieved better SSIM scores than AC, AT, and MD-based image interpolation algorithms. In addition, when the scaling ratio was 4, the MD-based algorithm achieved better SSIM scores than AC, AT, and HR-based image interpolation algorithms. It is important to remember that, in theory, the higher SSIM score (closest to 1), means the better image interpolation quality. Figure 10: Average MSE: traditional nearest neighbor (TN), traditional bicubic (TC), traditional bilinear (TB), normalized minimum side-based diameter-based (MD), normalized hypotenuse radius-based (HR), normalized virtual pixel length-based height for the area of the triangle-based (AT), and normalized virtual pixel length for hypotenuse-based radius for the area of the circle (AC) interpolation algorithms. Figure 9: Average time (in seconds): traditional nearest neighbor (TN), traditional bicubic (TC), traditional bilinear (TB), normalized minimum side-based diameter-based (MD), normalized hypotenuse radius-based (HR), normalized virtual pixel length-based height for the area of the triangle-based (AT), and normalized virtual pixel length for hypotenuse-based radius for the area of the circle (AC) interpolation algorithms. Figure 12 presents the average scores, each interpolation algorithm produced or achieved in terms of the PSNR.