# Image Magnification Based on Bicubic Approximation with Edge as Constraint
## 5 Experimental Results
### Discussion  
The results in Tables 1-3 and Figures 4-8 show that, among the 8 methods in the comparison, (1) overall, the quality of the magnified images by the new method is the best, followed by LPRGSS method; (2) the bicubic method has the shortest running time, followed by the new method, these two methods are suitable for real-time image magnification; (3) for areas without edges and textures in the image, there is little visual difference between the magnified images by the 8 methods, the 9 images in Figure 6 are examples. In fact, for areas without edges and textures in the image, bicubic method, as the most classical basic image magnification method, can produce the same PSNR and SSIM values as the new method, while for areas with edges and textures in the image, bicubic method generally produces image blocks with poor visual effect. The images (b) in Figures 4, 5, and 7 are examples. The main reason is that the bicubic method constructs each surface patch by passing 16 image pixels, which means that, when bicubic method is used, there is no degree of freedom in constructing bicubic surface; the constructed surface is unique. If the pixels are sampled from different objects, the surface patch constructed by bicubic method will produce larger oscillations, resulting in jagged or blurred pixels at the edges of the image. For magnifying the image without edges and textures, the new method has the advantages of bicubic method. Because the new method uses edge features as constraints to construct quadratic polynomial surface, for magnifying the image with edges and textures, the new method gets better magnified images than bicubic method.  
We also tested the images in data sets set5 and set14 and database BSD300. The test results were basically the same as those of the 12 typical images, the images in BSD200, Urban100, and AIS.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Image** & **Bicubic** & **DCCI** & **ICBI** & **SelfExSR** & **NAMM** & **SISPRFI** & **LPRGSS** & **New** \\ \hline Barbara & 0.018 & 1.849 & 5.297 & 183.453 & 332.389 & 320.068 & 176.514 & 0.020 \\ \hline Baboon & 0.018 & 1.614 & 5.000 & 170.285 & 351.381 & 318.440 & 180.015 & 0.020 \\ \hline Boat & 0.018 & 1.633 & 3.922 & 176.946 & 335.560 & 317.841 & 175.639 & 0.020 \\ \hline Chest & 0.018 & 1.623 & 5.548 & 189.318 & 394.686 & 317.895 & 161.575 & 0.020 \\ \hline Couple & 0.018 & 1.679 & 5.188 & 181.168 & 343.976 & 318.039 & 174.233 & 0.020 \\ \hline Crowd & 0.018 & 1.857 & 5.389 & 171.767 & 463.896 & 330.901 & 174.872 & 0.020 \\ \hline Dollar & 0.018 & 1.621 & 4.676 & 185.658 & 405.255 & 326.665 & 178.925 & 0.020 \\ \hline Goldhill & 0.018 & 1.617 & 4.391 & 174.468 & 405.280 & 325.677 & 176.006 & 0.020 \\ \hline Kod & 0.018 & 1.611 & 3.410 & 181.206 & 401.058 & 328.210 & 173.926 & 0.020 \\ \hline Lake & 0.018 & 1.669 & 4.490 & 175.183 & 392.478 & 330.892 & 175.263 & 0.020 \\ \hline Lenna & 0.018 & 1.578 & 4.960 & 173.818 & 347.464 & 340.423 & 173.287 & 0.020 \\ \hline Peppers & 0.018 & 1.584 & 4.151 & 171.785 & 343.719 & 334.731 & 173.759 & 0.020 \\ \hline Average & 0.018 & 1.849 & 5.297 & 183.453 & 332.389 & 320.068 & 174.501 & 0.020 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Runtime of 12 images with 8 methods (Unit: seconds).