# Image Interpolation with Regional Gradient Estimation
## 4 Experiments
for the images \"cameraman\", \"Barbara\", \"butterfly\", \"baboon\", \"airplane\", and \"house\". These results show that the proposed method was effective in preserving the edges of the images. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Test** & **CGI** & **CED** & **PCI** & **IEDI** & **PGI** & **WTCGI** & **IBI** & **GEI** \\
**Images** & [18] & [19] & [20] & [17] & [21] & [25] & [16] & **(Proposed)** \\ \hline Bike & 0.8258 & 0.8243 & 0.8325 & 0.8274 & 0.8313 & 0.8265 & 0.8236 & 0.8302 \\ Wheel & 0.8186 & 0.8189 & 0.8295 & 0.8111 & 0.8256 & 0.8274 & 0.8121 & 0.8259 \\ Boats & 0.7963 & 0.7865 & 0.7911 & 0.7895 & 0.7901 & 0.7898 & 0.7883 & 0.7916 \\ Butterfly & 0.8729 & **0.8775** & 0.8721 & 0.8703 & 0.8705 & 0.8749 & 0.8612 & 0.8753 \\ House & 0.7541 & 0.7533 & 0.7611 & 0.7615 & 0.7605 & 0.7596 & 0.7566 & 0.7624 \\ Cameraman & 0.7554 & 0.7525 & 0.7544 & 0.7494 & 0.7540 & 0.7556 & 0.7502 & 0.7601 \\ Baboon & 0.8029 & 0.8035 & 0.8051 & 0.8046 & 0.8069 & 0.8015 & 0.8014 & 0.8072 \\ Peppers & 0.7657 &  
The low computational complexity of our proposed method is an additional attractive feature. The average runtimes of each method for the interpolation of the 12 test images are documented in Table 5. Because the IBI method is based on the bicubic method, it does not have to consider image structure as much, making it the fastest. The CED method, which had the lowest runtime after IBI, replaces the edge-diffusion iterative process in the CGI method with thermal diffusion. Because of the inclusion of the regional gradient estimation strategy, the time complexity of the method proposed in this paper was slightly higher than that of PCI. IEDI was the slowest of all methods, with an average runtime nearly 11 times that of the method in this paper. The original author of the WTCGI method only provided C++ code, so it was not included in this comparison. For the subjective performance evaluation, we compared the performance of the methods in terms of visual effect. We conducted interpolation by \(4\times 4\) for the Wheel via 8 methods respectively, and select upper right part of \"wheel\" for subjective evaluation, as shown in Figure 11. The CGI and CED methods generated false edges at the junction edges, as shown in the yellow anchor boxes in Figure 11b,c; this was due to an ineffective gradient selection strategy, as shown in Equation (9). Although the CED method replaces the edge-diffusion iterative process in the CGI method with thermal diffusion, which increases running speed, false edges remain a problem. The PCI and PGI methods improve on the CGI method by using prediction correction and gradient prediction, respectively, to avoid the generation of false edges and produce sharper edges than the CGI method; however, their results yielded some edge loss in the red sight frames, as shown in Figure 11e,f. Although IEDE yielded more complete edges than the above-mentioned methods,'speckle'-like noise was present, as shown in Figure 11g. WTCGI and IBI blurred more edges and generated more distinct artifacts, such as jagged edges, as seen in Figure 11h,i. The proposed method produced clear edges, avoided false and missing edges, and caused minimal artifacts, as shown in Figure 11d. Figure 11: Comparison of interpolation results for top right part of the “wheel” image by different interpolation methods. (**a**) Upper right part of the “wheel” after interpolation; (**b**) CGI; (**c**) CED; (**d**) GEI; (**e**) PGI; (**f**) PCI; (**g**) IEDI; (**h**) WTCGI; (**i**) IBI. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**CGI** & **CED** & **PCI** & **IEDI** & **PGI** & **WTCGI** & **IBI** & **GEI** \\
[18] & [19] & [20] & [17] & [21] & [25] & [16] & **(Proposed)** \\ \hline
3.10 & 0.89 & 1.31 & 17.96 & 1.54 & - & 0.17 & 1.45 \\ \hline \end{tabular}
\end{table} 
Table 5: Average runtime (in seconds) for interpolating 12 test images. For the color images, CGI and the proposed method were applied to interpolate the R, G, and B channels of the color images and combine them into a single image.