# Image Interpolation with Regional Gradient Estimation
## 4 Experiments  
In order to evaluate the method presented in this paper, seven representative current methods were selected for experimentation: IBI [16], IEDI [17], CGI [18], CED [19], PGI [20], PCI [21], and WTCGI [25]. The source code of each method was either written by the method's proponent or implemented by the authors of this paper, and the individual parameter configurations used were the default parameters recommended by each method's proponent. The proposed method (GEI) is based on the concept of CGI edge diffusion and uses CED to replace the iterative process in the CGI method to reduce time complexity. In contrast, to improve upon the CGI method, PCI and PGI employ the prediction-correction and gradient-prediction strategies, respectively. WTCGI combines wavelet transformation and the contrast-guided approach from CGI. Our experiment included the above five methods, as well as IEDI and IBI. IEDI is an improvement of the edge-direction interpolation method, and IBI is an improvement of the bicubic method, so comparing them to the method proposed in this paper is meaningful. The twelve test images used in the image experiment are shown in Figure 10. The labels and sizes are as follows: cameraman (256 \(\times\) 256 pixels), house (256 \(\times\) 256 pixels), butterfly (512 \(\times\) 521 pixels), bike (500 \(\times\) 500 pixels), boats (512 \(\times\) 512 pixels), wheel (512 \(\times\) 512 pixels), airplane (256 \(\times\) 256 pixels), stars (600 \(\times\) 600 pixels), Barbara (512 \(\times\) 512 pixels), fence (500 \(\times\) 500 pixels), peppers (256 \(\times\) 256 pixels), and baboon (256 \(\times\) 256 pixels). These twelve images are frequently used in image processing and have a high reference value. We downsampled the reference images by direct extraction to generate LR images and then performed a 2 \(\times\) 2 image interpolation on the LR images to generate HR images of the same size as the reference images, enabling us to compare the experimental outcomes of each approach. Table 2 displays the PSNR results obtained from all of the interpolation methods under consideration, demonstrating that PCI and our proposed method outperformed all other methods. Furthermore, when comparing the methods for all of the test images, the average PSNR gain produced by the proposed method was close to that of PCI and better than all methods other than PCI. The proposed method provided the best PSNR perfor  
Figure 9: Structure of the proposed method. mance for images with sharper and more distinct edges, such as the test images \"baboon\" and \"wheel\". Aside from the common practice of measuring the PSNR for objective performance evaluation, another image quality assessment metric known as structural similarity (SSIM) [29] was used to assess image quality because it correlates well with human visual perception. Table 3 reports the SSIM results (in dB) for all of the interpolation methods under consideration, demonstrating that the proposed method provided better SSIM performance for images with sharper and more distinct edges, such as the test images \"butterfly\", \"wheel\", and \"baboon\". Although the PCI method was significantly better than all other methods, the proposed method was close to PCI, CED and better than all methods other than PCI and CED in terms of average SSIM values. The ability of a method to preserve the edges of an image is measured by the EPI (edge preservation index) [31]. Table 4 compares the edge preservation of each method when processing 12 images. The closer the EPI value is to 1, the better the method's edge preservation ability. The average EPI gain produced by the proposed method was better than other methods. Furthermore, the proposed method achieved the highest EPI values  
Figure 10: Test images. (**a**) cameraman; (**b**) house; (**c**) butterfly; (**d**) bike; (**e**) boats; (**f**) wheel; (**g**) airplane; (**h**) baboon; (**i**) stars; (**j**) barbara; (**k**) peppers; (**l**) fence.