Abstract: The quality of the image edge plays a crucial role in the visual effect of the image,and the existing image magnification methods keep the edge of the image insignificant.To this end,an image magnification method is proposed to construct a rational polynomial surface to fit the image.First,for each pixel,taking the edge of the image as the constraint,a local fitting quadratic polynomial surface patch which can better preserve the edge features of the image is constructed.Then,according to the approximation accuracy of each surface patch to adjacent images,a rational weight function is constructed.On each square grid,the weighted combination of four quadratic polynomial surfaces generates a rational polynomial surface patch,and all rational polynomial surface patches are combined to form an overall surface.The error of the overall surface at the edge of the image is relatively large,so the error surface is constructed.The overall surface is corrected to improve the accuracy of the overall surface and the ability to preserve edge features.The ex-perimental results compared with the other seven methods show that,for the four commonly used compari-son image sets,the average PSNR and SSIM values of the magnified images generated by this method are the highest in set5,set14 and Urban100,and are the second highest in BSD100.For the three images used to compare the effect of edge preservation,proposed method has the best edge preservation ability,so the vis-ual effect is the best.In addition,the complexity and algorithm speed of proposed method belong to the same order of magnitude as Bicubic,which is suitable for real-time image magnification processing,and is sig-nificantly faster than the other six methods.