Abstract: Image details and edge features play a very important role in the visual effect of images. Therefore, a key to image zooming is to keep image details and edges. In this paper, a new method for image zooming is proposed to construct the sampling surface piecewise defined by bicubic polynomials with the constraints of distance and edge. The method consists of two steps: constructing fitting surface and modifying surface. First, in each neighborhood region where the pixel is located, the new method constructs a quadratic polynomial sampling surface fitting pixels with distance and edge constraints; the weighted combination of all the quadratic polynomial sampling surfaces produces the general surface, which is defined piecewise by the bicubic polynomials. The magnified image obtained from the general surface has higher accuracy and better visual effect. Second, a method for constructing corrected surface is presented, which can improve the quality of the enlarged image. The corrected surface is constructed by the error image that is estimated via magnified image. Moreover, in order to reduce the computational cost of the method, the new method divides the coefficients of the quadratic polynomials into three categories, and proposes an algorithm for calculating each type of coefficients. The proposed method can magnify the image at arbitrary scales. Experimental results show that the new method not only improves the peak signal to noise ratio (PSNR) and structural similarity index (SSIM), but also improves the visual effect of the image.

Key words: image magnification, quadratic polynomial surface, corrected surface, detail and edge constraints