In this paper, an effective scheme was proposed to estimate simple convex surface and simple concave surface which exist in image. This scheme is applied to input image to estimate simple convex surface or simple concave surface. When simple convex surface or simple concave surface exists, another proposed efficient interpolation scheme is used for the interpolated pixel to have the characteristics of simple convex surface or simple concave surface. The magnified image using the proposed schemes is more similar to the real image than the magnified image using the previous schemes. The PSNR values of the magnified images using the proposed schemes are greater than those of the magnified images using the previous interpolation schemes.