1. A computer-implemented method for resizing an image which uses nonlinear filtering to preserve sharp detail, comprising: using a computer to perform the steps of: obtaining an original image, wherein the original image is a digital image which is comprised of a plurality of pixels; and resizing the original image, wherein resizing the original image involves: producing an initial resized image by using neighboring pixel values in the original image to produce initial values for subpixel locations in the original image, and applying a nonlinear filter using pixel values in both the original image and in the initial resized image to produce a resized output image, wherein the nonlinear filter weights the contributions of neighboring pixels nonlinearly while updating pixel values.