One embodiment of the present invention provides a system that uses nonlinear filtering while resizing an image to preserve sharp detail. The system starts with an original image, which is a digital image comprised of a plurality of pixels. Next, the system resizes the original image. This involves first producing an initial resized image by using neighboring pixel values in the original image (or a conventional resizing operation) to produce initial values for subpixel locations in the original image. The system then applies a nonlinear filter using pixel values in the original and initial resized images to produce a resized output image. When this nonlinear filter updates pixel values, it weights the contributions of neighboring pixels nonlinearly. This non-linear weighting of neighboring pixels can be used to significantly reduce (or eliminate) the mixing pixel values from both sides of a sharp edge caused by conventional linear filters, and can thereby alleviate the problem of blurring sharp edges during image resizing operations.