1. A computer-implemented process for multi-pass resampling of a digital image, comprising using a computer to perform the following process actions: in a first pass through the image, computing a vertical upsampling factor representing the degree to which the image is to be upsampled in the vertical direction, wherein the vertical upsampling factor is set to a prescribed value whenever there is no substantial possibility of horizontal aliasing during said resampling of the image, and upsampling the image in the vertical direction by said vertical upsampling factor, whenever said vertical upsampling factor does not equal said prescribed value; in a second pass through the image, horizontally shearing and scaling the image in a prescribed manner employing a horizontal filtering, computing a horizontal upsampling factor representing the degree to which the image is to be upsampled in the horizontal direction, wherein the horizontal upsampling factor is set to a prescribed value whenever there is no substantial possibility of vertical aliasing during said resampling of the image, and upsampling the image in the horizontal direction by said horizontal upsampling factor, whenever said horizontal upsampling factor does not equal said prescribed value; in a third pass through the image, applying a low pass filtering to the image in the vertical direction, vertically downsampling the image to a prescribed degree, whenever the image was vertically upsampled, and vertically shearing and scaling the image in a prescribed manner employing a vertical filtering; and in a fourth pass through the image, applying a low pass filtering to the image in the horizontal direction, and horizontally downsampling the image to a prescribed degree, whenever the image was horizontally upsampled.