Bakward Filtering of Images by Iterating Forward Filters

Given a filtering operation for images, we consider a problem for inverting it. If the algorithm of the original,i.e. forward filter is explicitly expressed, its inversion is tractable. However, if its algorithm is unknown exactly, it is hard to be reversed. We present, in this paper, a simple solution for this problem only by iterating the forward filter. This method can be used for a wide class of image filters including ones built in photo-retouch softwares. Examples are shown for smoothing, sharpening, halftoning and resizing filters.