GRADIENT PERCOLATION AND FRACTAL FRONTIERS IN IMAGE PROCESSING

In contrast to standard percolation where criticality is reached only for a particular value pc of the driving parameter p, gradient percolation exists without the precise tuning of a percolation parameter. For this reason it may be a common physical situation. Very generally, gradient percolation will appear in a uniform system whenever there exists a local random response to an excitation which varies in space. We show that such a situation exists in the example of photographic imaging, due to the random aspect of the photographic process. In this case gradient percolation may be used as a filter for recovering fuzzy images. This filter has the advantage of self-adjusting and to be neutral in regard to the size of the objects. In particular it could be used to increase artificially the depth of focus on photographs that are partially fuzzy.