Towards a better compression of self similar images. II. Proofing the edge maxima matching algorithm for the IFS encoding of affine self similar binary images

An iterated function system (IFS) is a set of affine and contractive transformations. The union (so-called collage) of the subimages generated by transforming the whole image produces the image again. In the edge maxima matching algorithm the IFS-codes for a single image are calculated by affinely mapping maxima of the edge of the entire image to the corresponding maxima of the edge of each of the subimages. The three principle ideas of this algorithm to be proofed are as follows: the decomposition of the image in a minimal set of subimages is found by two adjacent edge points (so-called touching points of a subimage). These touching points are recognized by being the only points which have no affine and expanded equivalent in the image. A unique representation for each of the subimages is found by choosing the most expanded affine mappings of four edge extremes to characterise each of these image parts. An affine mapping (the IFS-code) between the image and the subimages is calculated by using an affine invariant representation through such quadruples of edge extremes.