Fractal Image Compression

Standard graphics systems encode pictures by assigning an address and colour attribute for each point of the object resulting in a long list of addresses and attributes. Fractal geometry enables a newer class of geometrical shapes to be used to encode whole objects, thus image compression is achieved. Compression ratios of 10,000:1 have been claimed by researchers in this field. The fractal equations describing these shapes are very simple equations. Specifically, iterated function system (IFS) codes are investigated. The difficult inverse problem of finding a suitable IFS code whose fractal image is to represent the real image and hence achieve compression is investigated through the use of: a) a library of IFS codes and complex moments, b) the method of simulated annealing, for solving non-linear equations of many parameters. Image Compression Image compression is reducing the number of bits required to represent an image in such a way that either an exact replica of the image (lossless compression) or an approximate replica (lossy compression) of the image can be retrieved. 1 M.F. BARNSLEY, A.D. SLOAN, “A better way to compress images”, BYTE, Jan 1988, p.215-223. Canonical Representation of Digital Images A digital picture consists of an n × m array of integer numbers or picture elements (pels), see Fig.1.