Encoding time reduction in fractal image compression

Summary form only given. The mathematical interpretation of fractal image compression is strongly related to Banach´s fixed point theorem. More precisely, if (X,d) represents a metric space of digital images where d is a given suitable metric, we want to think of an element of X that we wish to encode as a fixed point of some operator. Since we are dealing with coding images, the choice of the metric space X as well as the metric d have an enormous effect on the complexity of the code. The coding of an image f consists of finding an iterated function system (IFS), a contractive mapping W whose fixed point f is the best approximation of f. The collage theorem states that by minimizing the distance between the fixed point f and Wf, it is expected that the distance between the fixed point f and the image f will be minimized. We present a method of mapping similar regions within an image by an approximation of the collage error; this will result in writing range blocks as a linear combination of domain blocks. We also address the complexity of the encoder, by proposing a new classification scheme based on the domain and range blocks moments which will reduce the encoding time by a factor of hundreds with insubstantial loss in the image quality. Extensive simulation results confirm our claims