Encoding time reduction in fractal image compression

Abstract

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.