Deferring range/domain comparisons in fractal image compression

Abstract

Fractals are a promising framework for several applications other than image coding and transmission, such as database indexing, texture mapping and pattern recognition problems such as writer authentication. However, fractal based algorithms are strongly asymmetric because, in spite of the linearity of the decoding phase, the coding process is very time consuming. Many different solutions have been proposed for this problem, but there is not yet a standard for fractal coding. In this paper we analyze the problem of complexity reduction of the image coding phase and providing a new classification technique based on an approximation error measure. We show formally that postponing range/domain comparisons with respect to a preset block, it is possible to reduce the amount of operations needed to encode each range and therefore whole the image. The proposed strategy allows a drastic complexity reduction of the coding phase. The proposed method has been compared with another fractal coding method, showing in which circumstances the proposed algorithm performs better in terms of both bit rate and/or computing time.