Fractal and linear pyramids

Pyramids are data structures with multiresolution information that have been applied successfully on many image processing and analysis tasks. We compare the properties of fractal and linear pyramids. The relations between the levels of a fractal pyramid are studied, generalising the results obtained by Baharav et al. (see Fractal Compression: Theory and applications to Digital Images, chapter 5, p.91-117. Springer-Verlag, New-York, 1995). As with linear pyramids, in order to go up one level in a fractal pyramid (decreasing resolution), a process of linear filtering and decimation must be iterated. We show that there is a direct relation between contraction and filter coefficients. Pyramids generated with several coefficient choices are also studied. The self-similarity property of PIFS (partitioned iterated function systems) becomes clear when descending one level in the fractal pyramid (increasing resolution), and unlike the case of linear pyramids, no detail signal must be added, because it is automatically created by the PIFS code.