A. Bogdan. The Fractal pyramid with application to image coding. In Proceedings of ICASSP-1995 IEEE International Conference on Acoustics, Speech and Signal Processing, Detroit, 1995.
We extend the iterated transformation theory (ITT) fractal image coding algorithm proposed by A. Jacquin [1] to generate a pyramid image representation. An ITT - coded image is modeled as the solution of a second kind functional equation. This representation is iterated to form an ITT - chain of functional equations which can serve as the framework for a multiscale signal decomposition. This formalism can be extended to accommodate hybrid ITT representations and, in the limit, ITT - coded signals as a solution of a homogeneous functional equation. Existence of the ITT - chain signal representation is shown to be connected to the eigen-structure of the linear operators of the associated functional equations. Cat each level of the ITT - chain representation, the signal is decomposed into two parts which are not orthogonal. We use this decomposition to build an ITT - pyramid representation for gray-tone images as well as for RGB color images.
@InProceedings{Bogd95a,
Author = {Bogdan, A.},
Title = {The Fractal pyramid with application to image coding},
BookTitle = {Proceedings of ICASSP-1995 IEEE International Conference on Acoustics, Speech and Signal Processing},
Address = {Detroit},
Year = {1995}
}