The fractal pyramid with applications to image coding
نویسنده
چکیده
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. At 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.
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