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An Encoding Algorithm for IFS Coding of Homogeneous Fractal Images Using Univariate Polynomial Manipulation
Toshimizu ABIKO Masayuki KAWAMATA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1999/08/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
fractal, iterated function system, inverse problem, polynomial manipulation, intelligent signal processing,
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This paper proposes a fast encoding algorithm for iterated function system (IFS) coding of gray-level homogeneous fractal images. In order to realize IFS coding of high order fractal images, it is necessary to solve a set of simultaneous equations with many unknowns. Solving the simultaneous equations using a multi-dimensional, numerical root-finding method is however very time consuming. As preprocessing of numerical computation, the proposed algorithm employs univariate polynomial manipulation, which requires less computation time than multivariate polynomial manipulation. Moreover, the symmetry of the simultaneous equations with respect to the displacement coefficients enables us to derive an equation with a single unknown from the simultaneous equations using univariate polynomial manipulation. An experimental result is presented to illustrate that the encoding time of the proposed algorithm is about 5 seconds on a personal computer with a 400 MHz Pentium II processor.