An encoding algorithm for IFS coding of homogeneous fractal images using univariate polynomial manipulation

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 equatio ns using a multi-dimensional, numerical root-finding method is however very time consuming. Bs preprocessing of numerical computation, the proposed al gorithm employs univariate polynomial manipulation. which requires less com putation time than multivariate polynomial manipulation. Moreover, the symm etry of the simultaneous equations with respect to the displacement coeffic ients enables us to derive an equation with a single unknown from the simul taneous equations using univariate polynomial manipulation. An experimental result is presented to illustrate that the encoding time of the proposed a lgorithm is about 5 seconds on a personal computer with a 400 MHz Pentium I I processor.