An Encoding Algorithm for IFS Coding of Homogeneous Fractal Images Using Univariate Polynomial Manipulation

摘要

This paper proposes a fast encoding algorithm for iterated function system (IFS) coding of gray-level homoge- neous fractal images. In order to realize IFS coding of high order fractal images, it is necessary to solve a set of simultaneous equa- tions with many unknowns. Solving the simultaneous equations using a multi-dimensional, numerical root-finding method is how- ever very time consuming. As preprocessing of numerical com- putation, the proposed algorithm employs univariate polynomial manipulation, which requires less computation time than mul- tivariate polynomial manipulation. Moreover, the symmetry of the simultaneous equations with respect to the displacement co- efficients enables us to derive an equation with a single unknown from the simultaneous equations using univariate polynomial ma- nipulation. 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.