IFS coding of non-homogeneous fractal images using Grobner basis techniques

This paper proposes a moment based encoding algorithm for iterated function system (IES) coding of nonhomogeneous fractal images with unequal probabil ities. Moment based encoding algorithms for IFS coding of non-homogeneous f ractal images require a solution of simultaneous algebraic equations that a re difficult to handle with numerical root-finding methods. The proposed al gorithm employs a variable elimination method using Grobner bases with floa ting-point coefficients in order to derive a numerically solvable equation with a, single unknown. The algorithm also employs a varying associated-pro babilities method for the purpose of decreasing the computational complexit y of calculating Grobner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256 x 256 pixels and 256 gray levels is about 200 seconds on a PC with a 400MHz AMD K 6-III processor.