IFS coding of non-homogeneous fractal images using Grobner bases

This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of nonhomogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. An experimental result shows that the computational time for encoding the non-homogeneous fractal image “Curl” of 256×256 pixels and 256 gray levels is 207 seconds on a PC with a 233 MHz Pentium II processor