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 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. 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 K6-III processor.
fractal grobner basis iterated function system image coding inverse problem