IFS Coding of Non-Homogeneous Fractal Images Using Gröbner Basis Techniques

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 Gröbner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associatedprobabilities method for the purpose of decreasing the computational complexity of calculating Gröbner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256× 256 pixels and 256 gray levels is about 200 seconds on a PC with a 400MHz AMD K6-III processor. key words: image coding, fractal, iterated function system, inverse problem, Gröbner basis