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

Toshimizu ABIKO  Masayuki KAWAMATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.8   pp.1575-1581
Publication Date: 2000/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Image/Visual Signal Processing
image coding,  fractal,  iterated function system,  inverse problem,  Grobner basis,  

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This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of non-homogeneous 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 256256 pixels and 256 gray levels is about 200 seconds on a PC with a 400 MHz AMD K6-III processor.