Simplified method of testing for convergence in fractal image coding schemes

In fractal image coding the original image is approximated by a unique fixpoint of a contractive affine transformation. To ensure convergence at the decoder an eigenvalue calculation of the transformation matrix during the encoding process is necessary to admit scaling coefficients larger than one. Due to the huge dimension of the transformation matrix the eigenvalue calculation is in general computationally infeasible. This paper presents a method to reduce the dimension of this matrix dramatically. The result of this method is a simple rule to create the reduced matrix directly without using the original matrix. Based on this rule a hierarchical method is presented, which allows us to test rather general fractal coding schemes for convergence.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.