Method for checking convergence in fractal image coding

摘要

A method is proposed for checking convergence in fractal image coding. In this case, a digitized image is divided into a number of range blocks (Ri, Ri+1) and into a number of domain blocks (Dj, Dk). A similar domain block is determined in relation to each range block. If necessary, in this process a transformation of a domain block is undertaken in order to map the domain block onto a range block. The assignment of the domain block to the range block including the transformation parameters represents the fractal code for the image. A reduced transformation matrix is set up to check convergence of the fractal code. The largest absolute eigenvalue of the transformation matrix is determined approximately. The entire method can be carried out in this case hierarchically. In a first approximation step, at least the row sum norm of each row of the reduced transformation matrix is checked. In further steps, further rows are combined to form square matrices of higher dimension. The latter are used to determine the largest absolute eigenvalues for the purpose of checking convergence.