Method for checking convergence in fractal image coding

Image analysis – Image compression or coding – Transform coding

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G06K 936, G06K 946

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active

059785160

ABSTRACT:
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 (R.sub.i, R.sub.i+1) and into a number of domain blocks (D.sub.j, D.sub.k). 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.

REFERENCES:
Saupe et al., "Complexity Reduction Methods for Fractal Image Compression", Sep. 1994, pp. 1-20, Image Processing: Mathematical and Applications.
Siepen et al., "The Question of Convergence in Fractal Image Coding", Oct. 1998, pp. 133-138, Proceedings of the 6th Dortmund Television Seminar.
Beaumont, "Advances in block based fractal coding of still pictures", pp. 3/1-3/6, IEE Colloquium.
Jacquin, "Image coding based on a fractal theory of iterated contractive image transformations", Jan. 1992, pp. 18-30, IEEE Transactions on Image Processing.
Fisher, "Fractal Image Conpression", 1994, pp. 11-14, 50-52, 59, 61, and 145-148.
Fischer, Yuval: Fractal Image Compression, Springer-Verlag, New York, Berlin, 1994, S.48-53, S. 214-228.
Jacquin, Arnaud E.: Fractal Image Coding: A Review In: Proceedings of the IEEE, vol. 81, No. 10, Oct. 1993, S. 1451-1465.
Jaggard, Dwight L.: Special Section on Fractals in Electrical Engineering. In: Proceedings of the IEE, vol. 81, No. 10, Oct. 1993, S. 1423-S1427.
Hurtgen, B.: Contractivity of fractaltransforms for image coding. In: Electronics Letters, 30. Sep. 1993, vol. 29, No. 20, S. 1749, 1750.

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