A New Probabilistic Approach for Fractal Based Image Compression

• Autorzy: Mitra S.K. , Kundu M.K. , Murthy C.A. , Bhattacharya Bhargab.B. , Acharya T.
• Języki publikacji: EN

Abstrakty

EN

Approximation of an image by the attractor evolved through iterations of a set of contractive maps is usually known as fractal image compression. The set of maps is called iterated function system (IFS). Several algorithms, with different motivations, have been suggested towards the solution of this problem. But, so far, the theory of IFS with probabilities, in the context of image compression, has not been explored much. In the present article we have proposed a new technique of fractal image compression using the theory of IFS and probabilities. In our proposed algorithm, we have used a multiscaling division of the given image up to a predetermined level or up to that level at which no further division is required. At each level, the maps and the corresponding probabilities are computed using the gray value information contained in that image level and in the image level higher to that level. A fine tuning of the algorithm is still to be done. But, the most interesting part of the proposed technique is its extreme fastness in image encoding. It can be looked upon as one of the solutions to the problem of huge computational cost for obtaining fractal code of images.

Słowa kluczowe

EN

Iterated function System (IFS); collage theorem; measure; Markov operator; image compression

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 87, nr 3-4
• Strony: 417--433
• Opis fizyczny: bibliogr. 19 poz., fot.,tab.,wykr.

Twórcy

autor

Mitra S.K.

autor

Kundu M.K.

autor

Murthy C.A.

autor

Bhattacharya Bhargab.B.

autor

Acharya T.

• Machine Intelligence Unit, Indian Statistical Institute, 203, B. T. Road, Calcutta 700108, India,

Bibliografia

• [1] Acharya, T., Bhattacharya, B. B. , Kundu,M. K.,Mitra,M.,Murthy, C. A :Method of compressing an image, U.S patent no. 6,738, 250 dt. May 18, 2004.
• [2] Barnsley, M. F.: Fractals Everywhere, Academic Press, New York, 1988.
• [3] Barnsley, M. F., Hurd, L. P.: Fractal Image Compression, AK Peters Ltd., Massachusetts, 1993.
• [4] Dudbridge, F.: Linear time fractal coding schemes, in: Fractal Image Encoding and Analysis, NATO ASI Series F, vol. 159 (Y. Fisher, Ed.), Springer Verlag, Berlin, 1998, 133-137.
• [5] Elton, J. H.: An ergodic theorem for iterated maps, Ergodic theory and Dynamical Systems, 7, 1987, 481-488.
• [6] Fisher, Y.: Fractal Image Compression: Theory and Application, Springer Verlag, New York, 1995.
• [7] Fisher, Y.: Fractal Image Encoding and Analysis. NATO ASI Series F, vol. 159, Springer Verlag, Berlin, 1998.
• [8] Fisher, Y., Jacbos, E.W., Boss, R. D.: Fractal Image Compression Using Iterated Transforms, in: Image and Text Compression (J. A.Storer, Ed.), Kluwer Academic Publishers, 1992, 35-61.
• [9] Forte, B., Vrscay, E. R.: Solving the inverse problem for measures using iterated function systems : a new approach, Adv. appl. Prob., 27, 1995, 800-820.
• [10] Graf, S.: Barnsley's scheme for the fractal encoding of images, Journal of Complexity, 8, 1992, 72-78.
• [11] Hutchinson, J.: Fractal and self similarity, Indiana Univ. J. Math., 30, 1981, 713-747.
• [12] Jacquin, A. E.: Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations, IEEE Transactions on Image Processing, 1(1), 1992, 18-30.
• [13] Jacquin, A. E.: Fractal Image Coding : A Review, Proceedings of the IEEE, 81(10), 1993, 1451-1465.
• [14] Mitra, S. K., Murthy, C. A., Kundu, M. K.: Technique for fractal image compression using Genetic Algorithm, IEEE Transactions on Image Processing, 7(4), 1998, 586-593.
• [15] Mitra, S. K., Murthy, C. A., Kundu, M. K.: Partitioned iterative function system: A new tool for digital imaging, IETE Journal of Research , 46(5),2000 ,363-370.
• [16] Thomas, L., Deravi, F.: Region-Based Fractal Image Compression using Heuristic Search, IEEE Transactions on Image Processing, 4(6), 1995, 832-838.
• [17] K. Culik II and S. Dube: Rational and affine expressions for image description, Discrete AppliedMathematics, 41, 1993, 85-120.
• [18] K. Culik II and J. Kari: Image Compression Using Weighted Finite Automata, Computer Graphics , 17(3), 1993, 305-313.
• [19] K. Culik II and J. Kari: Image-data Compression Using Edge-Optimizing Algorithm for WFA Inference, Journal of Information Processing and Management , 30(6), 1994, 829-838.