Abstract
A recent trend in computer graphics and image processing is to use Iterated Function System (IFS) to generate and describe both man-made graphics and natural images. Jacquin was the first to propose a fully automatic gray scale image compression algorithm which is referred to as a typical static fractal transform based algorithm in this paper. By using this algorithm, an image can be condensely described as a fractal transform operator which is the coombination of a set of fractal mappings. When the fractal transform operator is iteratedly applied to any initial image, a unique attractor (reconstructed image) can be achieved. In this paper, a dynamic fractal transform is presented which is a modification of the static transform. Instead of being fixed, the dynamic transform operator varies in each decoder iteration, thus differs from static transform operators. The new transform has advantages in improving coding efficiency and shows better convergence for the decoder.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Mandelbrot B B. The Fractal Geometry of Nature. Freeman, San Francisco, 1982.
Barnsley M F, Sloan A D. A better way to compress images.BYTE Magazine, 1988, 13(1): 215–223.
Jacquin A E. A fractal theory of iterated markov operators with applications to digital image coding. Ph.D. Dissertation, Georgia Institute of Technology, Aug. 1989.
Jacquin A E. Image coding based on a fractal theory of iterated contractive image transformations.IEEE Trans. on Image Processing, 1992, 1(1): 18–30.
Jacobs E W, Fisher Y, Boss R D. Image compression: A study of the iterated transform method.Signal Processing, 1992, 29(3): 251–263.
Fang Yudong, Yu Yinglin. A quick fractal image compression coding method. (in Chinese)Acta Electronica Sinica, 1996, 24(1): 29–34.
Wang Zhou, Yu Yinglin. A novel fractal image coding approach. (in Chinese)Journal of China Institute of Communications, 1996, 17(3): 84–90.
Author information
Authors and Affiliations
Additional information
This work is supported by the National Natural Science Foundation of China, the “Climbing” Project of China and the Natural Science Foundation of Guangdong Province.
Wang Zhou was born in January 1972. He received his B.S. degree from Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, in 1993, majoring in information engineering with a minor in applied mathematics. He received his M.S. degree in communication and electronic systems from South China University of Technology, Guangzhou, in 1995 and is currently pursuing his Ph. D degree at the same university. His research interests include image processing, fractals and neural networks.
Yu Yinglin was born in 1932. He graduated from South China University of Technology (formerly South China Institute of Technology) in 1953, majoring in electronic and electrical engineering. He received the Associate Doctor's degree from the Institute of Electronics, The Chinese Academy of Sciences in 1961. He is presently a professor of the Department of Electronic and Communication Engineering, South China University of Technology. His current research interests are in the fields of image processing, signal processing, pattern recognition and neural networks.
Rights and permissions
About this article
Cite this article
Wang, Z., Yu, Y. Dynamic fractal transform with applications to image data compression. J. of Comput. Sci. & Technol. 12, 202–209 (1997). https://doi.org/10.1007/BF02948970
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02948970