Abstract

Fractal image compressions is a lossy compression technique for digital images. It is based on the assumptions that the image redundancies can be efficiently exploited by means of block self-affine transformations . Unlike other compression techniques it considers the interrelations between local (range blocks) and global (domain blocks) data. Use of contractive transform on the space of images encompasses a wide variety of coding scheme. However, the high computational complexity of fractal image encoding greatly restricts its application. This review gives a study of different speed ups using DCT to reduce the searching time .

References

• M. F. Barnsley and S. Demko, "Iterated function systems and the global construction of fractals," Proc. R. Soc. Lond. A, vol. 399, pp. 243–275, 1985.
• M. F. Barnsley and L. P. Hurd, Fractal Image Compression. Wellesley, MA: A. K. Peter, 1993.
• A. E. Jacquin, "Image coding based on a fractal theory of iterated contractive image transformations," IEEE Trans. Image Processing, vol. 1, pp. 18–30, Jan. 1992.
• M. F. Barnsley, "Methods and apparatus for image compression by iterated function systems," U. S. Patent 4 941 193, July 1990.
• S. Graf, "Barnsley's scheme for the fractal encoding of images," J. Complex. , vol. 8, pp. 72–78, 1992.
• M. Pi, M. K. Mandal, and A. Basu, "Image retrieval based on histogram of fractal parameters,"IEEE Trans. Multimedia, vol. 7, no. 4,pp. 597–605, Aug. 2005.
• J. H. Jeng, C. C. Tseng, and J. G. Hsieh, "Study on Huber fractal image compression," IEEE Trans. Image Process. , vol. 18, no. 5, pp. 995–1003, May 2009.
• M. Ghazel, G. H. Freeman, and E. R. Vrscay, "Fractal image denoising," IEEE Trans. Image Process. , vol. 12, no. 12, pp. 1560–1578, Dec. 2003.
• M. Ghazel, G. H. Freeman, and E. R. Vrscay, "Fractal-wavelet image denoising revisited," IEEE Trans. Image Process. , vol. 15, no. 9, pp. 2669–2675, Sep. 2006.
• S. S. Wang and S. L. Tsai, "Automatic image authentication and recovery using fractal code embedding and image inpainting," Pattern Recognit. vol. 41, no. 2, pp. 701–712, 2008.
• S. G. Lian, "Image authentication based on fractal features," Fractals vol. 16, no. 4, pp. 287–297, 2008.
• K. T. Lin and S. L. Yeh, "Encrypting image by assembling the fractal- image addition method and the binary encoding method," Opt. Commun. vol. 285, no. 9, pp. 2335–2342, 2012
• X. Tang and C. Qu, "Facial image recognition based on fractal image encoding, Bell Labs Tech. J. , vol. 15, no. 1, pp. 209–214, 2010
• Arnaud E. Jacquin "Image Coding Based On "A Fractal Theory Of Iterated Contractive Image Transformations" IEEE transactions on image processing. vol. 1 no. 1. january 1992 .
• N. I. Cho and S. U. Lee, "Fast algorithm and implementation of 2-D discrete cosine transform," IEEE Trans. Circuits Syst. , vol. 38, Mar. 1991.
• Trieu-Kien Truong, Jyh-Horng Jeng, Irving S. Reed, P. C. Lee, and Alan Q. Li"A Fast Encoding Algorithm for Fractal Compression Using the DCT Inner Product Image" IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 4, APRIL 2000
• Harjeetpal singh, Sakhi Sharma "Hybrid Image Compression Using DWT, DCT & Huffman Encoding Techniques" International Journal of Emerging Technology and Advanced Engineering (ISSN 2250-2459, Volume 2, Issue 10, October 2012)
• Salarian, M. and ; Hassanpour, H. ," A new fast no search fractal image compression in DCT domain" Machine Vision, 2007. ICMV 2007. International Conference 62-66 (2007).
• Chong Fu ; Sch. of Inf. Sci. & Eng. , Northeastern Univ. , Shenyang, China ; Zhi-liang Zhu "A DCT-Based Fractal Image Compression Method" Chaos-Fractals Theories and Applications, 2009. IWCFTA '09. International Workshop 439-443 (2009)