Abstract
The development of compression techniques is crucial for several applications that require efficient storage and transmission of large data volumes. Fractal theory has been used in image and video compression due to advantages such as resolution independence, high compression rate, fast decoding, among others. Fractal compression approaches explore the presence of self-similarity to remove data redundancy, allowing high compression while maintaining low quality degradation. Early fractal compression methods presented prohibitive encoding time related to the search for similar regions in the image or video. This work describes a low bit-rate 3D searchless fractal video encoder to perform fast compression with high visual fidelity. Experiments demonstrate that the results of the proposed approach are superior when compared to those obtained by state-of-the-art x264 video encoder at very low bit rates in high motion video sequences.
Similar content being viewed by others
References
CIPR Sequences (2012). http://www.cipr.rpi.edu/resource/sequences/
Test Media (2012). http://media.xiph.org/video/derf/
x264 Video Encoder (2012). http://www.videolan.org/developers/x264.html
Bani-Eqbal, B.: Enhancing the speed of fractal image compression. Opt. Eng. 34(6), 1705–1710 (1995)
Barnsley, M.F.: Fractals Everywhere. Academic Press, San Diego (1988)
Caso, G., Obrador, P., Kuo, C.C.: Fast methods for fractal image encoding. In: SPIE Visual Communication and Image Processing, Taipei, Taiwan, vol. 2501, pp. 583–594. SPIE Press, Bellingham (1995)
Chabarchine, A., Creutzburg, R.: 3D fractal compression for real-time video. In: 2nd International Symposium on Image and Signal Processing and Analysis, Pula, Croatia, pp. 570–573 (2001)
Fisher, Y.: Fractal Image Compression—Theory and Application. Springer, New York (1994)
Fisher, Y., Rogovin, D., Shen, T.: Fractal (Self-VQ) encoding of video sequences. Vis. Commun. Image Process. 2308(1), 1359–1370 (1994)
Furao, S., Hasegawa, O.: A fast no search fractal image coding method. Signal Process. Image Commun. 19(5), 393–404 (2004)
Hsu, K.C.C.: Novel prediction- and subblock-based algorithm for fractal image compression. Chaos Solitons Fractals 29(1), 215–222 (2006)
Hurd, L., Gustavus, M., Barnsley, M.: Fractal video compression. In: Thirty-Seventh IEEE Computer Society International Conference (Digest of Papers, COMPCON Spring 1992), pp. 41–42 (1992)
Jackson, D., Ren, H., Wu, X., Ricks, K.: A hardware architecture for real-time image compression using a searchless fractal image coding method. J. Real-Time Image Process. 1(3), 225–237 (2007)
Jacquin, A.: Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans. Image Process. 1(1), 18–30 (1992)
Kim, C., Kim, R., Lee, S.: Fractal coding of video sequence using circular prediction mapping and noncontractive interframe mapping. IEEE Trans. Image Process. 7(4), 601–605 (1998)
Koli, N., Ali, M.: Lossy color image compression technique using fractal coding with different size of range and domain blocks. In: International Conference on Advanced Computing and Communications, Surathkal, India, pp. 236–239 (2006)
Koli, N., Ali, M.: A survey on fractal image compression key issues. Inf. Technol. J. 7(8), 1085–1095 (2008)
Kovács, T.: A fast classification based method for fractal image encoding. Image Vis. Comput. 26(8), 1129–1136 (2008)
Krause, P.: ftc—floating precision texture compression. Comput. Graph. 34(5), 594–601 (2010)
Lai, C., Lam, K., Siu, W.: A fast fractal image coding based on Kick-out and zero contrast conditions. IEEE Trans. Image Process. 12(11), 1398–1403 (2003)
Lazar, M., Bruton, L.: Fractal block coding of digital video. IEEE Trans. Circuits Syst. Video Technol. 4(3), 297–308 (1994)
Lee, C., Lee, W.: Fast fractal image block coding based on local variances. IEEE Trans. Image Process. 7(6), 888–891 (1998)
Li, H., Novak, M., Forchheimer, R.: Fractal-based image sequence compression scheme. Opt. Eng. 32(7), 1588–1595 (1993)
de Lima, V., Schwartz, W.R., Pedrini, H.: Fast low bit-rate 3D searchless fractal video encoding. In: Conference on Graphics, Patterns and Images, Maceio, AL, Brazil (2011)
Øien, G., Lepsøy, S.: A Class of Fractal Image Coders with Fast Decoder Convergence, pp. 153–175. Springer, London (1995). Chap. Fractal Image Compression
Said, A.: Lossless Compression Handbook. Academic Press, San Diego (2003). Chap. Arithmetic Coding. Communications, Networking, and Multimedia
Saupe, D., Ruhl, M., Hamzaoui, R., Grandi, L., Marini, D.: Optimal hierarchical partitions for fractal image compression. In: IEEE International Conference on Image Processing, Chicago, IL, USA, pp. 737–741 (1998)
Tong, C., Pi, M.: Fast fractal image encoding based on adaptive search. IEEE Trans. Image Process. 10(9), 1269–1277 (2001)
Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Weinberger, M., Seroussi, G., Sapiro, G.: LOCO-I: a low complexity, context-based, lossless image compression algorithm. In: Data Compression Conference, Snowbird, UT, USA, pp. 140–149 (1996)
Wu, X., Jackson, D., Chen, H.: Novel fractal image-encoding algorithm based on a full-binary-tree searchless iterated function system. Optical Engineering 44(10) (2005)
Yao, Z., Wilson, R.: Hybrid 3D fractal coding with neighbourhood vector quantisation. EURASIP J. Appl. Signal Process. 2004, 2571–2579 (2004)
Zhu, S., Wang, Z., Belloulata, K.: A novel fractal monocular and stereo video codec based on MCP and DCP. In: IEEE International Conference on Industrial Technology, pp. 168–172. Viña del Mar, Chile (2010)
Acknowledgements
The authors are grateful to FAPESP, CAPES and CNPq for the financial support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Lima, V., Schwartz, W.R. & Pedrini, H. 3D Searchless Fractal Video Encoding at Low Bit Rates. J Math Imaging Vis 45, 239–250 (2013). https://doi.org/10.1007/s10851-012-0357-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-012-0357-8