Fractal Image Compression using Hierarchical Classification of Sub-images

Nilavra Bhattacharya, Swalpa Kumar Roy, Utpal Nandi, Soumitro Banerjee

2015

Abstract

In fractal image compression (FIC) an image is divided into sub-images (domains and ranges), and a range is compared with all possible domains for similarity matching. However this process is extremely time-consuming. In this paper, a novel sub-image classification scheme is proposed to speed up the compression process. The proposed scheme partitions the domain pool hierarchically, and a range is compared to only those domains which belong to the same hierarchical group as the range. Experiments on standard images show that the proposed scheme exponentially reduces the compression time when compared to baseline fractal image compression (BFIC), and is comparable to other sub-image classification schemes proposed till date. The proposed scheme can compress Lenna (512x512x8) in 1.371 seconds, with 30.6 dB PSNR decoding quality (140x faster than BFIC), without compromising compression ratio and decoded image quality.

References

  1. Barnsley, M. F. (1988). Fractals Everywhere. Academic Press, New York.
  2. Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. (2009). Introduction to Algorithms. MIT press, Cambridge, MA, U.S.A.
  3. Duh, D.-J., Jeng, J., and Chen, S.-Y. (2005). Dct based simple classification scheme for fractal image compression. Image and vision computing, 23(13):1115-1121.
  4. Edgar, G. (2007). Measure, topology, and fractal geometry. Springer.
  5. Falconer, K. (2013). Fractal geometry: mathematical foundations and applications. John Wiley & Sons.
  6. Fisher, Y., editor (1994). Fractal Image Compression: Theory and Application. Springer-Verlag, New York.
  7. Han, J. (2008). Fast fractal image compression using fuzzy classification. In Fuzzy Systems and Knowledge Discovery, 2008. FSKD'08. Fifth International Conference on, volume 3, pages 272-276. IEEE.
  8. Jacquin, A. E. (1992). Image coding based on a fractal theory of iterated contractive image transformations. Image Processing, IEEE Transactions on, 1(1):18-30.
  9. Jayamohan, M. and Revathy, K. (2012). An improved domain classification scheme based on local fractal dimension. Indian Journal of Computer Science and Engineering (IJCSE), 3(1):138-145.
  10. Tong, C. S. and Pi, M. (2001). Fast fractal image encoding based on adaptive search. Image Processing, IEEE Transactions on, 10(9):1269-1277.
  11. Tseng, C.-C., Hsieh, J.-G., and Jeng, J.-H. (2008). Fractal image compression using visual-based particle swarm optimization. Image and Vision Computing, 26(8):1154-1162.
  12. Wang, J. and Zheng, N. (2013). A novel fractal image compression scheme with block classification and sorting based on pearson's correlation coefficient.
  13. Wang, Z., Zhang, D., and Yu, Y. (2000). Hybrid image coding based on partial fractal mapping. Signal Processing: Image Communication, 15(9):767-779.
  14. Wu, X., Jackson, D. J., and Chen, H.-C. (2005). A fast fractal image encoding method based on intelligent search of standard deviation. Computers & Electrical Engineering, 31(6):402-421.
  15. Xing, C., Ren, Y., and Li, X. (2008). A hierarchical classification matching scheme for fractal image compression. In Image and Signal Processing, 2008. CISP'08. Congress on, volume 1, pages 283-286. IEEE.
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Paper Citation


in Harvard Style

Bhattacharya N., Roy S., Nandi U. and Banerjee S. (2015). Fractal Image Compression using Hierarchical Classification of Sub-images . In Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015) ISBN 978-989-758-089-5, pages 46-53. DOI: 10.5220/0005265900460053


in Bibtex Style

@conference{visapp15,
author={Nilavra Bhattacharya and Swalpa Kumar Roy and Utpal Nandi and Soumitro Banerjee},
title={Fractal Image Compression using Hierarchical Classification of Sub-images},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015)},
year={2015},
pages={46-53},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005265900460053},
isbn={978-989-758-089-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015)
TI - Fractal Image Compression using Hierarchical Classification of Sub-images
SN - 978-989-758-089-5
AU - Bhattacharya N.
AU - Roy S.
AU - Nandi U.
AU - Banerjee S.
PY - 2015
SP - 46
EP - 53
DO - 10.5220/0005265900460053