Skip to main content
  • Research Article
  • Open access
  • Published:

Adaptation of Zerotrees Using Signed Binary Digit Representations for 3D Image Coding


Zerotrees of wavelet coefficients have shown a good adaptability for the compression of three-dimensional images. EZW, the original algorithm using zerotree, shows good performance and was successfully adapted to 3D image compression. This paper focuses on the adaptation of EZW for the compression of hyperspectral images. The subordinate pass is suppressed to remove the necessity to keep the significant pixels in memory. To compensate the loss due to this removal, signed binary digit representations are used to increase the efficiency of zerotrees. Contextual arithmetic coding with very limited contexts is also used. Finally, we show that this simplified version of 3D-EZW performs almost as well as the original one.



  1. Grossmann A, Morlet J: Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM Journal of Mathematical Analysis 1984,15(4):723-736. 10.1137/0515056

    Article  MathSciNet  MATH  Google Scholar 

  2. Mallat SG: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 1989,11(7):674-693. 10.1109/34.192463

    Article  MATH  Google Scholar 

  3. Daubechies I: The wavelet transform, time-frequency localization and signal analysis. IEEE Transactions on Information Theory 1990,36(5):961-1005. 10.1109/18.57199

    Article  MathSciNet  MATH  Google Scholar 

  4. Antonini M, Barlaud M, Mathieu P, Daubechies I: Image coding using wavelet transform. IEEE Transactions on Image Processing 1992,1(2):205-220. 10.1109/83.136597

    Article  Google Scholar 

  5. Ramchandran K, Vetterli M: Best wavelet packet bases in a rate-distortion sense. IEEE Transactions on Image Processing 1993,2(2):160-175. 10.1109/83.217221

    Article  Google Scholar 

  6. Information technology—JPEG 2000 image coding system: core coding system, ISO/IEC 15 444-1, 2002

  7. Shapiro JM: Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing 1993,41(12):3445-3462. 10.1109/78.258085

    Article  MATH  Google Scholar 

  8. Said A, Pearlman WA: A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology 1996,6(3):243-250. 10.1109/76.499834

    Article  Google Scholar 

  9. Taubman D: High performance scalable image compression with EBCOT. IEEE Transactions on Image Processing 2000,9(7):1158-1170. 10.1109/83.847830

    Article  Google Scholar 

  10. Christophe E, Mailhes C, Duhamel P: Best anisotropic 3-D wavelet decomposition in a rate-distortion sense. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), May 2006, Toulouse, France 2: 17-20.

    Google Scholar 

  11. Christophe E, Mailhes C, Duhamel P: Hyperspectral image compression: adapting SPIHT and EZW to anisotropic 3-D wavelet coding. submitted to IEEE Transactions on Image Processing

  12. He C, Dong J, Zheng YF: Optimal 3-D coefficient tree structure for 3-D wavelet video coding. IEEE Transactions on Circuits and Systems for Video Technology 2003,13(10):961-972. 10.1109/TCSVT.2003.816514

    Article  Google Scholar 

  13. Fowler JE: QccPack—Quantization, Compression, and Coding Library. 2006,

    Google Scholar 

  14. Bilgin A, Zweig G, Marcellin MW: Three-dimensional image compression with integer wavelet transforms. Applied Optics 2000,39(11):1799-1814. 10.1364/AO.39.001799

    Article  Google Scholar 

  15. Arno S, Wheeler FS: Signed digit representations of minimal Hamming weight. IEEE Transactions on Computers 1993,42(8):1007-1010. 10.1109/12.238495

    Article  Google Scholar 

  16. Prodinger H: On binary representations of integers with digit -1, 0, 1. Integers Electronic Journal of Combinatorial Number Theory 2000., 0:

    Google Scholar 

  17. Joye M, Yen S-M: Optimal left-to-right binary signed-digit recoding. IEEE Transactions on Computers 2000,49(7):740-748. 10.1109/12.863044

    Article  MATH  Google Scholar 

  18. Okeya K, Schmidt-Samoa K, Spahn C, Takagi T: Signed Binary representations revisited. In Advances in Cryptology—CRYPTO 2004, Lecture Notes in Computer Science. Volume 3152. Springer, New York, NY, USA; 2004:123-139. 10.1007/978-3-540-28628-8_8

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Emmanuel Christophe.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Christophe, E., Duhamel, P. & Mailhes, C. Adaptation of Zerotrees Using Signed Binary Digit Representations for 3D Image Coding. J Image Video Proc 2007, 054679 (2007).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: