Skip to content


  • Research Article
  • Open Access

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

EURASIP Journal on Image and Video Processing20072007:054679

  • Received: 15 August 2006
  • Accepted: 18 December 2006
  • Published:


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.


  • Image Processing
  • Pattern Recognition
  • Computer Vision
  • Wavelet Coefficient
  • Image Compression


Authors’ Affiliations

CNES, BPI 1219, 18 avenue Edourad Belin, Toulouse cedex 9, 31401, France
CNRS / LSS, Supelec Plateau de Moulon, Gif-sur-Yvette, 91192, France
TeSA / IRIT, 14 port St Etienne, Toulouse, 31000, France


  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. 10.1137/0515056MathSciNetView ArticleMATHGoogle 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. 10.1109/34.192463View ArticleMATHGoogle Scholar
  3. Daubechies I: The wavelet transform, time-frequency localization and signal analysis. IEEE Transactions on Information Theory 1990,36(5):961-1005. 10.1109/18.57199MathSciNetView ArticleMATHGoogle 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. 10.1109/83.136597View ArticleGoogle 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. 10.1109/83.217221View ArticleGoogle Scholar
  6. Information technology—JPEG 2000 image coding system: core coding system, ISO/IEC 15 444-1, 2002Google Scholar
  7. Shapiro JM: Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing 1993,41(12):3445-3462. 10.1109/78.258085View ArticleMATHGoogle 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. 10.1109/76.499834View ArticleGoogle Scholar
  9. Taubman D: High performance scalable image compression with EBCOT. IEEE Transactions on Image Processing 2000,9(7):1158-1170. 10.1109/83.847830View ArticleGoogle 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 ProcessingGoogle Scholar
  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.2003.816514View ArticleGoogle Scholar
  13. Fowler JE: QccPack—Quantization, Compression, and Coding Library. 2006, 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.39.001799View ArticleGoogle Scholar
  15. Arno S, Wheeler FS: Signed digit representations of minimal Hamming weight. IEEE Transactions on Computers 1993,42(8):1007-1010. 10.1109/12.238495View ArticleGoogle 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. 10.1109/12.863044View ArticleMATHGoogle 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_8View ArticleGoogle Scholar


© Emmanuel Christophe et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.