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An Edge-Sensing Predictor in Wavelet Lifting Structures for Lossless Image Coding

EURASIP Journal on Image and Video Processing volume 2007, Article number: 019313 (2007) Cite this article

Abstract

The introduction of lifting implementations for image wavelet decomposition generated possibilities of several applications and several adaptive decomposition variations. The prediction step of a lifting stage constitutes the interesting part of the decomposition since it aims to reduce the energy of one of the decomposition bands by making predictions using the other decomposition band. In that aspect, more successful predictions yield better efficiency in terms of reduced energy in the lower band. In this work, we present a prediction filter whose prediction domain pixels are selected adaptively according to the local edge characteristics of the image. By judicuously selecting the prediction domain from pixels that are expected to have closer relation to the estimated pixel, the prediction error signal energy is reduced. In order to keep the adaptation rule symmetric for the encoder and the decoder sides, lossless compression applications are examined. Experimental results show that the proposed algorithm provides good compression results. Furthermore, the edge calculation is computationally inexpensive and comparable to the famous Daubechies 5/3 lifting implementation.

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References

  1. Daubechies I, Sweldens W: Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications 1998,4(3):247-269. 10.1007/BF02476026

    Article  MATH  MathSciNet  Google Scholar 

  2. Claypoole RL, Davis GM, Sweldens W, Baraniuk RG: Nonlinear wavelet transforms, for image coding via lifting. IEEE Transactions on Image Processing 2003,12(12):1449-1459. 10.1109/TIP.2003.817237

    Article  MathSciNet  Google Scholar 

  3. Gerek ÖN, Çetin AE: Adaptive polyphase subband decomposition structures for image compression. IEEE Transactions on Image Processing 2000,9(10):1649-1660. 10.1109/83.869176

    Article  Google Scholar 

  4. Chan T, Zhou HM: Adaptive ENO—wavelet transforms for discontinuous functions. In Tech. Rep. CAM 99-21. Department of Mathematics, UCLA, Los Angeles, Calif, USA; 1999.

    Google Scholar 

  5. Piella G, Pesquet-Popescu B, Heijmans H: Adaptive update lifting with a decision rule based on derivative filters. IEEE Signal Processing Letters 2002,9(10):329-332. 10.1109/LSP.2002.804563

    Article  Google Scholar 

  6. Cohen A, Daubechies I, Guleryuz OG, Orchard MT: On the importance of combining wavelet-based nonlinear approximation with coding strategies. IEEE Transactions on Information Theory 2002,48(7):1895-1921. 10.1109/TIT.2002.1013132

    Article  MATH  MathSciNet  Google Scholar 

  7. Pau G, Tillier C, Pesquet-Popescu B: Optimization of the predict operator in lifting-based motion compensated temporal filtering. Visual Communications and Image Processing, January 2004, San Jose, Calif, USA, Proceedings of SPIE 5308: 712-720.

    Google Scholar 

  8. Mehrseresht N, Taubman D: Adaptively weighted update steps in motion compensated lifting based on scalable video compression. Proceedings of IEEE International Conference on Image Processing (ICIP '03), September 2003, Barcelona, Catalonia, Spain 2: 771-774.

    Google Scholar 

  9. Gouze A, Antonini M, Barlaud M, Macq B: Design of signal-adapted multidimensional lifting scheme for lossy coding. IEEE Transactions on Image Processing 2004,13(12):1589-1603. 10.1109/TIP.2004.837556

    Article  Google Scholar 

  10. Taubman D: Adaptive, non-separable lifting transforms for image compression. Proceedings of IEEE International Conference on Image Processing (ICIP '99), October 1999, Kobe, Japan 3: 772-776.

    Article  Google Scholar 

  11. Heijmans H, Piella G, Pesquet-Popescu B: Building adaptive 2D wavelet decompositions by update lifting. Proceedings of IEEE International Conference on Image Processing (ICIP '02), September 2002, Rochester, NY, USA 1: 397-400.

    Article  Google Scholar 

  12. Sweldens W: Lifting scheme: a new philosophy in biorthogonal wavelet constructions. In Wavelet Applications in Signal and Image Processing III, July 1995, San Diego, Calif, USA, Proceedings of SPIE Edited by: Laine AF, Unser MA. 2569: 68-79.

    Chapter  Google Scholar 

  13. WG01 IJS: JPEG-2000 part-1 standard. ISO/IEC 15444-1

  14. Christopoulos C, Skodras A, Ebrahimi T: The JPEG2000 still image coding system: an overview. IEEE Transactions on Consumer Electronics 2000,46(4):1103-1127. 10.1109/30.920468

    Article  Google Scholar 

  15. Taubman D, Zakhor A: Orientation adaptive subband coding of images. IEEE Transactions on Image Processing 1994,3(4):421-437. 10.1109/83.298396

    Article  Google Scholar 

  16. Velisavljević V, Beferull-Lozano B, Vetterli M, Dragotti PL: Directionlets: anisotropic multidirectional representation with separable filtering. IEEE Transactions on Image Processing 2006,15(7):1916-1933. 10.1109/TIP.2006.877076

    Article  Google Scholar 

  17. Peyré G, Mallat S: Surface compression with geometric bandelets. ACM Transactions on Graphics 2005,24(3):601-608. 10.1145/1073204.1073236

    Article  Google Scholar 

  18. Peyré G, Mallat S: Discrete bandelets with geometric orthogonal filters. Proceedings of IEEE International Conference on Image Processing (ICIP '05), September 2005, Genova, Italy 1: 65-68.

    Google Scholar 

  19. Ding W, Wu F, Li S: Lifting-based wavelet transform with directionally spatial prediction. Picture Coding Symposium, December 2004, San Francisco, Calif, USA 483-488.

    Google Scholar 

  20. Gerek ÖN, Çetin AE: A 2-D orientation-adaptive prediction filter in lifting structures for image coding. IEEE Transactions on Image Processing 2006,15(1):106-111. 10.1109/TIP.2005.859369

    Article  Google Scholar 

  21. Wang D, Zhang L, Vincent A, Speranza F: Curved wavelet transform for image coding. IEEE Transactions on Image Processing 2006,15(8):2413-2421. 10.1109/TIP.2006.875207

    Article  MathSciNet  Google Scholar 

  22. Chang C-L, Maleki A, Girod B: Direction adaptive discrete wavelet transform via directional lifting and bandeletization. Proceedings of IEEE International Conference on Image Processing (ICIP '06), October 2006, Atlanta, Ga, USA

    Google Scholar 

  23. Hibbard RH: Apparatus and method for adaptively interpolating a full color image utilizing luminance gradients. U.S. Patent 5,382,976

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Anadolu University, Eskişehir, 26470, Turkey

    ÖmerN Gerek

  2. Department of Electrical Engineering, Bilkent University, Bilkent, Ankara, 06533, Turkey

    AEnis Çetin

Authors
  1. ÖmerN Gerek
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  2. AEnis Çetin
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Correspondence to ÖmerN Gerek.

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

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Gerek, Ö., Çetin, A. An Edge-Sensing Predictor in Wavelet Lifting Structures for Lossless Image Coding. J Image Video Proc 2007, 019313 (2007). https://doi.org/10.1155/2007/19313

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  • DOI: https://doi.org/10.1155/2007/19313

Keywords

  • Decomposition Variation
  • Image Code
  • Edge Characteristic
  • Lossless Compression
  • Adaptation Rule