Skip to main content
SpringerLink
Log in

Discrete Cosine-Sine Type VII Transform and Fast Integer Transforms for Intra Prediction of Images and Video Coding

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The author proposes a matrix method for constructing an order N discrete cosine-sine type VII transform. Based on the method, two order 8 integer cosine-sine type VII transforms are constructed and algorithms for fast calculation of these transforms are developed, which require only integer operations. These algorithms are of low computational complexity that is 7 and 10.5 times lower and requires 23.3% and 44.2% less addition operations, respectively, compared to the well-known algorithms of the discrete sine type VII transform. These transforms have a higher coding gain performance for quality and compression ratio compared to the well-known sine transforms. Algorithms for fast calculation of 2D separable directional integer cosine and cosine-sine type VII adaptive transforms for intra prediction with 8 × 8 chroma blocks are developed. The algorithms have a low multiplicative complexity that is 6.6 and 16.5 times lower than that in the well-known algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. K. Jain, “A sinusoidal family of unitary transforms,” IEEE Trans. Patt. Anal. and Mach. Intell., Vol. 1, No. 4, 356–365 (1979).

    Article  Google Scholar 

  2. Z. Wang and B. R. Hunt, “The discrete W transform,” Appl. Math. and Comput., Vol. 16, Iss. 1, 19–48 (1985).

  3. Z. Wang, “Fast algorithms for the discrete W transform and for the discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Process, Vol. 32, No. 8, 803–816 (1984).

    Article  MathSciNet  Google Scholar 

  4. V. Britanak, K. R. Rao, and P. Yip, Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations, Academic Press Elsevier, Oxford (2007).

    Google Scholar 

  5. R. K. Chivukula and Y. A. Reznik, “Fast computing of discrete cosine and sine transforms of types VI and VII,” in: Proc. SPIE Appl. Digital Image Processing XXXIV Conf. (San Diego, California, USA, Aug 22–24, 2011), Vol. 8135, San Diego (2011), pp. 813505–813509.

  6. R. J. Clarke, Transform Coding of Images, Academic Press, London (1985).

    Google Scholar 

  7. R. J. Clarke, “Performance of Karhunen–Loève and discrete cosine transform for data having widely varying values of intersample correlation coefficient,” Electron. Lett., Vol. 19, Iss. 7, 251–253 (1983).

  8. H. B. Kekre and J. K. Solanki, “Comparative performance of various trigonometric unitary transforms for transform image coding,” Int. J. Electronics, Vol. 44, Iss. 3, 305–315 (1978).

  9. R. J. Clarke, “Application of sine transform in image processing,” Electron. Lett., Vol. 19, Iss. 13, 490–491 (1983).

  10. A. K. Jain, P. M. Famelle, and V. R. Algazi, “Image data compression,” in: M. P. Ekstrom (ed.), Digital Image Processing Technigues, Academic Press, New York (1984), pp. 188–226.

    Google Scholar 

  11. D. Salomon, A Guide to Data Compression Methods, Springer-Verlag, New York (2002).

    Book  Google Scholar 

  12. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 4th ed., Pearson, New York (2018).

    Google Scholar 

  13. A. K. Jain, “Image data compression: A review,” Proc. of IEEE, Vol. 69, Iss. 3, 349–389 (1981).

  14. J. Han, A. Saxena, and K. Rose, “Towards jointly optimal spatial prediction and adaptive transform in video/image coding,” in: Proc. IEEE Int. Conf. Acoust., Speech, Signal Process (ICASSP) (Dallas, TX, USA, March 14–19, 2010), Dallas (2010), pp. 726–729.

  15. L. O. Hnativ, “A method for constructing fast integer sine transform for image encoding and intra prediction in video encoding,” in: Proc. Intern. Sci. Conf. “Modern Informatics: Problems, Achievements and Prospects of Development” (Kyiv, Ukraine, Sept 12–13, 2013), Kyiv (2013), pp. 261–263.

  16. R. J. Clarke, “Relation between the Karhunen–Loève and cosine transforms,” IEE Proc. F (Commun., Radar & Signal Process), Vol. 128, Pt. F, No. 6, 359–360 (1981).

  17. R. J. Clarke, “Relation between the Karhunen–Loève and sine transforms,” Electron. Lett., Vol. 20, Iss. 1, 12–13 (1984).

  18. A. Saxena and F. C. Fernandes, “DCT/DST-based transform coding for intra prediction in image/video coding,” IEEE Trans. Image Process, Vol. 22, No. 10, 3974–3981 (2013).

    Article  MathSciNet  Google Scholar 

  19. Y. Ye andM. Karczewicz, “Improved intra coding,” ITU-T Q.6/SG16, Doc. VCEG-AG11, Shenzhen, China, Oct (2007).

  20. K. McCann, B. Bross, S. Sekiguchi, and W.-J. Han, “HM4: high efficiency video coding (HEVC) test model 4 encoder description,” ITU-T, Doc. JCTVC-F802, Torino, IT, July (2011).

  21. ITU-T Rec. H.265/ISO/IEC 23008-2 (2013), “Information technology — High efficiency coding and media delivery in heterogeneous environments,” Part 2: High Efficiency Video Coding (2013).

  22. C. Yeo, Y. H. Tan, Z. Li, and S. Rahardja, “Mode-dependent fast separable KLT for block-based intra coding,” ITU-T, Doc. ICTVC-B024, Geneva, CH, July (2010).

  23. J. An , X. Zhao , X. Guo, and S. Lei, “Non-CE 7: Boundary-dependent transform for inter-predicted residue,” ITU-T, Doc. JCTVC-G281, Geneva, CH, Nov (2011).

  24. A. Saxena and F. Fernandes, “CE7: Mode-dependent DCT/DST without 4 × 4 full matrix multiplication for intra prediction,” ITU-T, Doc. JCTVC-E125, Geneva, CH, March (2011).

  25. A. Saxena, F. C. Fernandes, and Y. A. Reznik, “Fast transforms for intra-prediction-based image and video coding,” in: Proc. Data Compression Conf. (Snowbird, UT, USA, March 20–22, 2013), IEEE (2013), pp. 13–22.

  26. Y. A. Reznik, “Relationship between DCT-II, DCT-VI and DST-VII transforms,” in: Proc. IEEE Intern. Conf. on Acoustics, Speech and Signal Processing (Vancouver, BC, Canada, May 26–31, 2013), IEEE (2013), pp. 5642–5646.

  27. M. Masera, M. Martina, and G. Masera, “Odd type DCT/DST for video coding: Relationships and low-complexity implementations,” in: 2017 IEEE Intern. Workshop on Signal Processing Systems (SIPS) (Lorient, France, Oct 3–5, 2017) IEEE (2017), pp. 1–6.

  28. L. O. Hnativ and V. K. Luts, “Integer modified sine-cosine transforms type VII. A construction method and separable directional adaptive transforms for intra prediction with 8 × 8 chroma blocks in image/video coding,” Cybern. Syst. Analysis, Vol. 57, No. 1, 155–164 (2021). https://doi.org/10.1007/s10559-021-00339-9.

    Article  MATH  Google Scholar 

  29. B. M. Shevchuk, V. K. Zadiraka, L. O. Hnativ, and S. V. Fraer, Technology of Multifunctional Data Processing and Transmission in Monitoring Networks [in Ukrainian], Naukova Dumka, Kyiv (2010).

  30. L. O. Hnativ and V. K. Luts, “A method for constructing mode-dependent fast separable integer KLT for adaptive coding of images and video,” in: Proc. Intern. Conf. “Computing Optimization Issues” (COI-2013), Katsyveli, Crimea, Ukraine (2013), pp. 68–69.

  31. L. O. Hnativ and V. K. Luts, “Algorithms for fast implementation of 4-point integer sine type VII transforms without multiplication and separable directional adaptive transforms for intra prediction in image/video coding,” Cybern. Syst. Analysis, Vol. 56, No. 1, 159–170 (2020). https://doi.org/10.1007/s10559-020-00231-y.

    Article  MATH  Google Scholar 

  32. L. O. Hnativ, “Integer cosine transforms for high-efficiency image and video coding,” Cybern. Syst. Analysis, Vol. 52, No. 5. 802–816 (2016). https://doi.org/10.1007/s10559-016-9881-7.

    Article  MathSciNet  MATH  Google Scholar 

  33. A. Fuldseth, G. Bjøntegaard, M. Sadafale, and V. Sze, “CE10: Core transform design for HEVC,” ITU-T, Doc. JCTVC-G495, Geneva, CH, Nov (2011).

  34. R. Joshi, Y. Reznik, J. K. Sole, and M. Karczewicz, “CE-10: Scaled orthogonal integer transforms supporting recursive factorization structure,” ITU-T, Doc. JCTVC-F352, Torino, IT, July (2011).

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    L. O. Hnativ

Authors
  1. L. O. Hnativ
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. O. Hnativ.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2021, pp. 175–185.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hnativ, L.O. Discrete Cosine-Sine Type VII Transform and Fast Integer Transforms for Intra Prediction of Images and Video Coding. Cybern Syst Anal 57, 827–835 (2021). https://doi.org/10.1007/s10559-021-00408-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-021-00408-z

Keywords

Search

Navigation