HEVC Intra Mode Selection Using Benford’s Law


In this paper, Benford’s law (BF) is analyzed and its feasibility is presented to solve the complexity issue of high-efficiency video coding (HEVC). Secondly, the intra modes selected for the current block are modeled using BF’s curve to identify the most important intra modes. Finally, the intra mode computation process is terminated when the probability of these intra modes does not follow BF’s curve. This termination results in an early mode decision algorithm that reduces the complexity of HEVC. Experimental results on HEVC’s dataset show that the proposed algorithm reduces the complexity of the HEVC by 32.77% and the increase in BD-BR (Bjontegaard delta bit rate) is only 1.62%.

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  1. 1.

    E. Acebo, M. Sbert, Benford’s law for natural and synthetic images. in Proceedings of the First Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging, (2005) pp. 169–176. Eurographics Association

  2. 2.

    G. Bjontegaard, Calculation of average PSNR differences between RD-curves. VCEG-M33 (2001)

  3. 3.

    Bossen, F. Common test conditions and software reference configurations. Joint Collaborative Team on Video Coding (JCT-VC), JCTVC-F900 (2011)

  4. 4.

    B. Frank, The law of anomalous numbers. Proc. Am. Philos. Soc. 78, 551–572 (1938)

    Google Scholar 

  5. 5.

    D. Gwon, H. Choi, Relative SATD based Minimum Risk Bayesian Framework for Fast Intra Decision of HEVC. KSII Trans. Internet Inf. Syst. 13(1), (2019)

  6. 6.

    S. Harize, H. Semira, M. Benouaret, N. Doghmane, Hardware implementation and performance evaluation of the HEVC intra-predicted \(4\times 4\) blocks transforms. Circuits Syst. Signal Process. 36(5), 2050–2074 (2017)

    Article  Google Scholar 

  7. 7.

    HEVC Test Model. url: https://hevc.hhi.frauhofer.de/svn/svn_HEVCSoftware/. Accessed Aug 2016

  8. 8.

    E. Hosseini, F. Pakdaman, M.R. Hashemi, M. Ghanbari, A computationally scalable fast intra coding scheme for HEVC video encoder. Multimed. Tools Appl. 78(9), 11607–11630 (2019)

    Article  Google Scholar 

  9. 9.

    Q. Hu, Z. Shi, X. Zhang, Z. Gao, Fast HEVC intra mode decision based on logistic regression classification, in IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB), 2016, (2016), pp. 1–4. IEEE

  10. 10.

    B. Huang, Z. Chen, Q. Cai, M. Zheng, D. Wu, Rate-distortion-complexity optimized coding mode decision for HEVC. IEEE Trans. Circuits Syst. Video Technol. (2019)

  11. 11.

    T. Junaid, Guided filter based intra mode accelerator for HEVC. Multimed. Tools Appl. pp. 1–20 (2020)

  12. 12.

    I.-K. Kim, J. Min, T. Lee, W.-J. Han, J.H. Park, Block partitioning structure in the HEVC standard. IEEE Trans. Circuits Syst. Video Technol. 22(12), 1697–1706 (2012)

    Article  Google Scholar 

  13. 13.

    S. Kuanar, C. Conly, K.R. Rao, Deep learning based HEVC in-loop filtering for decoder quality enhancement, in 2018 Picture Coding Symposium (PCS) (2018), pp. 164–168. IEEE

  14. 14.

    S. Kuanar, K.R. Rao, C. Conly, Fast Mode decision in HEVC intra prediction, using region wise CNN feature classification, in 2018 IEEE International Conference on Multimedia and Expo Workshops (ICMEW) (2018), pp. 1–4. IEEE

  15. 15.

    S. Kuanar, K.R. Rao, M. Bilas, J. Bredow, Adaptive CU mode selection in hEVC intra prediction: a deep learning approach. Circuits Syst. Signal Process. 38, 5081–5102 (2019)

    Article  Google Scholar 

  16. 16.

    K.-Y. Liao, J.-F. Yang, M.-T. Sun, Rate-distortion cost estimation for H. 264/AVC. IEEE Trans. Circuits Syst. Video Technol. 20(1), 38–49 (2010)

    Article  Google Scholar 

  17. 17.

    Z. Liu, Y. Xianyu, Y. Gao, S. Chen, X. Ji, D. Wang, CU partition mode decision for HEVC hardwired intra encoder using convolution neural network. IEEE Trans. Image Process. 25(11), 5088–5103 (2016)

    MathSciNet  Article  Google Scholar 

  18. 18.

    M.J. Nigrini, I’ve got your number. J. Account. 187(5), 79–83 (1999)

    Google Scholar 

  19. 19.

    J.R. Ohm, G.J. Sullivan, H. Schwarz, T.K. Tan, T. Wiegand, Comparison of the coding efficiency of video coding standards including high efficiency video coding (HEVC). IEEE Trans. Circuits Syst. Video Technol. 22(12), 1669–1684 (2012)

    Article  Google Scholar 

  20. 20.

    W. Peng, N. Cui, Z. Guangyuan, L. Kefeng, R-Lambda model based CTU-level rate control for intra frames in HEVC. Multimed. Tools Appl. pp. 1–15 (2017)

  21. 21.

    E.L. Presman, I.M. Sonin, The best choice problem for a random number of objects. Theory Probabl. Appl. 17(4), 657–668 (1973)

    Article  Google Scholar 

  22. 22.

    D. Ruiz, G. Fernandez-Escribano, V. Adzic, H. Kalva, J.L. Martinez, P. Cuenca, Fast CU partitioning algorithm for HEVC intra coding using data mining. Multimed. Tools Appl. 76(1), 861–894 (2017)

    Article  Google Scholar 

  23. 23.

    Z. Sheng, D. Zhou, H. Sun, S. Goto, Low-complexity rate-distortion optimization algorithms for HEVC intra prediction, in International Conference on Multimedia Modeling, (2014), pp. 541–552. Springer, Cham

  24. 24.

    Y. Song, Y. Zeng, X. Li, B. Cai, G. Yang, Fast CU size decision and mode decision algorithm for intra prediction in HEVC. Multimed. Tools Appl. 76(2), 2001–2017 (2017)

    Article  Google Scholar 

  25. 25.

    H.L. Tan, C.H. Yeo, Y.H. Tan, Z.G. Li, Non CE6: Unification of the number of intra prediction modes. Joint Collaborative Team Video Coding (JCT-VC) ITU-T VCEG ISO/IEC MPEG, document JCTVCH0166, San Jose, CA, USA (2012)

  26. 26.

    J. Tariq, S. Kwong, Efficient intra and most probable mode (MPM) selection based on statistical texture features, in IEEE International Conference on Systems, Man, and Cybernetics (SMC), 2015 (2015), pp. 1776–1781. IEEE

  27. 27.

    J. Tariq, S. Kwong, Hybrid fast intra mode decision and early termination of prediction unit (PU) splitting for HEVC, in IEEE International Conference on Systems, Man, and Cybernetics (SMC), (2015), pp. 1782–1786. IEEE

  28. 28.

    J. Tariq, RD-cost as statistical inference for early intra mode decision in HEVC. Multimed. Tools Appl. 78, 1–19 (2019)

    Article  Google Scholar 

  29. 29.

    J. Tariq, High-performance intra-mode accelerator for HEVC. Vis. Comput. 35, 1–15 (2019)

    Article  Google Scholar 

  30. 30.

    J. Tariq, Intra mode selection using classical secretary problem (CSP) in high efficiency video coding (HEVC). Multimed. Tools Appl. 78, 1–23 (2019)

    Article  Google Scholar 

  31. 31.

    J. Tariq, S. Kwong, Adaptive stopping strategies for fast intra mode decision in HEVC. J. Vis. Commun. Image Represent. 51, 1–13 (2018)

    Article  Google Scholar 

  32. 32.

    J. Tariq, S. Kwong, H. Yuan, HEVC intra mode selection based on rate distortion (RD) cost and sum of absolute difference (SAD). J. Vis. Commun. Image Represent. 35, 112–119 (2016)

    Article  Google Scholar 

  33. 33.

    J. Tariq, S. Kwong, H. Yuan, Spatial/temporal motion consistency based MERGE mode early decision for HEVC. J. Vis. Commun. Image Represent. 44, 198–213 (2017)

    Article  Google Scholar 

  34. 34.

    J. Tariq, A. Armghan, A. Ijaz, I. Ashraf, Pure intra mode decision in HEVC using optimized firefly algorithm. J. Vis. Commun. Image Represent. 68, 102766 (2020)

    Article  Google Scholar 

  35. 35.

    R. Tian, Y. Zhang, M. Duan, X. Li, Adaptive intra mode decision for HEVC based on texture characteristics and multiple reference lines. Multimed. Tools Appl. 78(1), 289–310 (2019)

    Article  Google Scholar 

  36. 36.

    K. Ugur, K. Andersson, A. Fuldseth, G. Bjontegaard, L.P. Endresen, J. Lainema, A. Hallapuro et al., High performance, low complexity video coding and the emerging HEVC standard. IEEE Trans. Circuits Syst. Video Technol. 20(12), 1688–1697 (2010)

    Article  Google Scholar 

  37. 37.

    L.-L. Wang, W.-C. Siu, Novel adaptive algorithm for intra prediction with compromised modes skipping and signaling processes in HEVC. IEEE Trans. Circuits Syst. Video Technol. 23(10), 1686–1694 (2013)

    Article  Google Scholar 

  38. 38.

    A.R. Yamghani, F. Zargari, Compressed domain video abstraction based on I-Frame of HEVC coded videos. Circuits Syst. Signal Process. 38(4), 1695–1716 (2019)

    Article  Google Scholar 

  39. 39.

    Z. Yan, S.-Y. Cho, S. Welsen, Fast Intra Prediction Mode Decision for HEVC Using Random Forest, in Proceedings of the 2019 International Conference on Image, Video and Signal Processing (2019), pp. 45–49. ACM

  40. 40.

    C.-H. Yeh, M.-F. Li, M.-J. Chen, M.-C. Chi, X.-X. Huang, H.-W. Chi, Fast mode decision algorithm through inter-view rate-distortion prediction for multiview video coding system. IEEE Trans. Ind. Inf. 10(1), 594–603 (2014)

    Article  Google Scholar 

  41. 41.

    H. Zhang, Z. Ma, Fast intra prediction for high efficiency video coding, in Pacific-Rim Conference on Multimedia, (2012), pp. 568–577. Springer, Berlin

  42. 42.

    H. Zhang, Z. Ma, Fast intra mode decision for high efficiency video coding (HEVC). IEEE Trans. Circuits Syst. Video Technol. 24(4), 660–668 (2014)

    Article  Google Scholar 

  43. 43.

    Y. Zhang, S. Kwong, G. Zhang, Z. Pan, H. Yuan, G. Jiang, Low complexity HEVC INTRA coding for high-quality mobile video communication. IEEE Trans. Ind. Inf. 11(6), 1492–1504 (2015)

    Article  Google Scholar 

  44. 44.

    T. Zhang, M.-T. Sun, D. Zhao, W. Gao, Fast intra-mode and CU size decision for HEVC. IEEE Trans. Circuits Syst. Video Technol. 27(8), 1714–1726 (2017)

    Article  Google Scholar 

  45. 45.

    L. Zhao, L. Zhang, S. Ma, D. Zhao, Fast mode decision algorithm for intra prediction in HEVC, in Visual Communications and Image Processing (VCIP), (2011), pp. 1–4. IEEE

  46. 46.

    T. Zhao, S. Kwong, H. Wang, C.-C.J. Kuo, H. 264/SVC mode decision based on optimal stopping theory. IEEE Trans. Image Process. 21(5), 2607–2618 (2012)

    MathSciNet  Article  Google Scholar 

  47. 47.

    J. Zhu, Z. Liu, D. Wang, Q. Han, Y. Song, Fast prediction mode decision with Hadamard transform based rate-distortion cost estimation for HEVC intra coding, in 20th IEEE International Conference on Image Processing (ICIP), 2013 (2013), pp. 1977–1981. IEEE

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Tariq, J., Ijaz, A. HEVC Intra Mode Selection Using Benford’s Law. Circuits Syst Signal Process (2020). https://doi.org/10.1007/s00034-020-01482-y

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  • Benford’s law
  • Intra mode
  • Video coding
  • Complexity reduction