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Madhu Peringassery Krishnan Multimedia Processing Lab, University of Texas at Arlington, TX, USA.

Implementation and Performance Analysis of 2-D Order 16 Integer Transforms in H.264/AVC and AVS-video for HD video coding. Madhu Peringassery Krishnan Multimedia Processing Lab, University of Texas at Arlington, TX, USA. Advisor: Dr. K. R. Rao. Outline. Discrete Cosine Transform (DCT-II)

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Madhu Peringassery Krishnan Multimedia Processing Lab, University of Texas at Arlington, TX, USA.

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  1. Implementation and Performance Analysis of 2-D Order 16 Integer Transforms in H.264/AVC and AVS-video for HD video coding Madhu Peringassery Krishnan Multimedia Processing Lab, University of Texas at Arlington, TX, USA. Advisor: Dr. K. R. Rao

  2. Outline • Discrete Cosine Transform (DCT-II) • Development of Integer Cosine Transform (ICT) • ICT in H.264/AVC • ICT in AVS-video • Order 16 ICT • 2-D order 16 ICT and HD video coding • Simple order 16 ICT (SICT) • Modified order 16 ICT (SICT) • binDCT-L • Implementation • Performance Analysis • Conclusions • References

  3. Discrete Cosine Transforms (ICT) • Discrete Cosine Transform (DCT-II) [1] • - • - • k, n = 0,1,2,……..,N-1 • 2-D transform is separable into two 1-D transforms evaluated • along rows followed by columns [2].

  4. Pros and Cons DCT-II • Pro : Good energy compaction capability Fast algorithms for implementation • Con : Involves floating-point arithmetic Mismatch between forward and inverse transform ICT [3] • Pro : Integer arithmetic implementation Avoid mismatch between forward and inverse transform Good energy compaction capability if well designed Fast algorithms can be developed • Con : Orthogonality depends on the elements of transform matrix

  5. Development of ICT • Approximation of DCT-II - [3] where k is scaling factor and T is ICT • Elements of T [3] - Maintain relative magnitude and signs - Posses dyadic symmetry [4] - Orthogonality

  6. H.264/AVC encoder Typical block diagram of a H.264/AVC encoder [5]

  7. H.264/AVC decoder Typical block diagram of a H.264/AVC decoder [5]

  8. ICT in H.264/AVC ICT • Order 4 ICT [6] • Order 8 ICT [7] Other transforms: • 4 × 4 Hadamard transform applied to the DC coefficients of 4 × 4 integer transforms (intra-predicted 16 x 16 macroblocks) • Additional 2 × 2 Hadamard transform applied to DC coefficients of 4 × 4 integer transforms for chroma components

  9. ICT in H.264/AVC • 4 x 4 ICT matrix - • 4 x 4/2 x 2 Hadamard matrix -

  10. ICT in H.264/AVC • 8 x 8 ICT matrix - • Non-normalized • Fast implementation [8]

  11. ICT in H.264/AVC • Flow diagram for 8 x 8 ICT [9] -

  12. ICT in H.264/AVC • Sparse matrix factors : where

  13. AVS-video encoder Typical block diagram of AVS-video encoder [10]

  14. AVS-video decoder Typical block diagram of AVS-video decoder [10]

  15. ICT in AVS-video • Order 8 ICT [11] - • Order 16 ICT : extended from order 8 ICT • Fast implementation

  16. ICT in AVS-video • Flow diagram for 8 x 8 ICT [9] -

  17. ICT in AVS-video • Sparse matrix factors : where

  18. Order 16 ICT • Approximated from order 16 DCT-II - [12] • General transform matrix [13] - ‘E’ denotes even symmetry and ‘O’ denotes odd symmetry about the solid line (mirror image and negative of mirror image)

  19. Order 16 ICT and HD video coding • Spatial correlation of HD videos are higher - [14] where E is the ensemble average operator x(n1) and x(n2): intensity values of n1,n2 1,2: mean 1,2: standard deviation • Better coding efficiency using higher order transforms

  20. Order 16 ICT and HD video coding • Prediction error : Difference between original and intra or inter predicted • macroblocks Table showing spatial correlation of prediction error

  21. Simple order 16 ICT (SICT) • Extension of order 8 ICT [15] • Low complexity • Comparable transform coding gain with DCT-II (Plot 1) • Transform matrix of order 16 SICT for AVS-video • Requires 24 shifts and 88 additions

  22. Simple order 16 ICT (SICT) • Transform matrix of order 16 SICT for H.264/AVC • Requires 20 shifts and 80 additions

  23. Simple order 16 ICT • Flow diagram 16 x 16 SICT [15]

  24. Simple order 16 ICT • Sparse matrix factors : H.264/AVC : where AVS-video : where where and order of input as shown in flow diagram

  25. Modified order 16 ICT • Low complexity (more complex than SICT) • Comparable transform coding gain (better than SICT) • Steps involved in development [9] - Order 8 ICT of H.264/AVC or AVS-video is borrowed as the even part (T8e) - Modified dyadic symmetry of odd part of order 16 DCT-II symmetry (M8o) [9]

  26. Modified order 16 ICT • Transform matrix of order 16 MICT for H.264/AVC

  27. Modified order 16 ICT • Transform matrix of order 16 MICT for AVS-video

  28. Modified order 16 ICT • Elements {x1, x3,….,x15} are {11, 11, 11, 9, 8, 6, 4, 1} • M8o is implemented in three stages M8o= M1.M2.M3 • Constraints for M1 , M2 ,M3 - Contain integers - Small magnitude - Sparse - Orthogonality • Requires 32 shifts and 150 additions

  29. Modified order 16 ICT • Flow diagram 16 x 16 MICT (shifts for M8o not shown for clarity) [9]

  30. Modified order 16 ICT • Sparse matrix factors : H.264/AVC : where AVS-video : where where and order of input as shown in flow diagram

  31. Order 16 binDCT-L • Based on Loeffler et al. factorization [16] • Planar rotation in DCT-II represented as lifting steps (shears) [17] where

  32. Order 16 binDCT-L • Rotation needing 4 multiplications and 2 additions implemented using 3 multiplications and 3 additions • Irrational parameters represented as dyadic-rational coefficients • Coding efficiency improved by tuning the approximations • Involves 51 shifts and 107 additions

  33. Order 16 binDCT-L • Flow diagram for 16 x 16 binDCT-L [18]

  34. Implementation in H.264/AVC • JM 17.2 reference software [19] • H.264 high profile • Integration of SICT, MICT and binDCT-L • Defining a parameter for selecting them (tLCT) • Simulations run on an i7 quad 4, 2.60 GHz processor ,6GB RAM I : Intra predicted frames P : Predicted frames B : Bidirectionally predicted Configuration parameters

  35. Implementation in AVS-video • RM 52e reference software [20] • AVS-video enhanced profile • Integration of SICT, MICT and binDCT-L • Defining a parameter for selecting them (tLCT) • Simulations run on an i7 quad 4, 2.60 GHz processor ,6GB RAM Configuration parameters

  36. Transform Coding gain • Measures energy compaction efficiency of transforms • Source : 1-D, zero mean, unit variance first order Markov process • Transform coding gain : - = [21] where is the covariance of the coefficients in transform domain

  37. Transform Coding gain Plot 1 Variation of transform coding gain with correlation coefficient for order 16 SICT, MICT, binDCT-L and order 16 DCT-II

  38. Transform Coding gain Comparison of transform coding gains of order 16 SICT, MICT, binDCT-L with order 16 DCT-II

  39. SICT in H.264/AVC (1280 x 720) • BD-bitrate savings [22] : 2.57 % • BD-PSNR gain [22] : 0.19 dB

  40. MICT in H.264/AVC (1280 x 720) • BD-bitrate savings : 5.30 % • BD-PSNR gain : 0.31 dB

  41. binDCT-L in H.264/AVC (1280 x 720) • BD-bitrate savings : 4.73 % • BD-PSNR gain : 0.36 dB

  42. SICT in AVS-video (1280 x 720) • BD-bitrate savings : 5.18 % • BD-PSNR gain : 0.29 dB

  43. MICT in AVS-video (1280 x 720) • BD-bitrate savings : 2.57 % • BD-PSNR gain : 0.34 dB

  44. binDCT-L in AVS-video (1280 x 720) • BD-bitrate savings : 7.45 % • BD-PSNR gain : 0.41 dB

  45. Vidyo1(1280 x 720) First frame of vidyo1

  46. Conclusions • 2-D order 16 ICTs give considerable bitrate savings or PSNR gain for HD videos • Low complexity (SICT); easy to implement • MICT and binDCT-L ; though requiring more operations, give better bitrate savings or PSNR gain

  47. References [1] N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput., vol. C-23, pp. 90-93, Jan. 1974. [2] K. R. Rao and P. Yip, “Discrete cosine transform: Algorithms, advantages, applications,” Boca Raton FL: Academic Press, 1990. [3] W. K. Cham, “Development of integer cosine transforms by the principle of dyadic symmetry”, IEE Proc. I: Communications, Speech and Vision, Vol. 136, No. 4, pp. 276-282, Aug. 1989. [4] W. K. Cham and R.J. Clarke, “Application of the principle of dyadic symmetry to the generation of orthogonal transform”, IEE Proc. F: Communications, Radar and Signal Processing, Vol. 133, No. 3, pp. 264-270, June 1986. [5] H. Kalva, “The H.264 video coding standard,” IEEE Multimedia, vol. 13, no. 4, pp. 86–90, Oct. 2006. [6] A. Luthra, G. J. Sullivan, and T. Wiegand, Eds., Special issue on the “H.264/AVC video coding standard,” IEEE Tran. CSVT, vol. 13, no. 7, pp. 148-153, July 2003.

  48. References [7] D. Marpe and T. Wiegand, “H.264/MPEG4-AVC fidelity range extensions: Tools, profiles, performance, and application Areas”, Proc. IEEE ICIP, vol. 1, pp. 592 - 596, 11-14 Sept. 2005. [8] H. S. Malvar et al, “Low-complexity transform and quantization in H.264/AVC”, IEEE Trans. Circuits and Systems for Video Technology, Vol. 13, No. 7, pp. 598-603, July 2003. [9] J. Dong et al, "2D order-16 integer transforms for HD video coding", IEEE Trans. Circuits and Systems for Video Technology, Vol.19, No.10, pp.1462-1474, Oct. 2009. [10] L. Fan, S. Ma and F. Wu, “Overview of AVS video standard,” IEEE ICME, vol. 1, pp. 423-426, June 2004. [11] L. Yu et al, “Overview of AVS-Video: Tools, performance and complexity,” SPIE VCIP, vol. 5960, pp. 596021-1~ 596021-12, July 2005.

  49. References [12] W. K. Cham and Y. T. Chan, “An Order-16 integer cosine transform”, IEEE Trans. on Signal Processing, Vol. 39, No. 5, pp. 1205-1208, May 1991. [13] W. Cham and C. Fong “Simple order-16 integer transform for video coding” IEEE ICIP 2010, pp. 161-165, Hong Kong, Sept.2010. [14] S. Naito and A. Koike, “Efficient coding scheme for super high definition video based on extending H.264 high profile,” in Proc. SPIE Vis. Commun. Image Process., vol. 6077, pp. 607727-1-607727-8, Jan. 2006. [15] J. Dong et al, “A universal approach to developing fast algorithm for simplified order-16 ICT,” IEEE ISCAS, pp. 281-284, June 2007. [16] C. Loeffler, A. Lightenberg, and G. Moschytz, “Practical fast 1-D DCT algorithms with 11 multiplications,” Proc. IEEE ICASSP, vol. 2, pp. 988-991, Feb. 1989.

  50. References [17] I. Daubechies and W. A. Pearlman, “Factoring wavelet transforms into lifting steps,” J. Fourier Anal. Appl., vol. 4, pp. 247-269, 1998. [18] J. Liang and T. D. Tran, "Fast multiplierless approximations of the DCT with the lifting scheme," IEEE Trans. on Signal Processing, vol. 49, pp. 3032-3044, Dec. 2001. [19] Link for H.264/AVC reference software: http://iphome.hhi.de/suehring/tml/download/ [20] Link for AVS reference software (RM 52e): ftp://159.226.42.57/public/avs_doc/avs_software. [21] N. S. Jayant and P. Noll, Digital coding of waveforms: principles and applications to speech and video. Englewood Cliffs, NJ: Prentice-Hall, 1984. [22] G. Bjontegaard, Calculation of Average PSNR differences between RD curves, VCEG-M33, April 2001. [23] Special issue on “AVS and its applications,” SP : IC, vol. 24, pp. 245-246, April 2009.

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