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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

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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

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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].

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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

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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

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

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

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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

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

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

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

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

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

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

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

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

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ICT in AVS-video Sparse matrix factors : where

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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)

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

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Order 16 ICT and HD video coding Table showing spatial correlation of prediction error Test sequencesResolution r(1)r(2) MeanStandard Deviation MeanStandard Deviation Kimono 1920 × 1080 (HD) 0.86730.12840.73110.1434 Parkscene0.74310.18200.66950.1967 Cactus0.85420.16920.74830.1245 Vidyo1 1280 × 720 (HD) 0.75390.24010.40730.1842 Vidyo20.66430.19820.30600.1569 Vidyo30.54740.11250.32210.2923 PartyScene 832 × 480 (WVGA) 0.49530.15980.20190.1757 BQMall0.45170.21450.19660.2450 BasketballDrill0.55940.11830.23010.1032 BQSquare 416 × 240 (WQVGA) 0.35430.29350.09640.1722 BlowingBubbles0.28790.15150.04730.1906 BaketballPass0.21770.17840.03550.2098 Prediction error : Difference between original and intra or inter predicted macroblocks

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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

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

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Simple order 16 ICT Flow diagram 16 x 16 SICT [15]

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

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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 (T 8e ) - Modified dyadic symmetry of odd part of order 16 DCT-II symmetry (M 8o ) [9]

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

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

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Modified order 16 ICT Elements {x 1, x 3,….,x 15 } are {11, 11, 11, 9, 8, 6, 4, 1} M 8o is implemented in three stages M 8o = M 1.M 2.M 3 Constraints for M 1, M 2,M 3 - Contain integers - Small magnitude - Sparse - Orthogonality Requires 32 shifts and 150 additions

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Modified order 16 ICT Flow diagram 16 x 16 MICT (shifts for M 8o not shown for clarity) [9]

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

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

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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

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

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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 Group of pictures (GOP) size8 GOP structureIBBBBBBP Intra frame period0.5 s R-D optimizationon QP22, 27, 32, 37 Reference frames2 Fast motion estimationon Search range± 32 Deblocking filteron Entropy codingCABAC Configuration parameters

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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 Group of pictures (GOP) size8 GOP structureIBBBBBBP Intra frame period0.5 s R-D optimizationon QP22, 27, 32, 37 Reference frames2 Fast motion estimationon Search range± 32 Deblocking filteron Entropy codingCABAC Configuration parameters

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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

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

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

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

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

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

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

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

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

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Vidyo1(1280 x 720) First frame of vidyo1

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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

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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.

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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.

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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.

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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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