implementation and performance analysis of 2-d order 16 integer transforms in h.264/avc and...
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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(n1) and x(n2): intensity values of n1,n2
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 sequences Resolutionr(1) r(2)
Mean Standard Deviation
Mean Standard Deviation
Kimono1920 × 1080 (HD)
0.8673 0.1284 0.7311 0.1434
Parkscene 0.7431 0.1820 0.6695 0.1967
Cactus 0.8542 0.1692 0.7483 0.1245
Vidyo11280 × 720 (HD)
0.7539 0.2401 0.4073 0.1842
Vidyo2 0.6643 0.1982 0.3060 0.1569
Vidyo3 0.5474 0.1125 0.3221 0.2923
PartyScene832 × 480 (WVGA)
0.4953 0.1598 0.2019 0.1757
BQMall 0.4517 0.2145 0.1966 0.2450
BasketballDrill 0.5594 0.1183 0.2301 0.1032
BQSquare416 × 240 (WQVGA)
0.3543 0.2935 0.0964 0.1722
BlowingBubbles 0.2879 0.1515 0.0473 0.1906
BaketballPass 0.2177 0.1784 0.0355 0.2098
• 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 (T8e)
- Modified dyadic symmetry of odd part of order 16 DCT-II
symmetry (M8o) [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 {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
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Modified order 16 ICT
• Flow diagram 16 x 16 MICT (shifts for M8o 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) size 8
GOP structure IBBBBBBP
Intra frame period 0.5 s
R-D optimization on
QP 22, 27, 32, 37
Reference frames 2
Fast motion estimation on
Search range ± 32
Deblocking filter on
Entropy coding CABAC
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) size 8
GOP structure IBBBBBBP
Intra frame period 0.5 s
R-D optimization on
QP 22, 27, 32, 37
Reference frames 2
Fast motion estimation on
Search range ± 32
Deblocking filter on
Entropy coding CABAC
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.