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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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Page 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.

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

Page 2: 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.

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

Page 3: 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.

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].

Page 4: 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.

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

Page 5: 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.

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

Page 6: 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.

H.264/AVC encoder

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

Page 7: 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.

H.264/AVC decoder

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

Page 8: 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.

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

Page 9: 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.

ICT in H.264/AVC

• 4 x 4 ICT matrix

-

• 4 x 4/2 x 2 Hadamard matrix

-

Page 10: 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.

ICT in H.264/AVC

• 8 x 8 ICT matrix

-

• Non-normalized• Fast implementation [8]

Page 11: 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.

ICT in H.264/AVC

• Flow diagram for 8 x 8 ICT [9]

-

Page 12: 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.

ICT in H.264/AVC

• Sparse matrix factors :

where

Page 13: 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.

AVS-video encoder

Typical block diagram of AVS-video encoder [10]

Page 14: 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.

AVS-video decoder

Typical block diagram of AVS-video decoder [10]

Page 15: 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.

ICT in AVS-video

• Order 8 ICT [11]

-

• Order 16 ICT : extended from order 8 ICT• Fast implementation

Page 16: 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.

ICT in AVS-video

• Flow diagram for 8 x 8 ICT [9]

-

Page 17: 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.

ICT in AVS-video

• Sparse matrix factors :

where

Page 18: 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.

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)

Page 19: 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.

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

Page 20: 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.

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

Page 21: 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.

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

Page 22: 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.

Simple order 16 ICT (SICT)

• Transform matrix of order 16 SICT for H.264/AVC

• Requires 20 shifts and 80 additions

Page 23: 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.

Simple order 16 ICT

• Flow diagram 16 x 16 SICT [15]

Page 24: 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.

Simple order 16 ICT

• Sparse matrix factors :

H.264/AVC : where

AVS-video : where

where and order of input as shown in flow diagram

Page 25: 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.

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]

Page 26: 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.

Modified order 16 ICT

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

Page 27: 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.

Modified order 16 ICT

• Transform matrix of order 16 MICT for AVS-video

Page 28: 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.

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

Page 29: 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.

Modified order 16 ICT

• Flow diagram 16 x 16 MICT (shifts for M8o not shown for clarity) [9]

Page 30: 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.

Modified order 16 ICT

• Sparse matrix factors :

H.264/AVC : where

AVS-video : where

where and order of input as shown in flow diagram

Page 31: 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.

Order 16 binDCT-L

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

where

Page 32: 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.

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

Page 33: 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.

Order 16 binDCT-L

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

Page 34: 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.

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

Page 35: 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.

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

Page 36: 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.

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

Page 37: 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.

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

Page 38: 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.

Transform Coding gain

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

Page 39: 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.

SICT in H.264/AVC (1280 x 720)

• BD-bitrate savings [22] : 2.57 %• BD-PSNR gain [22] : 0.19 dB

Page 40: 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.

MICT in H.264/AVC (1280 x 720)

• BD-bitrate savings : 5.30 %• BD-PSNR gain : 0.31 dB

Page 41: 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.

binDCT-L in H.264/AVC (1280 x 720)

• BD-bitrate savings : 4.73 %• BD-PSNR gain : 0.36 dB

Page 42: 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.

SICT in AVS-video (1280 x 720)

• BD-bitrate savings : 5.18 %• BD-PSNR gain : 0.29 dB

Page 43: 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.

MICT in AVS-video (1280 x 720)

• BD-bitrate savings : 2.57 %• BD-PSNR gain : 0.34 dB

Page 44: 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.

binDCT-L in AVS-video (1280 x 720)

• BD-bitrate savings : 7.45 %• BD-PSNR gain : 0.41 dB

Page 45: 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.

Vidyo1(1280 x 720)

First frame of vidyo1

Page 46: 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.

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

Page 47: 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.

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.

Page 48: 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.

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.

Page 49: 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.

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.

Page 50: 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.

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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