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COMPARISON OF 8 × 8 INTEGER DCTs USED IN H.264, AVS-CHINA AND VC-1 VIDEO CODECS Submitted by, Ashwini Urs and Sharath Patil Under guidance of Dr.K.R.Rao

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Introduction

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Integer DCT KLT is the statistically optimal transform. The performance of DCT is close to the performance of KLT [1]. DCT is a well-known transform and is widely used by majority of coding standards. Though integer DCT contains only integers, it has similar energy-packing ability as that of DCT [1].

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Integer DCT (Continued) Integer cosine transform does not involve floating point computations and hence is used in video coding standards such as H.264 [2], VC-1 [3] and AVS [4]. Integer cosine transform has been implemented with transform sizes of 4, 8 and 16 [1]. Even larger size transforms (up to 64) have been used for high resolution videos to achieve higher coding gain [1].

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Integer DCTs compared

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Integer DCT matrix for AVS-China, H.264 and VC-1 AVS-China [2] H.264 [3] VC-1 [4]

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Integer DCT matrix for AVS-China, H.264 and VC-1 The orthogonality of the 3 matrices was checked by evaluating [INTDCT i ] x [INTDCT i ] *T. The orthogonalised matrices are: 1.AVS-China = diag (512, 442, 464, 442, 512, 442, 464, 442) 2.H.264 = diag (512, 578, 320, 578, 512, 578, 320, 578) 3.VC-1 = diag (1152, 1156, 1168, 1156, 1152, 1156, 1168, 1156)

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Order-16 Integer DCT matrix used in AVS-China [26]

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Comparison of the properties of integer DCTs

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Comparison of interger DCT matrices The properties of the 3 integer DCT matrices were compared by considering a covariance matrix R for a Markov-I process with ρ = 0.95 and N=8. R jk = [ρ |j-k| ] for j, k = 0, 1,…, N-1, where ρ is the adjacent correlation coefficient. Covariance matrix in transform domain is given by where DOT is discrete orthogonal transform and [Σ] is the covariance matrix in spatial

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Properties used for comparison of integer DCTs 1.Variance distribution: The diagonal elements of correspond to the variances in the transform domain [7]. 2.Rate versus distortion: R D is the minimum average rate (bits/sample) for coding a signal at a specified distortion D [7]. For fixed average distortion D, rate distortion function R D is computed as Choose values of θ betweent 0.1 and 1. For the same values of θ, D and R D are calculated [7].

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Properties used for comparison of integer DCTs 3.Normalized basis restriction error, J m : The compaction of energy in a few transform coefficients can be represented by the normalized basis restriction error defined as [7]: where are arranged in decreasing order [7].

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Properties used for comparison of integer DCTs 4.Residual correlation: An indication of the extent of decorrelation in transform domain can be gauged by correlation left undone by the discrete transform, which is measured by the absolute sum of cross-covariance (off diagonal elements) in the transform domain i.e., for N = 8 as a function of ρ [7].

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Properties used for comparison of integer DCTs 5.Transform coding gain G TC : Transform coding gain is defined as the ratio of arithmetic mean to geometric mean of variances where is the variance of the ith co-efficient in the transform domain. As sum of all the variances is in invariant under orthogonal transformation, by minimizing geometric mean G TC can be maximized [7].

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Results and Conclusion

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Variance distribution versus N

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Rate versus distortion

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Normalized basis restriction error versus samples retained m

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Residual correlation versus correlation co-efficient

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Conclusion Variance distribution, normalized basis restriction error and transform coding gain of these 3 codecs are almost comparable. Transform coding gain, GTC for AVS, H.264 and VC-1 are , and respectively. From this, we observe that AVS achieves maximum GTC. For a fixed average distortion D, the rate distortion function characteristics of H.264 and AVS are indistinguishable. The residual correlation for ρ > 0.5 is indistinguishable for these 3 codecs.

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References [1] C. Fong and W. Cham, “Simple order-16 integer transform for video coding”, The Chinese university of Hong Kong, Shatin, Hong Kong. [2] S.K.Kwon, A.Tamhankar and K.R.Rao, “Overview of H.264 / MPEG-4 Part 10” J. Visual Communication and Image Representation, vol. 17, pp , April [3] S. Srinivasan, et al, “Windows Media Video 9: overview and applications”, Signal Processing: Image Communication, vol. 19, Issue 9, pp , Oct [4] W. Gao et al., “AVS – The Chinese next-generation video coding standard,” National association of broadcasters, Las Vegas, 2004 [5] R. Joshi, Y. Reznik and M. Karczewicz, “Efficient large size transforms for high- performance video coding”, Qualcomm Inc., San Diego, CA, USA. [6] “Integer DCT for AVS China”, INTDCT6 - ee.uta.edu/dip/Courses/EE5355/ee5355.htm.http://www- ee.uta.edu/dip/Courses/EE5355/ee5355.htm

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References [7] “Comparison of discrete transforms”, ee.uta.edu/dip/Courses/EE5355/ee5355.htm. [8] N.Ahmed, T.Natarajan and K.R.Rao, “Discrete cosine transform”, IEEE trans. computers, Vol. X, pp.90-93, [9] A.K.Jain, “Fundamentals of digital image processing”, Prentice hall, [10] A.T. Hinds, “Design of high-performance fixed-point transforms using the common factor method”, Ricoh I infoprint solutions company, Boulder, CO, USA. [11] T.Wiegand, et al “Overview of the H.264/AVC video coding standard”, IEEE Trans. on Circuit and Systems for Video Technology, vol.13, pp , July [12] T. Wiegand and G. J. Sullivan, “The H.264 video coding standard”, IEEE Signal Processing Magazine, vol. 24, pp , March 2007.

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References [13] D. Marpe, T. Wiegand and G. J. Sullivan, “The H.264/MPEG-4 AVC standard and its applications”, IEEE Communications Magazine, vol. 44, pp , Aug [14] A. Puri, X. Chen and A. Luthra, “Video coding using the H.264/MPEG-4 AVC compression standard”, Signal processing: image communication, vol. 19, pp , Oct [15] M.Fieldler, “Implementation of basic H.264/AVC decoder”, seminar paper at Chemnitz university of technology, June [16 ]R. Schäfer, T. Wiegand and H. Schwarz, “The emerging H.264/AVC standard”, EBU Technical Review, Jan [17]D. Marpe, T. Wiegand, and S. Gordon, "H.264/MPEG4-avc fidelity range extensions: tools, profiles, performance, and application areas," in, IEEE international conference on image processing, vol. 1, pp. I , [18] S. Saponara et al, "The JVT advanced video coding standard: complexity and performance analysis on a tool-by-tool basis," in Packet Video Workshop, Nantes, France, April [19] VC-1 technical overview -

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References [20] S. Srinivasan and S. L. Regunathan, “An overview of VC-1”, SPIE / VCIP, vol. 5960, pp , July [21] AVS Video Expert Group, “Information technology – Advanced coding of audio and video – Part 2: Video (AVS1-P2 JQP FCD 1.0),” Audio Video Coding Standard Group of China (AVS), Doc. AVS-N1538, Sept [22] AVS Video Expert Group, “Information technology – Advanced coding of audio and video – Part 3: Audio,” Audio Video Coding Standard Group of China (AVS), Doc. AVS-N1551, Sept [23] L Yu et al., “Overview of AVS-Video: Tools, performance and complexity,” SPIE VCIP, vol. 5960, pp ~ , Beijing, China, July [24] L. Fan, S. Ma and F. Wu, “Overview of AVS video standard,” IEEE Int’l Conf. on Multimedia and Expo, ICME '04, vol. 1, pp. 423–426, Taipei, Taiwan, June [25] Special issue on 'AVS and its Applications' Signal processing: image communication, vol. 24, pp , April [26] C. K. Fong and W. K. Cham, “Simple order-16 integer transform for video coding”, ee.uta.edu/Dip/Courses/EE5355/INTDCT5.pdf

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