1. 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

2. Introduction

3. 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].

4. 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].

5. Integer DCTs compared

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

7. 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)

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

9. Comparison of the properties of integer DCTs

10. 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

11. 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].

12. 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].

13. 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].

14. 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].

15. Results and Conclusion

16. Variance distribution versus N

17. Rate versus distortion

18. Normalized basis restriction error versus samples retained m

19. Residual correlation versus correlation co-efficient

20. 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 8.2916, 8.0155 and 7.5477 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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