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COMPARISON OF 8 × 8 INTEGER DCTs USED IN H.264, AVS-CHINA AND VC-1 VIDEO CODECS

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COMPARISON OF 8 × 8 INTEGER DCTs USED IN H.264, AVS-CHINA AND VC-1 VIDEO CODECS

Submitted by,

Ashwini Ursand Sharath Patil

Under guidance of

Dr.K.R.Rao

Introduction

- 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].

- 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].

Integer DCTs compared

AVS-China [2]

H.264 [3]

VC-1 [4]

- The orthogonality of the 3 matrices was checked by evaluating [INTDCTi] x [INTDCTi]*T.
- The orthogonalisedmatrices are:
- AVS-China = diag(512, 442, 464, 442, 512, 442, 464, 442)
- H.264 = diag(512, 578, 320, 578, 512, 578, 320, 578)
- VC-1 = diag(1152, 1156, 1168, 1156, 1152, 1156, 1168, 1156)

Comparison of the properties of integer DCTs

- The properties of the 3 integer DCT matrices were compared by considering a covariance matrix Rfor a Markov-I process with ρ = 0.95 and N=8.
- Rjk = [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

- Variance distribution: The diagonal elements of correspond to the variances in the transform domain [7].
- Rate versus distortion: RD 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 RD is computed as
Choose values of θ betweent 0.1 and 1. For the same values of θ, D and RD are calculated [7].

- Normalized basis restriction error, Jm: 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].

- 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].

- Transform coding gain GTC: 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 GTC can be maximized [7].

Results and 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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