EE5355 - Project Below are INTDCT’s used in AVS China, H.264 and WMV-9. AVS China: [INTDCT1] = [ ] H.264: [INTDCT2] = WMV9: [INTDCT3] =1. Check for the orthogonality of the above NxN Integer cosine transform matrices. (Note: It is acceptable even if the diagonal elements of [INTDCTi]x[INTDCTi]*T are not equal, where i =1,2,3…,N and superscript T stands for transpose). Display the orthogonalised matrix. 2. Consider a Markov I Process with ρ=0.95 and N=8. Find out the NxN correlation matrix R with the elements of R given by: Rjk = [ρ|j-k|] j, k = 0, 1,…,N-1 Covariance matrix in transform domain is given by where DOT stands for discrete orthogonal transform and is the covariance matrix in the spatial domain. Perform comparison with the following properties of these transforms: a. Transform coding gain. Note: Transform coding gain GTC is given by where is the variance in the transform domain (diagonal elements). b. Residual correlation: Sum of the off-diagonal elements of the correlation matrix in the transform domain. Use formula below: Note: Compute residual correlation for ρ = 0.05 to 0.95 in steps of 0.1. Plot the residual correlation in % versus ρ. c. Variance distribution in the transform domain. Note: Tabulate the variances computed and also plot Variance versus N. (Please refer to Table 5.2, page 171 for an example of calculation of variances of transform co-efficients in Fundamentals of Digital Image Processing, by Anil K. Jain, Prentice Hall, 1989).d. Normalized basis restriction error (Jm). Note: Compute and plot Percentage values of Jm versus samples retained (m). Jm is given by the following expression e. Normalized MSE. where nmx , is the original data and nmx , is the reconstructed data. f. Rate versus distortion. Note: Plot rate distortion function RD versus fixed average distortion D. Choose θ to get D. Use θ same to get RD. References: Please refer “comparison of discrete transforms” file for the definition of properties. Please refer to files on Integer DCT for video coding standards: H.264, WMV9, AVS-China in the course website. Please refer to INTDCT3, INTDCT4, INTDCT5 and INTDCT6 files on the course website for understanding the basics of integer DCT. Also, refer to “Video codecs standards review” file on EE5356 website to get familiarized with the working of video codecs. Please refer to class notes (DCT- part 2 file) pages : 32- 37 for sample graphs of the properties listed above. Also, refer to the books mentioned below for details on the properties of discrete transforms if required. [1] K. R. Rao and P. Yip “Discrete Cosine Transform”, Academic Press, 1990. [2] K.R. Rao and P.C. Yip, The Transform and Data Compression Handbook. Page 1 Boca Raton, FL: CRC Press, 2001. [3] P. Yip, V. Britanak and K.R. Rao, Discrete Cosine and Sine Transforms. Oxford, UK: Elsevier, 2007. INDCT1,INTDCT2,INTDCT3,INTDCT4,INTDCT5 &
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