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Investigation of Motion-Compensated Lifted Wavelet Transforms

Investigation of Motion-Compensated Lifted Wavelet Transforms. Markus Flierl and Bernd Girod. Information Systems Laboratory Department of Electrical Engineering Stanford University. Outline. Can motion-compensated wavelet coding really do better

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Investigation of Motion-Compensated Lifted Wavelet Transforms

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  1. Investigation ofMotion-Compensated Lifted Wavelet Transforms Markus Flierl and Bernd Girod Information Systems Laboratory Department of Electrical Engineering Stanford University

  2. Outline Can motion-compensated wavelet coding really do better than motion-compensated predictive coding? Why? • Motion-compensated wavelet coding scheme • Experimental results for temporal Haar and 5/3 wavelets • Mathematical model and performance bounds • Comparison to predictive coding

  3. H 7 H 6 5 4 3 2 1 0 Motion-Compensated Wavelet Coder Original frames H H LH LH LLH LLL Temporal Decomposition Intraframe Coder • DWT/ MC-Lifting • Haar and 5/3 wavelet • 16x16 block motion compensation • ½ pixel accuracy • 8x8 DCT coder • Run-level entropy coding • Same quantizer step-size in all frames

  4. Motion-Compensated Haar Wavelet Low Even frames Odd frames High Update step uses negative motion vector of corresponding prediction step

  5. Motion-Compensated 5/3 Wavelet Frame 0 Low Frame 1 High Frame 2 Low Update steps uses negative motion vectors of corresponding prediction steps

  6. 46 45 44 43 42 41 40 39 PSNR Y [dB] 38 37 36 35 34 5/3, K=32 Haar, K=32 33 Haar, K=16 32 Haar, K=8 31 Haar, K=2 30 0 100 200 300 400 500 600 700 800 R [kbit/s] R-D Performance of M.C.Wavelet Coder Mother & Daughter, QCIF, 30 fps +

  7. 41 40 39 38 37 36 35 34 PSNR Y [dB] 33 32 31 30 29 5/3, K=32 Haar, K=32 28 Haar, K=16 27 Haar, K=8 26 Haar, K=2 25 0 500 1000 1500 2000 2500 3000 3500 R [kbit/s] R-D Performance of M.C. Wavelet Coder Mobile & Calendar, QCIF, 30 fps

  8. Mathematical Model • Can we explain the experimental findings by a mathematical model? Yes! • Extend rate-distortion analysis of motion-compensated hybrid coding to motion-compensated subband coding B. Girod, "Efficiency Analysis of Multi-Hypothesis Motion-Compensated Prediction for Video Coding," IEEE Trans. Image Processing, vol. 9, no. 2, pp. 173-183, February 2000. B. Girod, "Motion-Compensating Prediction with Fractional-Pel Accuracy," IEEE Transactions on Communications, vol. 41, no. 4, pp. 604-612, April 1993. B. Girod, "The Efficiency of Motion-compensating Prediction for Hybrid Coding of Video Sequences," IEEE Journal on Selected Areas in Communications, vol. SAC-5, no. 7, pp. 1140-1154, August 1987.

  9. Equivalent Motion-Compensated Haar Transform Assume invertible motion compensation operations Low Even frames Odd frames High

  10. Equivalent Motion-Compensated Haar Transform

  11. Mathematical Model of Motion-Compensated Transform Any input picture can be reference picture

  12. Coding Gain of Motion-Compensated Transform • Rate difference for each picture k • Difference of rate-distortion functions at high rates • Compares m.c. transform coding to independent coding of frames • . . . for the same mean squared reconstruction error • . . . for Gaussian signals • Total rate difference

  13. 0 K=2 K=8 K=32 -1 K= ¥ -2 rate difference [bit/sample] -3 -4 -5 -6 -4 -3 -2 -1 0 1 2 displacement inaccuracy b Rate Difference with Negligible Noise Calibration:  = 0.5log2(122)

  14. 0 K=2 K=8 K=32 -0.5 K= ¥ -1 rate difference [bit/sample] -1.5 -2 -2.5 -3 -4 -3 -2 -1 0 1 2 displacement inaccuracy b Rate Difference with White Noise Calibration:  = 0.5log2(122) White noise at -30 dB

  15. Comparison to Predictive Coding • Predictive coding scheme: • Motion-compensated hybrid coder (like MPEG, H.263, . . . ) • 16x16 block motion compensation with half-pel accuracy • Previous reference frame only • Intra-frame coding with 8x8 DCT and run-length coding • Only one I-frame in the beginning of the sequence • Same quantizer step-size for all P-frames • Same components as motion-compensated wavelet coding scheme

  16. 47 46 45 44 43 42 41 40 PSNR Y [dB] 39 38 37 36 35 5/3, K=32 34 Haar, K=32 33 Prediction, K=288 32 0 50 100 150 200 250 300 350 400 R [kbit/s] Comparison to Predictive Coding Mother & Daughter, QCIF, 30 fps

  17. 41 40 39 38 37 36 35 34 PSNR Y [dB] 33 32 31 30 29 5/3, K=32 28 Haar, K=32 27 Prediction, K=288 26 0 500 1000 1500 2000 2500 R [kbit/s] Comparison to Predictive Coding Mobile & Calendar, QCIF, 30 fps

  18. 0 K=2 K=8 K=32 -0.5 K= ¥ MCP -1 -1.5 rate difference [bit/sample] -2 0.5 bits -2.5 -3 -4 -3 -2 -1 0 1 2 displacement inaccuracy b Comparison to Predictive Coding Calibration:  = 0.5log2(122)

  19. Conclusions • Investigated motion-compensated wavelet transform followed by intra-frame coder both experimentally and theoretically • Biorthogonal 5/3 wavelet outperforms Haar wavelet • Wavelet transform can outperform predictive coding with single reference frame • Theory offers insights and some possible explanations • Rate can decrease up to 1 bpp per displacement accuracy step • Gain by accurate motion compensation is limited by residual noise • Motion-compensated transform can outperform predictive coding by up to 0.5 bpp, due to better noise suppression • Long GOPs needed for wavelet subband decomposition

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