Fast Lossless Multi-Resolution Motion Estimation for Scalable Wavelet Video Coding

1. Fast Lossless Multi-Resolution Motion Estimation for Scalable Wavelet Video Coding Yu Liu and King Ngi Ngan Department of Electronic Engineering The Chinese University of Hong Kong ISCAS2006, May 21-24, Island of Kos, Greece

2. Outline • Introduction • Background • Proposed Algorithm • Experimental Results • Conclusion

3. Introduction • Motion Estimation in Critically-Sampled Wavelet Domain • Pro: basically free form the blocking effects • Con: inefficient in high bands • Motion Estimation in Shift-Invariant Wavelet Domain • Pro: perform ME more precisely and efficiently • Con: computational complexity • e.g. low-band-shift (LBS) and complete-to-overcomplete DWT (CODWT)

4. BackgroundMotion Estimation in Shift-Invariant Wavelet Domain (1) • Two Level Shift-Invariant Wavelet Decomposition by using Low-Band-Shift (LBS) or Complete-to-Overcomplete DWT (CODWT)

5. Generation of Wavelet Blocks BackgroundMotion Estimation in Shift-Invariant Wavelet Domain (2) • The v-pixel-shifted or {dx,dy}-pixel-shifted coefficient of the pth wavelet block of reference frame t’can be represented by • The coefficient of the pth wavelet block of current frame t can be represented by

6. BackgroundMotion Estimation in Shift-Invariant Wavelet Domain (3) • The sum of absolute difference (SAD) of the pth wavelet block for the motion vector v is computed as follows: • The optimum motion vector v∗ of the pth wavelet block, which has minimum displacement error, is given by:

7. BackgroundPartial Distortion Elimination • Partial Distortion Elimination (PDE) is a fast algorithm which has identical quality as that of FSA. • The partial SAD (PSAD) is used to eliminate impossible candidates before the complete calculation of the SAD:

8. Proposed AlgorithmWavelet Matching Error Characteristic • To improve the computational saving of PDE, if the expected values of the matching error dp+v(i, j) in the search window w fulfills the following criterion: • then we assume that this matching order will be generally effective for all of the candidate vectors in the search window. • Therefore, to fulfill the above objective, we use ep(i, j) to predict the matching error.

9. To obtain the predicted matching error ep(i, j), solve this equation Proposed AlgorithmWavelet Matching Error Characteristic • We finally can obtain an approximate solution of Eq. (6): • Larger wavelet coefficientmagnitude in the current wavelet block tends to produce larger matching error

10. Proposed AlgorithmMR-WMEC-PDE • Three key factors which affect the performance of PDE • the Searching Order • in which the wavelet blocks are tested during the searching phase. • the Matching Order • in which the coefficients within a wavelet block are picked up to compute the SAD. • the Comparison Interval • in which comparison between PSAD and SADmin is performed. • Three new strategies for PDE by using wavelet matching error characteristic (WMEC) are proposed.

11. Proposed AlgorithmMR-WMEC-PDE • Searching Order Strategy based on Wavelet Multi-Resolution Property • Instead of the spiral search order, the proposed searching order strategy uses the normalized partial SAD in LL subband level as the estimated SAD (ESAD) • Then, sort the ESAD using the counting sort algorithm inascending order to obtain the searching order SO = {vn|n = 0, ...,w−1}.

12. Proposed AlgorithmMR-WMEC-PDE • Matching Order Strategy based on Wavelet-tree Grouping Scheme • A wavelet-tree grouping scheme according to spatial self-similarity property and matching error clustering property of wavelet coefficient • Sort Ep(Bl,bl,m) using the quick sort algorithm in descending order to obtain the matching order of level l: MOl = {bl,m | m = 0, ...,M − 1}

13. Proposed AlgorithmMR-WMEC-PDE • Comparison Interval Strategy based on Adaptive Sub-blocks Checking Unit • In conventional PDE methods, fixed comparison interval, such as eight-pixels or sixteen-pixels checking unit, is usually adopted. • Combined with the wavelet-tree grouping scheme, an adaptive comparison interval strategy is proposed. • In the proposed strategy, every 2l−1 sub-blocks in the decomposition level l are used as the checking unit.

14. Experimental Results (1) • Simulation results are reported in the following ways: • operation number : used to compute the partial distortion • speed-up ratio : for motion estimation including the required overheads for comparison. • For performance comparison with other algorithms • Full Search Algorithm (FSA) • Spiral-PDE [5] • CPME-PDS [6] • proposed MR-WMEC-PDE

15. Experimental Results (2) • Average Operation Number per Block for Tested Algorithms On average speed-up ratio in terms of operation number, MR-WMEC-PDE is better than Spiral-PDE and CPME-PDS by about 92% and 34%, respectively.

16. Experimental Results (3) • Average Execution Time per Frame for Tested Algorithms On average speed-up ratio in terms of execution time, MR-WMEC-PDE is better than Spiral-PDE and CPME-PDS by about 84% and 63%, respectively.

17. Conclusion • Fast Lossless Multi-Resolution Motion Estimation Algorithm • Wavelet Matching Error Characteristic (WMEC) • Three New Strategies for PDE • Searching Order Strategy based on Wavelet Multi-Resolution Property • Matching Order Strategy based on Wavelet-tree Grouping Scheme • Comparison Interval Strategy based on Adaptive Subblocks Checking Unit