1. New Sorting-Based Lossless Motion Estimation Algorithms and a Partial Distortion Elimination Performance Analysis Bartolomeo Montrucchio and Davide Quaglia IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, 2005

2. Outline Introduction Taylor Series of the Distortion Matching Algorithm Experimental Results References

3. Introduction Motion estimation in an inter frame Current frame Reference frame

4. Introduction Stages in motion estimation – Searching Choose a candidate motion vector. Lossy vs. lossless – Matching Calculate SAD between the candidate block and current block. Lossy vs. lossess SAD SAD = pixel value

5. Introduction Searching stage – Lossless Raster ordered full search, SpiralPDE, Successive elimination algorithm, … – Lossy Three-step search, Diamond search, … … … Search range SpiralPDE for searching

6. Introduction successive elimination algorithm – For an obtained candidate M(a,b) and SAD(a,b), We have to find M(x,y) s.t. SAD(x,y)  SAD(a,b) – SAD(a,b)  R – M(x,y), SAD(a,b)  M(x,y) – R R – SAD(a,b)  M(x,y)  SAD(a,b) + R – Before the calculation of SAD(x,y), check M(x,y) first. currentcandidate  currentcandidate RM(x,y) SAD(x,y) |a| - |b|  |a – b| AlgorithmDFDPSNR(dB)Check points Full search233531.6471089 SEA233531.647144 TSS348829.11333

7. Introduction Matching stage Lossless – Raster ordered full matching, PDE, … Lossy – Down sampling, … N N v t  If then stop p th block pixel (i,j) in a block current candidate

8. Introduction Matching criterion (lossless) – SAD – PDE N N v t   S : Generic matching order Main purpose of this paper m  {(1, 1), (1, 2), …, (N, N)}

9. Taylor Series of the Distortion Taylor series – Taylor series of the distortion – – e.g. >> (i’,j’) (i”,j”)

10. Matching Algorithm 1. Compute SAD min (p) (every eight pixels). 2. Compute d(v,i,j) for all (i,j) in a block. 3. Sort d(v,i,j) in decreasing order. 4. Check if 5. Goto the next (i,j) and return to 1. m  {(1, 1), (1, 2), …, (N, N)} Searching stage is the same as spiralPDE

11. Matching Algorithm Fast full search with sorting by distortion (FFSSD) – Use the first term in the Taylor’s series. Fast full search with sorting by gradient (FFSSG) – Use the second term in the Taylor’s series. –  v d(0,i,j) is approximated by

12. Experimental Results Comparisons – SpiralPDE – Sobol partial distortion algorithm (SPD) Sobol sequence – Gradient-based adaptive matching scan algorithm (P4) Candidate MVReal MVPixel position Distortion at position p in (t+1) th frame

13. Experimental Results

16. References SEA – W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process.,1999. SPD – D. Quaglia and B. Montrucchio, “Sobol partial distortion algorithm for fast full search in block motion estimation,” in Proc. 6th Eurographics Workshop Multimedia, 2001. P4 – J. N. Kim and T. S. Choi, “Adaptive matching scan algorithm based on gradient magnitude for fast full search in motion estimation,” IEEE Trans. Consumer Electron., 1999.