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Olga Veksler NEC Labs America

Compact Windows for Visual Correspondence via Minimum Ratio Cycle Algorithm. Olga Veksler NEC Labs America. Global Approach. Look at the whole image Solve one large problem Slower, more accurate. Local Approach.

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Olga Veksler NEC Labs America

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  1. Compact Windows for Visual Correspondence via Minimum Ratio Cycle Algorithm Olga Veksler NEC Labs America

  2. Global Approach • Look at the whole image • Solve one large problem • Slower, more accurate Local Approach • Look at one image patch at at time • Solve many small problems independently • Fast, sufficient for some problems

  3. Local Approach • Sufficient for some problems • Central problem: window shape selection • Efficiently solved using Minimum Ratio Cycle algorithm for graphs

  4. Visual Correspondence stereo motion disparity = x1-x2 left image right image (x1,y) (x2,y) vertical motion first image second image (x1,y1) (x2,y2) horizontal motion

  5. p 3 2 1 = i which gives best 2 2 + + = 2 2 + Common C Local Approach [Levine’73] left image right image

  6. Fixed Window Shape Problems need different window shapes left image true disparities fixed small window fixed large window

  7. ……. Variable Window: Previous Work • Two inefficient methods proposed previously • Local greedy search [Levine CGIP’73, Kanade’PAMI94] • Direct search [Intille ECCV94,Geiger IJCV95] • Need efficient optimization algorithm over sizes and shapes

  8. image pixels • Find cycle C which minimizes: W = t Minimum Ratio Cycle • G(V,E) and w(e), t(e): E R

  9. 1 1 1 blueedge 1 1 1 + 1 rededge 5 -2 sum up terms inside using weights of edges From Area to Cycle

  10. 2 2 OK for any graphs + … + size of W not OK for any graph negative positive Window Cost C(W) = =

  11. we construct graph s.t. Compact Windows p only clockwise cycles one-to-one simple graph cycles C W compact windows correspondence

  12. ( ) in this case: ( ) = m m C C Cycle which is not Simple cycle C cycle C

  13. ( ) å w e ( ) å t e ( ) å - ) l £ 0 w e ( å t e ( ) - ( ) l w e t e Solving MRC find smallest s.t. for some cycle • search for smallest s.t. there is negative cycle on graph with edge weights: • negative cycle detection takes time due to the special structure of our graphs

  14. examples of compact windows (small ) perimeter area • there are are compact windows, if the largest allowed window is n by n • Contains all possible rectangles but much more general than just rectangles • Find optimal window in in theory, linear ( ) in practice • Search over in time

  15. Sample Compact Windows

  16. Speedup for pixel p, the algorithm extends windows over pixels which are likely to have the same disparity as p use the optimal window computed for p to approximate for pixels inside that window

  17. Comparison to Fixed Window true disparities Compact windows:16% errors fixed small window: 33% errors fixed large window: 30% errors

  18. motion motion

  19. all global Results 13 other algorithms, local and global Running time: 8 to 22 seconds

  20. Future Work • Generalize the window class • Generalize objective function • mean? • variance?

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