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2D matching part 2

2D matching part 2. Review of alignment methods and errors in using them Introduction to more 2D matching methods. Review of roadmap: algorithms to control matching. Rigid transformation review. Affine includes scaling and shear. Problems with error.

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2D matching part 2

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  1. 2D matching part 2 • Review of alignment methods and • errors in using them • Introduction to more 2D matching • methods CSE 803 Fall 2009

  2. Review of roadmap: algorithms to control matching CSE 803 Fall 2009

  3. Rigid transformation review CSE 803 Fall 2009

  4. Affine includes scaling and shear CSE 803 Fall 2009

  5. Problems with error • Least squares fitting uses n >> 3 point pairs • Significantly reduces error across field • Will still be thrown off by outliers * can throw out pairs with high error and then refit * can set the “weight” of any pair to be inversely proportional to error squared CSE 803 Fall 2009

  6. Sources of error * Wrong matching in the pair of points yields outlier CSE 803 Fall 2009

  7. 2-Point alignment error due to error in locations of Q1, Q2 Plastic slides can actually be overlaid for better viewing. CSE 803 Fall 2009

  8. Remove outlier and refit Plastic slides show concept better. CSE 803 Fall 2009

  9. Sometimes a halucination 6 points match, but the objects do not. Can verify using more model points. CSE 803 Fall 2009

  10. Local Feature FocusMethod (Bolles) CSE 803 Fall 2009

  11. Local focus feature matching • Local features tolerate occlusion by other objects (binpicking problem) • Subgraph matching provides several features (distances, angles, connections, etc.) • Method can be used to support different higher level strategies and alignment parameters CSE 803 Fall 2009

  12. Focus features matching attempts CSE 803 Fall 2009

  13. Pose clustering (generalized Hough transform) • Use m minimal sets of matching features, each just enough to compute alignment • Vector of alignment parameters is put as evidence into “parameter space” • When all m units of evidence computed, examine parameter space for cluster[s] CSE 803 Fall 2009

  14. Pose clustering CSE 803 Fall 2009

  15. Line segment junctions for matching CSE 803 Fall 2009

  16. “Abstract vectors” subtending detected junctions MAP IMAGE Abstract vector with tail at T and tip at Y, or tail at L and tip at X CSE 803 Fall 2009

  17. Parameter space resulting from 10 vector matches Rotation, scale, translation computed as in single match alignment. Use the cluster center to estimate best alignment parameters. CSE 803 Fall 2009

  18. Detecting airplanes on airfield CSE 803 Fall 2009

  19. Airplane model of abstract vectors; detected image features CSE 803 Fall 2009

  20. Relational matching method CSE 803 Fall 2009

  21. Some relations between parts CSE 803 Fall 2009

  22. Recognition via consistent labeling CSE 803 Fall 2009

  23. Parts, labels, relations CSE 803 Fall 2009

  24. In a consistent labeling “image” parts relate as do “model” parts CSE 803 Fall 2009

  25. Distance relation often used CSE 803 Fall 2009

  26. What model labels apply to detected holes H1, H2, H3? CSE 803 Fall 2009

  27. Partial Interpretation Tree to find a distance consistent labeling The IT shows matching attempts that can be tried using a backtracking algorithm. If a relation fails the algorithm tries a different branch. CSE 803 Fall 2009

  28. Detailed IT algorithm Current matching pairs can be stored in the recursive stack. If a new pair is consistent with the previous pairs, continue forward; if not, then back up (and retract the recent pairing). CSE 803 Fall 2009

  29. CSE 803 Fall 2009

  30. Discrete relaxation labeling constrains possible labels A sometimes useful method that once drew much interest (see pubs by Rosenfeld, Zucker, Hummel, etc.) The Marr-Poggio stereo matching algorithm has the character of relaxation. CSE 803 Fall 2009

  31. Discrete relaxation labeling constrains possible labels CSE 803 Fall 2009

  32. Kleep matching via relaxation CSE 803 Fall 2009

  33. Removing a possible label for one part affects labels for related parts CSE 803 Fall 2009

  34. Relaxation labeling • Can work truly in parallel • Pairwise constraints are weaker than what the IT method can check, so sometimes the IT must follow the relaxation method • There is “probabalistic relaxation” which changes probability of labels rather than just keeping or deleting them • Relaxation was once thought to model human visual processes. CSE 803 Fall 2009

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