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What To Do Next? (Two Choices)

Some Evidence That LSH May Not Be Useful. Another Option: Bayesian Sequential Hypothesis Testing. What To Do Next? (Two Choices). Outline. Outline. Review. Outline. Review Why this problem may not be a good match for the LSH algorithm. Outline. Review

brandon-luby
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What To Do Next? (Two Choices)

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  1. Some Evidence That LSH May Not Be Useful.Another Option: Bayesian Sequential Hypothesis Testing. What To Do Next?(Two Choices)

  2. Outline

  3. Outline • Review

  4. Outline • Review • Why this problem may not be a good match for the LSH algorithm

  5. Outline • Review • Why this problem may not be a good match for the LSH algorithm • Another possible direction

  6. Outline • Review • Why this problem may not be a good match for the LSH algorithm • Another possible direction

  7. Outline • Review • Why this problem may not be a good match for the LSH algorithm • Another possible direction • Decision to make…

  8. part model observed patch Euclidean distance?

  9. part model observed patch Euclidean distance?

  10. part model observed patch Euclidean distance? foreground 0.0 0.1 0.0 0.0 0.2 0.0 0.6 0.2 0.0 0.8 0.7 0.9 0.6 1.0 0.0 0.1 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.9 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.2 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.1 0.0 0.0 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5

  11. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.0 0.8 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.0 0.9 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5

  12. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  13. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  14. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  15. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  16. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  17. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  18. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  19. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  20. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.2 0.0 0.1 0.0 0.1 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  21. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.2 0.1 0.0 0.1 0.0 patch “goodness” 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.8 0.0 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.9 0.0 0.0 0.9 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  22. part model observed patch Euclidean distance? foreground 0.1 0.0 0.1 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.1 0.0 0.2 0.0 pixel “goodness” 0.1 0.0 0.0 0.2 0.0 0.2 0.0 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.2 0.0 0.2 0.1 0.1 0.0 0.0 0.2 0.0 0.1 0.0 0.0 0.0 0.1 0.2 0.0 0.2 0.1 0.0 0.1 0.0 patch “goodness” 0.0 0.2 0.1 0.0 0.1 0.2 0.0 0.0 0.0 0.2 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.6 0.2 0.0 0.8 0.7 0.9 0.6 1.0 0.0 0.2 0.1 0.0 0.1 0.2 0.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.1 0.0 0.9 0.9 0.0 0.5 0.6 0.8 0.7 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.2 0.1 0.0 0.1 0.2 0.5 06 0.8 0.6 0.5 0.9 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.2 0.0 1.0 0.2 0.1 0.0 0.1 0.6 0.2 0.0 0.0 0.1 0.0 0.0 0.8 0.4 0.5 0.5 0.7 0.8 0.7 0.7 0.8 0.6 0.9 0.5 background 0.1 0.2 0.0 0.1 0.6

  23. part model observed patch Euclidean distance? • What if we let each observed patch and part model be a point? pixel “goodness” patch “goodness”

  24. part model observed patch Euclidean distance? • What if we let each observed patch and part model be a point? • Can we arrange these points in space such that the distances represent the “goodness” values? pixel “goodness” patch “goodness”

  25. part model observed patch Euclidean distance? pixel “goodness” patch “goodness”

  26. part model observed patch Euclidean distance? pixel “goodness” patch “goodness”

  27. part model observed patch Euclidean distance? pixel “goodness” patch “goodness”

  28. part model observed patch Euclidean distance? pixel “goodness” patch “goodness” If we can arrange the points with correct distances in low-dimensional pixel space,

  29. part model observed patch Euclidean distance? pixel “goodness” patch “goodness” If we can arrange the points with correct distances in low-dimensional pixel space, then we can append these coordinates in the high-dimensional patch space…

  30. part model observed patch Euclidean distance? Consider low-dimensional pixel space: If we can arrange the points with correct distances in low-dimensional pixel space, then we can append these coordinates in the high-dimensional patch space…

  31. part model observed patch Euclidean distance? Consider low-dimensional pixel space: e edge orientations If we can arrange the points with correct distances in low-dimensional pixel space, then we can append these coordinates in the high-dimensional patch space…

  32. part model observed patch Euclidean distance? Consider low-dimensional pixel space: n = p*o edge orientations (o object models, p parts per object) e edge orientations If we can arrange the points with correct distances in low-dimensional pixel space, then we can append these coordinates in the high-dimensional patch space…

  33. part model observed patch Euclidean distance? Consider low-dimensional pixel space: n = p*o edge orientations (o object models, p parts per object) e edge orientations e+n points with e*n distance constraints If we can arrange the points with correct distances in low-dimensional pixel space, then we can append these coordinates in the high-dimensional patch space…

  34. Why this problem may not be a good match for the LSH algorithm.

  35. Why this problem may not be a good match for the LSH algorithm. • Theory suggests that the most straightforward optimization method is non-convex.

  36. Why this problem may not be a good match for the LSH algorithm. • Theory suggests that the most straightforward optimization method is non-convex. • Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database

  37. Why this problem may not be a good match for the LSH algorithm. • Theory suggests that the most straightforward optimization method is non-convex. • Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database • LSH running time: dn1/c2+o(1)

  38. Why this problem may not be a good match for the LSH algorithm. • Theory suggests that the most straightforward optimization method is non-convex. • Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database • LSH running time: dn1/c2+o(1) • Since d=n, LSH running time becomes n1/c2+1+o(1) which is no longer sublinear

  39. Why this problem may not be a good match for the LSH algorithm. • Theory suggests that the most straightforward optimization method is non-convex. • Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database • LSH running time: dn1/c2+o(1) • Since d=n, LSH running time becomes n1/c2+1+o(1) which is no longer sublinear • However, theory says the optimization it can be made convex…

  40. Another possible direction

  41. Another possible direction

  42. Recall:Winning Parts vs. Backgrounds Background Winning Part

  43. Decision to make…

  44. Decision to make… • Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.

  45. Decision to make… • Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n. • Try to apply Werman’s technique to the k-Fan probability model.

  46. Decision to make… • Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n. • Learn more about euclidean distance geometry & optimization • Try to apply Werman’s technique to the k-Fan probability model.

  47. Decision to make… • Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n. • Learn more about euclidean distance geometry & optimization • Possible dead-end (may still not be fast) • Try to apply Werman’s technique to the k-Fan probability model.

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