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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

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outline1
Outline
  • Review
outline2
Outline
  • Review
  • Why this problem may not be a good match for the LSH algorithm
outline3
Outline
  • Review
  • Why this problem may not be a good match for the LSH algorithm
  • Another possible direction
outline4
Outline
  • Review
  • Why this problem may not be a good match for the LSH algorithm
  • Another possible direction
outline5
Outline
  • Review
  • Why this problem may not be a good match for the LSH algorithm
  • Another possible direction
  • Decision to make…
slide8

part model

observed patch

Euclidean distance?

slide9

part model

observed patch

Euclidean distance?

slide10

part model

observed patch

Euclidean distance?

foreground

0.0

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0.0

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06

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0.6

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slide11

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

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0.1

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0.0

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0.0

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0.0

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0.0

0.0

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0.1

0.0

0.0

0.1

0.0

0.0

0.0

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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

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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

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0.0

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0.0

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0.5

06

0.8

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0.5

0.9

0.0

0.0

0.0

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0.0

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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

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0.7

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0.7

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slide12

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

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1.0

0.0

0.2

0.1

0.0

0.1

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0.0

0.0

0.2

0.0

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0.0

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0.9

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0.0

0.0

0.0

0.0

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0.1

0.0

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0.2

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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

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0.5

0.7

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0.7

0.7

0.8

0.6

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background

0.1

0.2

0.0

0.1

0.6

slide13

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

slide14

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

slide15

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

slide16

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

slide17

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

slide18

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

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0.9

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0.9

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0.0

0.0

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06

0.8

0.6

0.5

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0.0

0.0

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0.0

0.2

0.0

1.0

0.2

0.1

0.0

0.1

0.6

0.2

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0.0

0.1

0.0

0.0

0.8

0.4

0.5

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background

0.1

0.2

0.0

0.1

0.6

slide19

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

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0.0

0.0

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0.1

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0.2

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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

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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

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0.5

background

0.1

0.2

0.0

0.1

0.6

slide20

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

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0.0

0.0

0.2

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0.0

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0.2

0.5

06

0.8

0.6

0.5

0.9

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0.0

0.0

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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

slide21

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

slide22

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

slide23

part model

observed patch

Euclidean distance?

  • What if we let each observed patch and part model be a point?

pixel

“goodness”

patch

“goodness”

slide24

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”

slide25

part model

observed patch

Euclidean distance?

pixel

“goodness”

patch

“goodness”

slide26

part model

observed patch

Euclidean distance?

pixel

“goodness”

patch

“goodness”

slide27

part model

observed patch

Euclidean distance?

pixel

“goodness”

patch

“goodness”

slide28

part model

observed patch

Euclidean distance?

pixel

“goodness”

patch

“goodness”

If we can arrange the points with correct distances in low-dimensional pixel space,

slide29

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…

slide30

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…

slide31

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…

slide32

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…

slide33

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…

why this problem may not be a good match for the lsh algorithm1
Why this problem may not be a good match for the LSH algorithm.
  • Theory suggests that the most straightforward optimization method is non-convex.
why this problem may not be a good match for the lsh algorithm2
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
why this problem may not be a good match for the lsh algorithm3
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)
why this problem may not be a good match for the lsh algorithm4
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
why this problem may not be a good match for the lsh algorithm5
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…
decision to make1
Decision to make…
  • Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
decision to make2
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.
decision to make3
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.
decision to make4
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.
decision to make5
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.
    • “hacking the code” style speed-up
decision to make6
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.
    • “hacking the code” style speed-up
    • Replacing Hamming distance may not work