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Efficient Part-Based Recognition of Multiple Object Classes

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Object Class Recognition Systems

- Model Representation
- Part-based model
- Learning Algorithm
- Recognition Algorithm

5

Object Class Recognition Systems

- Model Representation
- Part-based model
- Part appearance
- Learning Algorithm
- Recognition Algorithm

6

Object Class Recognition Systems

- Model Representation
- Part-based model
- Part appearance
- Part position
- Learning Algorithm
- Recognition Algorithm

7

Object Class Recognition Systems

- Model Representation
- Part-based model
- Part appearance
- Part position
- Learning Algorithm
- Recognition Algorithm

8

History of Part-BasedObject Recognition

Hoffman 1999

Bag of Parts

Crandall et al. 2005, 2006

k-Fans

Proposed

Algorithm

Template

Matching

Part-Based

Burl et al. 1998

Constellation

Model

Fergus et al. 2003, 2005

9

k-Fan

this

Templ

Part

Const

Template Matching- Efficient? (N = # pixels) – Yes, O(N)
- Robust? – No, inflexible

36

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)

44

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels)

53

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels)

P

54

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels)

N

P

55

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels)

…

N

P

56

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels)

N

…

N

P

57

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels) – No, O(PN^P)

N

…

N

P

58

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels) – No, O(PN^P)
- Robust?

N

…

N

P

59

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels) – No, O(PN^P)
- Robust? Yes!

N

…

N

P

60

k-Fan

this

Templ

Part

Const

Part-Based- Part appearance (template matching)
- Part location (fully connected)
- Efficient? (P = #parts, N = #pixels) – No, O(PN^P)
- Robust? Yes!
- All following algorithms try to approach the accuracy of this method, while gaining efficiency

N

…

N

P

61

k-Fan

this

Templ

Part

Const

Constellation ModelSparse Interest Points (n<<N)

Dense Image (n=N)

Robust

Efficient

Trade-off

63

k-Fan

this

Templ

Part

Const

Constellation Model- Efficient O(Pn^P) (n = # interest points, P = # parts)
- Approximation:
- Sparse image: only consider interest points (n<<N)

65

k-Fan

this

Templ

Part

Const

Constellation Model- Efficient O(Pn^P) (n = # interest points, P = # parts)
- Approximation:
- Sparse image: only consider interest points (n<<N)
- Interest point detector too general
- regions of the image discarded without considering particular parts that may be there

66

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)

71

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)

max

max

78

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels)

79

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels)

N

80

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels)

P

N

81

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

P

N

82

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?

83

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?

84

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?
- No localization

85

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?
- No localization

86

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?
- No localization

87

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?
- No localization
- More likely to find false detections

88

k-Fan

this

Templ

Part

Const

Bag of Parts- Part appearance (template matching)
- Part location (ignored, disconnected)
- Efficient? (P = #parts, N = #pixels) – Yes, O(NP)

- Robust?
- No localization
- More likely to find false detections
- …but still in common use

89

1-Fans

BoP

k-Fan

this

Templ

Part

Const

- Efficient? (N = # pixels, P = # parts) Yes, O(PN^2)
- Use Dynamic Programming:

N

P

N

134

1-Fans

BoP

k-Fan

this

Templ

Part

Const

- Efficient? (N = # pixels, P = # parts) Yes, O(PN^2)
- Use Dynamic Programming:
- Precompute DTj image in O(N)

N

P

N

135

1-Fans

BoP

k-Fan

this

Templ

Part

Const

- Efficient? (N = # pixels, P = # parts) Yes, O(PN^2)
- Use Dynamic Programming:
- Precompute DTj image in O(N)
- Then add the A1 and DTj images

N

P

N

136

1-Fans

BoP

k-Fan

this

Templ

Part

Const

- Efficient? (N = # pixels, P = # parts) Yes, O(PN^2) O(NP) – Same as bag of parts!
- Use Dynamic Programming:
- Precompute DTj image in O(N)
- Then add the A1 and DTj images

N

P

N

137

1-Fans

BoP

k-Fan

this

Templ

Part

Const

- Efficient? (N = # pixels, P = # parts) Yes, O(PN^2) O(NP) – Same as bag of parts!
- Robust?

138

1-Fans

BoP

k-Fan

this

Templ

Part

Const

- Efficient? (N = # pixels, P = # parts) Yes, O(PN^2) O(NP) – Same as bag of parts!
- Robust? – Yes, better than bag of parts.

139

Aren’t We Done?

- Object Recognition is efficient and robust. Can’t we stop here?

Aren’t We Done?

- Object Recognition is efficient and robust. Can’t we stop here?
- What about…

Aren’t We Done?

- Object Recognition is efficient and robust. Can’t we stop here?
- What about…
- Detecting multiple object classes? (M = # objects… think 30,000) O(MNP)

Recap: History of Part-BasedObject Recognition

Hoffman 1999

Bag of Parts

Crandall et al. 2005, 2006

k-Fans

Proposed

Algorithm

Template

Matching

Part-Based

Burl et al. 1998

Constellation

Model

Fergus et al. 2003, 2005

143

k-Fan

this

Templ

Part

Const

Proposed Algorithm1-fan

Accurate

Efficient

Sparse Appearance Image

(thresholded)

Does not rely on ageneral

interest point detector

144

k-Fan

this

Templ

Part

Const

Proposed Algorithm- How do we threshold appearances in sublinear time (i.e. < O(MNP)? M = # objects, N = # pixels, P = # parts/object)

k-Fan

this

Templ

Part

Const

Proposed Algorithm- How do we threshold appearances in sublinear time (i.e. < O(MNP)? M = # objects, N = # pixels, P = # parts/object)
- View thresholded appearance detection as an R-nearest neighbor problem

k-Fan

this

Templ

Part

Const

R-Nearest Neighbors- What is the set of points in a database that are within a radius R from the query point q?

q

k-Fan

this

Templ

Part

Const

R-Nearest Neighbors- What is the set of points in a database that are within a radius R from the query point q?

R

q

k-Fan

this

Templ

Part

Const

R-Nearest Neighbors- What is the set of points in a database that are within a radius R from the query point q?

q

R-Nearest Neighbors

- The space part appearances (high dimensions)
- Assume part appearances are identically distributed spherical Gaussians (iΣi =cI)

q

R-Nearest Neighbors

- The space part appearances (high dimensions)
- Assume part appearances are identically distributed spherical Gaussians (iΣi =cI)
- Database points are the means (μi)

q

R-Nearest Neighbors

- The space part appearances (high dimensions)
- Assume part appearances are identically distributed spherical Gaussians (iΣi =cI)
- Database points are the means (μi)
- 1-Fan part appearances can be expressed this way

q

R-Nearest Neighbors

- Okay, how fast can it be solved?
- In low dimensions (<8), kD trees solve it in sublinear time

q

R-Nearest Neighbors

- Okay, how fast can it be solved?
- In low dimensions (<8), kD trees solve it in sublinear time
- But the conjectured “curse of dimensionality” prevents it from being solved efficiently for high dimensions

q

R-Nearest Neighbors

- Okay, how fast can it be solved?
- In low dimensions (<8), kD trees solve it in sublinear time
- But the conjectured “curse of dimensionality” prevents it from being solved efficiently for high dimensions
- Locality Sensitive Hashing solves the problem approximately,
- misses some points with probability 1-δ
- Solves it in O(nd1/c+o(1))
- Trades off probability of false negative for efficiency

Proposed Algorithm

- Lazy distance transforms, and HA*LD
- Coming soon

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