Ensemble segmentation using efficient integer linear programming
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Ensemble Segmentation Using Efficient Integer Linear Programming. Amir Alush and Jacob Goldberger , “ Ensemble Segmentation Using Efficient Integer Linear Programming ” , IEEE Transactions on PAMI , 2012. Ju-Hsin Hsieh Advisor : Sheng- Jyh Wang 2013/07/22. Outline. Introduction Method

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Ensemble Segmentation Using Efficient Integer Linear Programming

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Ensemble segmentation using efficient integer linear programming

Ensemble Segmentation Using EfficientInteger Linear Programming

Amir Alush and Jacob Goldberger , “ Ensemble Segmentation Using Efficient

Integer Linear Programming ” , IEEE Transactions on PAMI , 2012.

Ju-Hsin Hsieh

Advisor : Sheng-Jyh Wang

2013/07/22


Outline

Outline

  • Introduction

  • Method

  • Experiment result

  • Conclusion

  • Reference


Outline1

Outline

  • Introduction

    • What is segmentation?

    • Challenge

    • Main idea

  • Method

  • Experiment result

  • Conclusion

  • Reference


What is segmentation

What is segmentation?

  • Partitioning of an image into several constituent components.

  • Assign each pixel in the image to one of the image components.


Outline2

Outline

  • Introduction

    • What is segmentation?

    • Challenge

    • Main idea

  • Method

  • Experiment result

  • Conclusion

  • Reference


Challenge

Challenge

  • Segmentation is not a well-defined task.


Challenge1

Challenge

  • Segmentations have different numbers of segments and are inconsistent.

  • How to estimate the quality of each segmentation algorithm in an unsupervised manner?

34 segments

77 segments


Outline3

Outline

  • Introduction

    • What is segmentation?

    • Challenge

    • Main idea

  • Method

  • Experiment result

  • Conclusion

  • Reference


Main idea

Main idea

  • Combine segmentations of the same image obtained by different algorithms.

  • Average of all the segmentations.

  • The quality of segmentation is based on the consistency of the segmentation compared to the other algorithms.


Main idea1

Main idea

Input image

0.93

0.93

0.69

0.74

0.65

0.70

Average segmentation


Outline4

Outline

  • Introduction

  • Method

    • Probabilistic framework

      - Definition

      - EM algorithm

    • Integer Linear Programming

    • ProcessingProcedure

    • Additional information

  • Experiment result

  • Conclusion

  • Reference


Probabilistic framework

Probabilistic framework

  • Formalizing a clustering as a binary classification task.

  • Origin :

    A clustering of a set S = { 1 , … , n } into nc clusters

  • Transform :

    A set of n-over-2 binary decisions

    such that xij= 1 if i and j are in the same cluster

    and xij = 0 otherwise.

  • Transitive relation :

    i , j and j , k are in the same cluster.

     i , k should be in the same cluster.


Probabilistic framework1

Probabilistic framework

  • An expert l (l =1,…,m)is associated with an unknown probability pl(denote by )of making the correct binary decision xij for each object pair i , j.

    be the judgment of the lth expert

    whether objects i and j are in the same cluster or not.

  • In order to find the unknown parameter p1,…,pm and the unobserved clustering x , we try to use EM algorithm.


Outline5

Outline

  • Introduction

  • Method

    • Probabilistic framework

      - Definition

      - EM algorithm

    • Integer Linear Programming

    • ProcessingProcedure

    • Additional information

  • Experiment result

  • Conclusion

  • Reference


Probabilistic framework2

Probabilistic framework

  • E-step :

    Compute marginal posterior probabilities

     approximate it by computing the most likely clustering

  • correct object label

  • expert judgment


Probabilistic framework3

Probabilistic framework

  • M-step : (approximated)

  • correct object label

  • expert judgment

  • plreliability parameters


Probabilistic framework4

Probabilistic framework

  • correct object label

  • expert judgment


Outline6

Outline

  • Introduction

  • Method

    • Probabilistic framework

      - Definition

      - EM algorithm

    • Integer Linear Programming

    • ProcessingProcedure

    • Additional information

  • Experiment result

  • Conclusion

  • Reference


Integer linear programming

Integer Linear Programming

  • Optimization problem :

  • No informative prior ( maximum likelihood )

Integer Linear Programming


Integer linear programming1

Integer Linear Programming

  • ,

Transitive relation

If xij = xjk = 1 then xik = 1

The complexity of ILP is high.


Outline7

Outline

  • Introduction

  • Method

    • Probabilistic framework

      - Definition

      - EM algorithm

    • Integer Linear Programming

    • ProcessingProcedure

    • Additional information

  • Experiment result

  • Conclusion

  • Reference


Processing procedure

ProcessingProcedure

Negative weight

Positive weight

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs


Processing procedure1

ProcessingProcedure

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs


Processing procedure2

ProcessingProcedure

1. Divided into “positively connected components”

G( V , E )

G( V , E )

c

(V1,E1)

Crossing edge

E12

Negative edge

c

(V2,E2)


Processing procedure3

ProcessingProcedure

1. Divided into “positively connected components”

  • Approach


Processing procedure4

ProcessingProcedure

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs


Processing procedure5

ProcessingProcedure

2. Transform to “Single Edge Partition Tree”

  • Approach

    • Case 1

Cycle-free graph(tree)

V1

V1

V4

V4

V5

V

V2

V2

V3

V3


Processing procedure6

ProcessingProcedure

2. Transform to “Single Edge Partition Tree”

  • Approach

    • Case 2

V1

V1

V4

V4

V

V2

V2

V3

V3


Processing procedure7

ProcessingProcedure

2. Transform to “Single Edge Partition Tree”

  • Approach

    • Case 3

V1

V1

V4

V4

V

V2

V3

V3


Processing procedure8

ProcessingProcedure

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs


Processing procedure9

ProcessingProcedure

3. Divided into subgraphs

V1

V1

V4

V4

V5

V5

V2

V2

V3

V3


Outline8

Outline

  • Introduction

  • Method

    • Probabilistic framework

      - Definition

      - EM algorithm

    • Integer Linear Programming

    • ProcessingProcedure

    • Additional information

  • Experiment result

  • Conclusion

  • Reference


Additional information

Additionalinformation

  • Image spatial consistency

     Neighboring pixels are more likely to be in the same cluster than pixels that are far apart .

  • Approach

     Use mean-shift algorithm to oversegment the image into small, homogeneous regions, known as superpixels.

     Merging the MS superpixels, based on consensus among the experts.


Averaging multiple unreliable segmentations amus

Averaging Multiple Unreliable Segmentations ( AMUS )

AMUS

0.93

0.74

Averaging

Segmentation

0.69

0.70

0.65

0.93


Averaging multiple unreliable segmentations amus1

Averaging Multiple Unreliable Segmentations ( AMUS )

G=(V,E)with{wij}

Use MS to get superpixels

Divided into “positively connected components”

Transform to “Single Edge Partition Tree”

Divided into subgraphs

Apply ILP to each subgraphs


Outline9

Outline

  • Introduction

  • Method

  • Experiment result

    • AMUS algorithm

    • Compare with other algorithms

  • Conclusion

  • Reference


Amus algorithm

AMUS algorithm

0.62

0.74

0.73

0.87

0.95

0.89

Result

Averaging segmentation


Outline10

Outline

  • Introduction

  • Method

  • Experiment result

    • AMUS algorithm

    • Compare with other algorithms

  • Conclusion

  • Reference


Compare with other algorithms

Compare with other algorithms

AMUS

Image

CTM

TBES

MNC

UCM

  • PRI(probabilistic Rand index)

  • VOI(Variation of information )

  • GCE(Global Consistency Error)

  • Boundary-based F-measure


Outline11

Outline

  • Introduction

  • Method

  • Experiment result

    • AMUS algorithm

    • Compare with other algorithms

  • Conclusion

  • Reference


Conclusion

Conclusion

  • Segmentation is not a well-defined task.

  • This paper present a method for combining several segmentations of an image into a single one ( the averaging segmentation ) in order to achieve a more reliable and accurate segmentation result.

  • This paper also reports the reliability of each segmentation.


Outline12

Outline

  • Introduction

  • Method

  • Experiment result

    • AMUS algorithm

    • Compare with other algorithms

  • Conclusion

  • Reference


Reference

Reference

  • Amir Alush and Jacob Goldberger , “ Ensemble Segmentation Using Efficient Integer Linear Programming ” , IEEE Transactions on PAMI , 2012.


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