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# Ensemble Segmentation Using Efficient Integer Linear Programming - PowerPoint PPT Presentation

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 EfficientInteger Linear Programming

Amir Alush and Jacob Goldberger , “ Ensemble Segmentation Using Efficient

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

Ju-Hsin Hsieh

2013/07/22

### Outline

• Introduction

• Method

• Experiment result

• Conclusion

• Reference

### Outline

• Introduction

• What is segmentation?

• Challenge

• Main idea

• Method

• Experiment result

• Conclusion

• Reference

### What is segmentation?

• Partitioning of an image into several constituent components.

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

### Outline

• Introduction

• What is segmentation?

• Challenge

• Main idea

• Method

• Experiment result

• Conclusion

• Reference

### Challenge

• Segmentation is not a well-defined task.

### 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

### Outline

• Introduction

• What is segmentation?

• Challenge

• Main idea

• Method

• Experiment result

• Conclusion

• Reference

### 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 idea

Input image

0.93

0.93

0.69

0.74

0.65

0.70

Average segmentation

### Outline

• Introduction

• Method

• Probabilistic framework

- Definition

- EM algorithm

• Integer Linear Programming

• ProcessingProcedure

• Experiment result

• Conclusion

• Reference

### 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 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.

### Outline

• Introduction

• Method

• Probabilistic framework

- Definition

- EM algorithm

• Integer Linear Programming

• ProcessingProcedure

• Experiment result

• Conclusion

• Reference

### Probabilistic framework

• E-step :

Compute marginal posterior probabilities

 approximate it by computing the most likely clustering

• correct object label

• expert judgment

### Probabilistic framework

• M-step : (approximated)

• correct object label

• expert judgment

• plreliability parameters

### Probabilistic framework

• correct object label

• expert judgment

### Outline

• Introduction

• Method

• Probabilistic framework

- Definition

- EM algorithm

• Integer Linear Programming

• ProcessingProcedure

• Experiment result

• Conclusion

• Reference

### Integer Linear Programming

• Optimization problem :

• No informative prior ( maximum likelihood )

Integer Linear Programming

### Integer Linear Programming

• ,

Transitive relation

If xij = xjk = 1 then xik = 1

The complexity of ILP is high.

### Outline

• Introduction

• Method

• Probabilistic framework

- Definition

- EM algorithm

• Integer Linear Programming

• ProcessingProcedure

• Experiment result

• Conclusion

• Reference

### 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

### ProcessingProcedure

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

### ProcessingProcedure

1. Divided into “positively connected components”

G( V , E )

G( V , E )

c

(V1,E1)

Crossing edge

E12

Negative edge

c

(V2,E2)

### ProcessingProcedure

1. Divided into “positively connected components”

• Approach

### ProcessingProcedure

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

### 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

### ProcessingProcedure

2. Transform to “Single Edge Partition Tree”

• Approach

• Case 2

V1

V1

V4

V4

V

V2

V2

V3

V3

### ProcessingProcedure

2. Transform to “Single Edge Partition Tree”

• Approach

• Case 3

V1

V1

V4

V4

V

V2

V3

V3

### ProcessingProcedure

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

### ProcessingProcedure

3. Divided into subgraphs

V1

V1

V4

V4

V5

V5

V2

V2

V3

V3

### Outline

• Introduction

• Method

• Probabilistic framework

- Definition

- EM algorithm

• Integer Linear Programming

• ProcessingProcedure

• Experiment result

• Conclusion

• Reference

• 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.

AMUS

0.93

0.74

Averaging

Segmentation

0.69

0.70

0.65

0.93

### 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

### Outline

• Introduction

• Method

• Experiment result

• AMUS algorithm

• Compare with other algorithms

• Conclusion

• Reference

### AMUS algorithm

0.62

0.74

0.73

0.87

0.95

0.89

Result

Averaging segmentation

### Outline

• Introduction

• Method

• Experiment result

• AMUS algorithm

• Compare with other algorithms

• Conclusion

• Reference

### 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

### Outline

• Introduction

• Method

• Experiment result

• AMUS algorithm

• Compare with other algorithms

• Conclusion

• Reference

### 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.

### Outline

• Introduction

• Method

• Experiment result

• AMUS algorithm

• Compare with other algorithms

• Conclusion

• Reference

### Reference

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