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 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.

Averaging Multiple Unreliable Segmentations ( AMUS )

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.