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Ensemble Segmentation Using Efficient Integer Linear Programming

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### Ensemble Segmentation Using EfficientInteger Linear Programming

OutlineOutlineOutline

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
- 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.

Outline

- Introduction
- Method
- Probabilistic framework

- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information
- 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
- Additional information
- 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
- Additional information
- 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.

- Introduction
- Method
- Probabilistic framework

- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information
- 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

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

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

- Introduction
- Method
- Probabilistic framework

- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information
- Experiment result
- Conclusion
- Reference

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 )

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

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.

- 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.

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