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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

Advisor : Sheng-Jyh Wang

2013/07/22

- Introduction
- Method
- Experiment result
- Conclusion
- Reference

- Introduction
- What is segmentation?
- Challenge
- Main idea

- Method
- Experiment result
- Conclusion
- Reference

- Partitioning of an image into several constituent components.
- Assign each pixel in the image to one of the image components.

- Introduction
- What is segmentation?
- Challenge
- Main idea

- Method
- Experiment result
- Conclusion
- Reference

- Segmentation is not a well-defined task.

- 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

- Introduction
- What is segmentation?
- Challenge
- Main idea

- Method
- Experiment result
- Conclusion
- Reference

- 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.

Input image

0.93

0.93

0.69

0.74

0.65

0.70

Average segmentation

- Introduction
- Method
- Probabilistic framework
- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information

- Probabilistic framework
- Experiment result
- Conclusion
- Reference

- 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.

- 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.

- Introduction
- Method
- Probabilistic framework
- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information

- Probabilistic framework
- Experiment result
- Conclusion
- Reference

- E-step :
Compute marginal posterior probabilities

approximate it by computing the most likely clustering

- correct object label
- expert judgment

- M-step : (approximated)

- correct object label
- expert judgment
- plreliability parameters

- correct object label
- expert judgment

- Introduction
- Method
- Probabilistic framework
- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information

- Probabilistic framework
- Experiment result
- Conclusion
- Reference

- Optimization problem :
- No informative prior ( maximum likelihood )

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

- Probabilistic framework
- Experiment result
- Conclusion
- Reference

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

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

1. Divided into “positively connected components”

G( V , E )

G( V , E )

c

(V1,E1)

Crossing edge

E12

Negative edge

c

(V2,E2)

1. Divided into “positively connected components”

- Approach

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

2. Transform to “Single Edge Partition Tree”

- Approach
- Case 1

Cycle-free graph(tree)

V1

V1

V4

V4

V5

V

V2

V2

V3

V3

2. Transform to “Single Edge Partition Tree”

- Approach
- Case 2

V1

V1

V4

V4

V

V2

V2

V3

V3

2. Transform to “Single Edge Partition Tree”

- Approach
- Case 3

V1

V1

V4

V4

V

V2

V3

V3

G=(V,E)with{wij}

1. Divided into

“positively connected components”

2. Transform to

“Single Edge Partition Tree”

3. Divided into subgraphs

3. Divided into subgraphs

V1

V1

V4

V4

V5

V5

V2

V2

V3

V3

- Introduction
- Method
- Probabilistic framework
- Definition

- EM algorithm

- Integer Linear Programming
- ProcessingProcedure
- Additional information

- Probabilistic framework
- 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

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

- Introduction
- Method
- Experiment result
- AMUS algorithm
- Compare with other algorithms

- Conclusion
- Reference

0.62

0.74

0.73

0.87

0.95

0.89

Result

Averaging segmentation

- Introduction
- Method
- Experiment result
- AMUS algorithm
- Compare with other algorithms

- Conclusion
- Reference

AMUS

Image

CTM

TBES

MNC

UCM

- PRI(probabilistic Rand index)
- VOI(Variation of information )
- GCE(Global Consistency Error)
- Boundary-based F-measure

- Introduction
- Method
- Experiment result
- AMUS algorithm
- Compare with other algorithms

- Conclusion
- Reference

- 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

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