# Mean-Field Theory and Its Applications In Computer Vision4 - PowerPoint PPT Presentation

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Mean-Field Theory and Its Applications In Computer Vision4. Motivation. Helps in incorporating region/segment consistency in the model. Pairwise CRF. Higher order CRF. Motivation. Higher order terms can help in incorporating detectors into our model. Without detector. With detector. Image.

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Mean-Field Theory and Its Applications In Computer Vision4

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## Mean-Field Theory and Its Applications In Computer Vision4

### Motivation

Helps in incorporating region/segment consistency in the model

Pairwise CRF

Higher order CRF

### Motivation

Higher order terms can help in incorporating detectors into our model

Without detector

With detector

Image

### Marginal update

General form of meanfield update

Expectation of the cost given variable vi takes a label

### Marginal Update

General form of meanfield update

Expectation of the clique given variable vi takes a label

• Summation over the possible states of the clique

### Marginal Update in Meanfield

Some possible states

labels

Total number of possible states: 36

### Marginal Update in Meanfield

Exponential # of possible states for clique of size |c| and labels L: |L|C

Expectation evaluation (summation) becomes infeasible

### Marginal Update in Meanfield

• Use restricted form of cost

• Pattern based potential

### Marginal Update in Meanfield

Restrict the number of states to certain number of patterns

Simple patterns

Segment takes a label from label set of 4 patterns Or none

### Marginal Update in Meanfield

Expectation calculation is quite efficient

### Pattern based cost

Segment takes one of the forms

### Pattern based cost

Segment does not take one of the forms

### Pattern based cost

• Simple patterns

Simple patterns

• Pattern based higher order terms

### PN Potts based patterns

• PN Potts based patterns

Potts patterns

• Potts cost

Potts patterns

### Marginal Update in Meanfield

General form of meanfield update

Expectation of the cost given variable vi takes a label

### Expectation update

Probability of segment taking that label

Potts patterns

### Expectation update

Probability of segment not taking that label

Potts patterns

### Expectation update

Expectation update

Potts patterns

### Complexity

• Expectation Updation:

• Time complexity

• O(NL)

• Preserves the complexity of original filter based method

### PascalVOC-10 dataset

• Inclusion of PN potts term:

• Slight improvement in I/U score compared to more complex model which includes Pn Potts + cooccurrence terms

• Almost 8-9 times faster than the alpha-expansion based method