Mean-Field Theory and Its Applications In Computer Vision4

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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

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Mean-Field Theory and Its Applications In Computer Vision4

Helps in incorporating region/segment consistency in the model

Pairwise CRF

Higher order CRF

Higher order terms can help in incorporating detectors into our model

Without detector

With detector

Image

General form of meanfield update

Expectation of the cost given variable vi takes a label

General form of meanfield update

Expectation of the clique given variable vi takes a label

- Summation over the possible states of the clique

Some possible states

labels

Total number of possible states: 36

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

Expectation evaluation (summation) becomes infeasible

- Use restricted form of cost

- Pattern based potential

Restrict the number of states to certain number of patterns

Simple patterns

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

Expectation calculation is quite efficient

Segment takes one of the forms

Segment does not take one of the forms

- Simple patterns

Simple patterns

- Pattern based higher order terms

- PN Potts based patterns

Potts patterns

- Potts cost

Potts patterns

General form of meanfield update

Expectation of the cost given variable vi takes a label

Probability of segment taking that label

Potts patterns

Probability of segment not taking that label

Potts patterns

Expectation update

Potts patterns

- Expectation Updation:

- Time complexity
- O(NL)

- Preserves the complexity of original filter based method

- 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