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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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Presentation Transcript
motivation
Motivation

Helps in incorporating region/segment consistency in the model

Pairwise CRF

Higher order CRF

motivation1
Motivation

Higher order terms can help in incorporating detectors into our model

Without detector

With detector

Image

marginal update
Marginal update

General form of meanfield update

Expectation of the cost given variable vi takes a label

marginal update1
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
Marginal Update in Meanfield

Some possible states

labels

Total number of possible states: 36

marginal update in meanfield1
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 meanfield2
Marginal Update in Meanfield
  • Use restricted form of cost
  • Pattern based potential
marginal update in meanfield3
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 meanfield4
Marginal Update in Meanfield

Expectation calculation is quite efficient

pattern based cost
Pattern based cost

Segment takes one of the forms

pattern based cost1
Pattern based cost

Segment does not take one of the forms

pattern based cost2
Pattern based cost
  • Simple patterns

Simple patterns

  • Pattern based higher order terms
p n potts based patterns
PN Potts based patterns
  • PN Potts based patterns

Potts patterns

potts cost
Potts cost
  • Potts cost

Potts patterns

marginal update in meanfield5
Marginal Update in Meanfield

General form of meanfield update

Expectation of the cost given variable vi takes a label

expectation update
Expectation update

Probability of segment taking that label

Potts patterns

expectation update1
Expectation update

Probability of segment not taking that label

Potts patterns

expectation update2
Expectation update

Expectation update

Potts patterns

complexity
Complexity
  • Expectation Updation:
  • Time complexity
    • O(NL)
  • Preserves the complexity of original filter based method
pascalvoc 10 dataset
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
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