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.

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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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