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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Mean-Field Theory and Its Applications In Computer Vision4

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Mean field theory and its applications in computer vision4

Mean-Field Theory and Its Applications In Computer Vision4


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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