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Mean-Field Theory and Its Applications In Computer Vision4 1

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Motivation 2 Helps in incorporating region/segment consistency in the model Pairwise CRF Higher order CRF

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Motivation 3 Higher order terms can help in incorporating detectors into our model Image Without detector With detector

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Marginal update 4 General form of meanfield update Expectation of the cost given variable v i takes a label

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Marginal Update 5 General form of meanfield update Expectation of the clique given variable v i takes a label Summation over the possible states of the clique

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Marginal Update in Meanfield 6 Some possible states Total number of possible states: 3 6 labels

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Marginal Update in Meanfield 7 Exponential # of possible states for clique of size |c| and labels L: |L| C Expectation evaluation (summation) becomes infeasible

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Marginal Update in Meanfield 8 Use restricted form of cost Pattern based potential

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Marginal Update in Meanfield 9 Restrict the number of states to certain number of patterns Simple patterns Segment takes a label from label set of 4 patterns Or none

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Marginal Update in Meanfield 10 Expectation calculation is quite efficient

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Pattern based cost 11 Segment takes one of the forms

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Pattern based cost 12 Segment does not take one of the forms

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Pattern based cost 13 Simple patterns Pattern based higher order terms

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P N Potts based patterns 14 P N Potts based patterns Potts patterns

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Potts cost 15 Potts cost Potts patterns

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Marginal Update in Meanfield 16 General form of meanfield update Expectation of the cost given variable v i takes a label

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Expectation update 17 Probability of segment taking that label Potts patterns

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Expectation update 18 Probability of segment not taking that label Potts patterns

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Expectation update 19 Expectation update Potts patterns

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Complexity 20 Expectation Updation: Time complexity O(NL) Preserves the complexity of original filter based method

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PascalVOC-10 dataset 21 Inclusion of PN potts term: AlgorithmTime (s)OverallAv. RecallAv. I/U AHCRF+Cooc Dense CRF Dense + PN Potts 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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