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Published byLauren Myers Modified over 2 years ago

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Mean-Field Theory and Its Applications In Computer Vision2 1

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Problem Formulation 2 Grid CRF construction Grid CRF leads to over smoothing around boundaries Dense CRF is able to recover fine boundaries Dense CRF construction

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Long Range Interaction 3 Able to recover proper flow for objects Teddy arms recovered using Global interaction image Local interactionGlobal interaction Ground truth Optical flow

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Marginal Update 4 Marginal Update for large neighbourhood: Very Expensive Step (O(n 2 ))

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Inference in Dense CRF 5 Time complexity increases Neighbourhood size MCMC takes 36 hours on 50K variables Graph-cuts based algorithm takes hours

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Inference in Dense CRF 6 Time complexity increases Neighbourhood size MCMC takes 36 hours on 50K variables Graph-cuts based algorithm takes hours Not practical for vision applications

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Inference in Dense CRF 7 Time complexity increases Neighbourhood size MCMC takes 36 hours on 50K variables Graph-cuts based algorithm takes hours Filter-based Mean-field Inference takes 0.2 secs Possibility of development of many exciting vision applications

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Efficient inference 8 Assume Gaussian pairwise weight Label compatibility function

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Efficient inference 9 Assume Gaussian pairwise weight Mixture of Gaussians Bilateral Spatial

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Bilateral filter 10 outputinput reproduced from [Durand 02] outputinput

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Marginal update 11 Assume Gaussian pairwise weight

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How does it work 12 Very Expensive Step (O(n 2 ))

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Message passing from all Xj to all Xi 13 Accumulates weights from all other pixels except itself

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Message passing from all Xj to all Xi 14 Convert as Gaussian filtering step: Accumulate weights from all other pixels except itself

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Message passing from all Xj to all Xi 15 Convert as Gaussian filtering step: Accumulate weights from all other pixels except itself

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Efficient filtering steps 16 Now discuss how to do efficient filtering step

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