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Published byLauren Myers Modified over 3 years ago

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**Mean-Field Theory and Its Applications In Computer Vision2**

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**Dense CRF construction**

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

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**Long Range Interaction**

Able to recover proper flow for objects Teddy arms recovered using Global interaction Optical flow Optical flow and stereo reconstruction image Local interaction Global interaction Ground truth

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**Very Expensive Step (O(n2))**

Marginal Update Marginal Update for large neighbourhood: Very Expensive Step (O(n2))

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**Inference in Dense CRF 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 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 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 Assume Gaussian pairwise weight**

Label compatibility function

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**Efficient inference Assume Gaussian pairwise weight**

Mixture of Gaussians Spatial Bilateral

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Bilateral filter output input output input reproduced from [Durand 02]

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Marginal update Assume Gaussian pairwise weight

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**Very Expensive Step (O(n2))**

How does it work Very Expensive Step (O(n2))

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**Message passing from all Xj to all Xi**

Accumulates weights from all other pixels except itself

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**Message passing from all Xj to all Xi**

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**

Convert as Gaussian filtering step: Accumulate weights from all other pixels except itself

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**Efficient filtering steps**

Now discuss how to do efficient filtering step

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