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Mean-Field Theory and Its Applications In Computer Vision2
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Problem Formulation
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Grid CRF
construction
Grid CRF leads to over smoothing around boundariesDense CRF is able to recover fine boundaries
Dense CRF construction
Long Range Interaction
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• Able to recover proper flow for objects• Teddy arms recovered using Global interaction
image Local interaction Global interaction Ground truth
Optical flow
Marginal Update
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• Marginal Update for large neighbourhood:
Very Expensive Step (O(n2))
Inference in Dense CRF
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• Time complexity increases• Neighbourhood size• MCMC takes 36 hours on 50K variables• Graph-cuts based algorithm takes hours
Inference in Dense CRF
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• Time complexity increases• Neighbourhood size• MCMC takes 36 hours on 50K variables• Graph-cuts based algorithm takes hours
• Not practical for vision applications
Inference in Dense CRF
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• 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
Efficient inference
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• Assume Gaussian pairwise weight
Label compatibility function
Efficient inference
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• Assume Gaussian pairwise weight
Mixture of Gaussians
Bilateral Spatial
Bilateral filter
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pp
output input
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output input
Marginal update
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• Assume Gaussian pairwise weight
How does it work
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Very Expensive Step (O(n2))
Message passing from all Xj to all Xi
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Accumulates weights from all other pixels except itself
Message passing from all Xj to all Xi
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Convert as Gaussian filtering step: Accumulate weights from all other pixels except itself
Message passing from all Xj to all Xi
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Convert as Gaussian filtering step: Accumulate weights from all other pixels except itself
Efficient filtering steps
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Now discuss how to do efficient filtering step
