1. Mean-Field Theory and Its Applications In Computer Vision2

2. 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

3. 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

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

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

6. 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

7. 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

8. Efficient inference Assume Gaussian pairwise weight
Label compatibility function

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

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

11. Marginal update
Assume Gaussian pairwise weight

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

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

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

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

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