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Markov Nets

Markov Nets. Dhruv Batra , 10-708 Recitation 10 /30/ 2008. Contents. MRFs Semantics / Comparisons with BNs Applications to vision HW4 implementation. Semantics. Bayes Nets. Semantics. Markov Nets. Semantics. Decomposition Bayes Nets Markov Nets. Semantics. Factorization

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Markov Nets

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  1. Markov Nets DhruvBatra,10-708 Recitation 10/30/2008

  2. Contents • MRFs • Semantics / Comparisons with BNs • Applications to vision • HW4 implementation

  3. Semantics • Bayes Nets

  4. Semantics • Markov Nets

  5. Semantics • Decomposition • Bayes Nets • Markov Nets

  6. Semantics • Factorization • What happens in BNs?

  7. Semantics • Active Trails in MNs • What happens in BNs?

  8. Semantics • Independence Assumptions Markov Nets Bayes Nets Global IndAssumption, d-sep Local IndAssumptions MarkovBlanket

  9. Representation Theorem for Markov Networks Then H is an I-map for P joint probability distribution P: If joint probability distribution P: If H is an I-map for P and P is a positive distribution Then 10-708 – Carlos Guestrin 2006-2008

  10. Semantics • Factorization • Energy functions • Equivalent representation

  11. Semantics • Log Linear Models

  12. Semantics • Energies in pairwiseMRFs • What is encoded on nodes and edges?

  13. Semantics • Priors on edges • Ising Prior / Potts Model • Metric MRFs

  14. Metric MRFs • Energies in pairwiseMRFs

  15. Applications in Vision • Image Labelling tasks • Denoising • Stereo • Segmentation, Object Recognition • Geometry Estimation

  16. MRF nodes as pixels Winkler, 1995, p. 32

  17. MRF nodes as patches image patches scene patches image F(xi, yi) Y(xi, xj) scene

  18. Network joint probability 1 Õ Õ = Y F P ( x , y ) ( x , x ) ( x , y ) i j i i Z , i j i scene Scene-scene compatibility function Image-scene compatibility function image neighboring scene nodes local observations

  19. Application • Motion Estimation

  20. Stereo

  21. Geometry Estimation

  22. Geometry Estimation

  23. HW4 • Interactive Image Segmentation

  24. HW4 • Pairwise MRF

  25. HW4

  26. HW4 • Step 1: GMMs • Step 2: Adjacency matrix / MRF Structure • Step 3: MRF parameters • Step 4: Loopy BP • Step 5: Segmentation Masks

  27. Slide Credits • Bill Freeman, Fredo Durand, Lecture at MIT • http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/2006March21MRF.ppt • Charles A. Bouman • https://engineering.purdue.edu/~bouman/ece641/mrf_tutorial/view.pdf • Fast Approximate Energy Minimization via Graph Cuts, Yuri Boykov, Olga Veksler and RaminZabih. IEEE PAMI 23(11), November 2001. • Make3D: Learning 3-D Scene Structure from a Single Still Image, AshutoshSaxena, Min Sun, Andrew Y. Ng, To appear in IEEE PAMI 2008

  28. Questions?

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