Markov Nets Dhruv Batra, 10-708 Recitation 10/30/2008.

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Presentation transcript:

Markov Nets Dhruv Batra, 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 What happens in BNs?

Semantics Active Trails in MNs What happens in BNs?

Semantics Independence Assumptions Markov NetsBayes Nets Global Ind Assumption, d-sep Local Ind Assumptions Markov Blanket

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

Semantics Factorization Energy functions Equivalent representation

Semantics Log Linear Models

Semantics Energies in pairwise MRFs What is encoded on nodes and edges?

Semantics Priors on edges –Ising Prior / Potts Model –Metric MRFs

Metric MRFs Energies in pairwise MRFs

Applications in Vision Image Labelling tasks –Denoising –Stereo –Segmentation, Object Recognition –Geometry Estimation

MRF nodes as pixels Winkler, 1995, p. 32

MRF nodes as patches image patches  (x i, y i )  (x i, x j ) image scene scene patches

Network joint probability scene image Scene-scene compatibility function neighboring scene nodes local observations Image-scene compatibility function   i ii ji ji yxxx Z yxP),(),( 1 ),(,

Application Motion Estimation

Stereo

Geometry Estimation

HW4 Interactive Image Segmentation

HW4 Pairwise MRF

HW4

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

Slide Credits Bill Freeman, Fredo Durand, Lecture at MIT – lecturenotes/2006March21MRF.ppt Charles A. Bouman – ew.pdfhttps://engineering.purdue.edu/~bouman/ece641/mrf_tutorial/vi ew.pdf Fast Approximate Energy Minimization via Graph Cuts, Yuri Boykov, Olga Veksler and Ramin Zabih. IEEE PAMI 23(11), November Make3D: Learning 3-D Scene Structure from a Single Still Image, Ashutosh Saxena, Min Sun, Andrew Y. Ng, To appear in IEEE PAMI 2008

Questions?