1. Markov Random Fields for Edge Classification
Grant Schindler
CS 7636 Final Project

2. Problem: Edge Classification
Given vanishing points of a scene, classify each pixel according to vanishing direction

3. MAP Edge Classifications
Red: VP1 Green: VP2 Blue: VP3 Gray: Other White: Off

4. p(M | G,V) = p(G | M,V) p(M) / Z
Bayesian Model
p(M | G,V) = p(G | M,V) p(M) / Z
M = classifications, G = gradient magnitude/direction, V = vanishing points
Independent Prior
MRF Prior m
Prior: p(m)
Likelihood: p(g | m,V) g

5. Classifications w/MRF Prior
Gibbs sampling over 4-neighbor lattice w/ clique potentials defined as: A if i=j, B if i <> j

6. Gibbs Sampling & MRFs
Sample from distribution over labels for one site conditioned on all other sites in its Markov blanket
Gibbs sampling approximates posterior distribution over classifications at each site (by iterating and accumulating statistics)

7. Directional MRF vp
Give more weight to potentials of neighbors which lie along the vanishing direction of current model

8. Original Image

9. Independent Prior

10. MRF Prior

11. Directional MRF Prior

12. Conclusion, Discussion
This is really the E-Step of an EM process that alternates between edge classification and vanishing point estimation - will MRFs improve the vanishing point estimates?
Questions?