## Perturb-and-MAP Random Fields: Reducing Random Sampling to Optimization
## OverviewWe have been developing a new ## Problem statement
## Discrete-Label Markov Random Fields (ICCV-11 paper)In discrete-label MRFs the nodes can take one out of possible labels. This class of models, rooted to the classic Ising and Potts models in statistical physics, is widely used in image analysis and computer vision in applications such as image segmentation, stereo, and optical flow estimation. Powerful algorithms such as graph cuts, dual decomposition, and linear programming relaxations can efficiently find or approximate the minimum energy configuration for many discrete-label energy models used in practice. ## Perturb-and-MAP geometry
## Perturbation design: Full and reduced order Gumbel perturbations
What is the most efficient way to generate in Matlab random samples from a discrete distribution specified in terms of a probability or energy table? Check out this. ## Learning the model parameters from training data by moment matching
## Application: Interactive image segmentation
## Application: Tiered scene labeling
## Gaussian Markov Random Fields (NIPS-10 paper)
## Exact sampling by local perturbations in Gaussian MRFs
## Variance estimation
## Non-Gaussian continuous MRFs with sparse potentialsMost modern continuous-valued models used in signal and image analysis are
non-Gaussian, but instead use ideas from sparse signal modeling. However,
Gaussian MRFs turn out to be very useful as building blocks within sparse
models. In our work we have shown that efficient Gaussian MRF sampling can be
a key ingredient that allows both Monte-Carlo and variational Bayesian
approaches scale up to large-scale data. ## PeopleGeorge Papandreou (contact person)
## Publications-
G. Papandreou and A. Yuille,
**Perturb-and-MAP Random Fields: Using Discrete Optimization to Learn and Sample from Energy Models**, Proc. IEEE Int. Conf. on Computer Vision (ICCV-11), Barcelona, Spain, Nov. 2011. [pdf] [bib] [appendix] [ICCV talk] [slides] [poster] -
G. Papandreou and A. Yuille,
**Gaussian Sampling by Local Perturbations**, Proc. Int. Conf. on Neural Information Processing Systems (NIPS-10), Vancouver, B.C., Canada, Dec. 2010. [pdf] [bib] [poster] -
G. Papandreou, P. Maragos, and A. Kokaram,
**Image Inpainting with a Wavelet Domain Hidden Markov Tree Model**, Proc. IEEE Int. Conference on Acoustics, Speech, and Signal Processing (ICASSP-08), pp. 773-776, Las Vegas, NV, U.S.A., Mar.-Apr. 2008. [pdf] [bib]
## AcknowledgmentsOur work has been supported by the U.S. Office of Naval Research under MURI grant N000141010933; the NSF under award 0917141; the AFOSR under grant 9550-08-1-0489; and the Korean Ministry of Education, Science, and Technology, under the National Research Foundation WCU program R31-10008. This is gratefully acknowledged. |