Presentation is loading. Please wait.

Presentation is loading. Please wait.

Markov Random Fields Probabilistic Models for Images

Published byGordon Hunter Modified over 9 years ago

Similar presentations

Presentation on theme: "Markov Random Fields Probabilistic Models for Images"— Presentation transcript:

1 Markov Random Fields Probabilistic Models for Images
Applications in Image Segmentation and Texture Modeling Ying Nian Wu UCLA Department of Statistics IPAM July 22, 2013

2 Outline Basic concepts, properties, examples
Markov chain Monte Carlo sampling Modeling textures and objects Application in image segmentation

3 Markov Chains Pr(future|present, past) = Pr(future|present)
future past | present Markov property: conditional independence limited dependence Makes modeling and learning possible

4 Markov Chains (higher order)
Temporal: a natural ordering Spatial: 2D image, no natural ordering

5 Markov Random Fields Markov Property all the other pixels
Nearest neighborhood, first order neighborhood From Slides by S. Seitz - University of Washington

6 Markov Random Fields Second order neighborhood

7 Markov Random Fields Can be generalized to any undirected graphs (nodes, edges) Neighborhood system: each node is connected to its neighbors neighbors are reciprocal Markov property: each node only depends on its neighbors Note: the black lines on the left graph are illustrating the 2D grid for the image pixels they are not edges in the graph as the blue lines on the right

8 Markov Random Fields What is

9 Hammersley-Clifford Theorem
normalizing constant, partition function potential functions of cliques Cliques for this neighborhood From Slides by S. Seitz - University of Washington

10 Hammersley-Clifford Theorem
Gibbs distribution a clique: a set of pixels, each member is the neighbor of any other member Cliques for this neighborhood From Slides by S. Seitz - University of Washington

11 Hammersley-Clifford Theorem
Gibbs distribution a clique: a set of pixels, each member is the neighbor of any other member Cliques for this neighborhood ……etc, note: the black lines are for illustrating 2D grids, they are not edges in the graph

12 Ising model Cliques for this neighborhood
From Slides by S. Seitz - University of Washington

13 Ising model pair potential Challenge: auto logistic regression

14 Gaussian MRF model Challenge: auto regression continuous
pair potential Challenge: auto regression

15 Sampling from MRF Models
Markov Chain Monte Carlo (MCMC) Gibbs sampler (Geman & Geman 84) Metropolis algorithm (Metropolis et al. 53) Swedeson & Wang (87) Hybrid (Hamiltonian) Monte Carlo

16

17 Gibbs Sampler Repeat: Randomly pick a pixel
Simple one-dimension distribution Repeat: Randomly pick a pixel Sample given the current values of

18 Gibbs sampler for Ising model
Challenge: sample from Ising model

19 Metropolis Algorithm Repeat:
energy function Repeat: Proposal: Perturb I to J by sample from K(I, J) = K(J, I) If change I to J otherwise change I to J with prob

20 Metropolis for Ising model
Ising model: proposal --- randomly pick a pixel and flip it Challenge: sample from Ising model

21 Modeling Images by MRF Ising model
Hidden variables, layers, RBM Exponential family model, log-linear model maximum entropy model unknown parameters features (may also need to be learned) reference distribution

22 Modeling Images by MRF Given How to estimate Maximum likelihood
Pseudo-likelihood (Besag 1973) Contrastive divergence (Hinton)

23 Maximum likelihood Given Challenge: prove it

24 Stochastic Gradient Given Generate Analysis by synthesis

25 Texture Modeling

26

27

28

29

30

31

32

33

34

35

36

37

38 Modeling image pixel labels as MRF (Ising)
MRF for Image Segmentation Modeling image pixel labels as MRF (Ising) Bayesian posterior 1 real image label image Slides by R. Huang – Rutgers University

39 Model joint probability
region labels image pixels model param. image-label compatibility Function enforcing Data Constraint label-label compatibility Function enforcing Smoothness constraint label image local Observations neighboring label nodes Slides by R. Huang – Rutgers University

40 MRF for Image Segmentation
Slides by R. Huang – Rutgers University

41 Inference in MRFs Classical Gibbs sampling, simulated annealing
Iterated conditional modes State of the Art Graph cuts Belief propagation Linear Programming Tree-reweighted message passing Slides by R. Huang – Rutgers University

42 Summary MRF, Gibbs distribution Gibbs sampler, Metropolis algorithm
Exponential family model

Download ppt "Markov Random Fields Probabilistic Models for Images"

Similar presentations

Basic Steps 1.Compute the x and y image derivatives 2.Classify each derivative as being caused by either shading or a reflectance change 3.Set derivatives.

Basic Steps 1.Compute the x and y image derivatives 2.Classify each derivative as being caused by either shading or a reflectance change 3.Set derivatives.
Mean-Field Theory and Its Applications In Computer Vision1 1.

Mean-Field Theory and Its Applications In Computer Vision1 1.
Bayesian Belief Propagation

Bayesian Belief Propagation
Linear Time Methods for Propagating Beliefs Min Convolution, Distance Transforms and Box Sums Daniel Huttenlocher Computer Science Department December,

Linear Time Methods for Propagating Beliefs Min Convolution, Distance Transforms and Box Sums Daniel Huttenlocher Computer Science Department December,
Deep Learning Bing-Chen Tsai 1/21.

Deep Learning Bing-Chen Tsai 1/21.
CS590M 2008 Fall: Paper Presentation

CS590M 2008 Fall: Paper Presentation
Introduction to Markov Random Fields and Graph Cuts Simon Prince

Introduction to Markov Random Fields and Graph Cuts Simon Prince
Exact Inference in Bayes Nets

Exact Inference in Bayes Nets
Bayesian Estimation in MARK

Bayesian Estimation in MARK
Undirected Probabilistic Graphical Models (Markov Nets) (Slides from Sam Roweis)

Undirected Probabilistic Graphical Models (Markov Nets) (Slides from Sam Roweis)
Learning to estimate human pose with data driven belief propagation Gang Hua, Ming-Hsuan Yang, Ying Wu CVPR 05.

Learning to estimate human pose with data driven belief propagation Gang Hua, Ming-Hsuan Yang, Ying Wu CVPR 05.
Introduction to Belief Propagation and its Generalizations. Max Welling Donald Bren School of Information and Computer and Science University of California.

Introduction to Belief Propagation and its Generalizations. Max Welling Donald Bren School of Information and Computer and Science University of California.
EE462 MLCV Lecture 11-12 Introduction of Graphical Models Markov Random Fields Segmentation Tae-Kyun Kim 1.

EE462 MLCV Lecture Introduction of Graphical Models Markov Random Fields Segmentation Tae-Kyun Kim 1.
Probabilistic Inference Lecture 1

Probabilistic Inference Lecture 1
Markov Networks.

Markov Networks.
Markov Random Fields (MRF)

Markov Random Fields (MRF)
Markov random field Institute of Electronics, NCTU

Markov random field Institute of Electronics, NCTU
Graphical models, belief propagation, and Markov random fields 1.

Graphical models, belief propagation, and Markov random fields 1.
Chapter 8-3 Markov Random Fields 1. Topics 1. Introduction 1. Undirected Graphical Models 2. Terminology 2. Conditional Independence 3. Factorization.

Chapter 8-3 Markov Random Fields 1. Topics 1. Introduction 1. Undirected Graphical Models 2. Terminology 2. Conditional Independence 3. Factorization.
Learning to Detect A Salient Object Reporter: 鄭綱 (3/2)

Learning to Detect A Salient Object Reporter: 鄭綱 (3/2)

Similar presentations

Ads by Google