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Integration and Graphical Models

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P(place, car, person, toaster, micro, hydrant) ... Graphical Models. Pros and cons. Very powerful if dependency structure is sparse and known ... – PowerPoint PPT presentation

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Title: Integration and Graphical Models


1
Integration and Graphical Models
  • Derek Hoiem
  • CS 598, Spring 2009
  • April 14, 2009

2
Why?
  • The goal of vision is to make useful inferences
    about the scene.
  • In most cases, this requires integrative
    reasoning about many types of information.

3
Example 3D modeling
4
Object context
From Divvala et al. CVPR 2009
5
How?
  • Feature passing
  • Graphical models

6
Class Today
  • Feature passing
  • Graphical models
  • Bayesian networks
  • Markov networks
  • Various inference and learning methods
  • Example

7
Properties of a good mechanism for integration
  • Modular different processes/estimates can be
    improved independently
  • Symbiotic each estimate improves
  • Robust mistakes in one process are not fatal for
    others that partially rely on it
  • Feasible training and inference is fast and easy

8
Feature Passing
  • Compute features from one estimated scene
    property to help estimate another

Image
X Estimate
X Features
Y Estimate
Y Features
9
Feature passing example
Use features computed from geometric context
confidence images to improve object detection
Features average confidence within each window
Above
Object Window
Below
Hoiem et al. ICCV 2005
10
Feature Passing
  • Pros and cons
  • Simple training and inference
  • Very flexible in modeling interactions
  • Not modular
  • if we get a new method for first estimates, we
    may need to retrain
  • Requires iteration to be symbiotic
  • complicates things
  • Robust in expectation but not instance

11
Probabilistic graphical models
  • Explicitly model uncertainty and dependency
    structure

Directed
Undirected
Factor graph
a
a
a
b
b
b
c
d
c
d
c
d
Key concept Markov blanket
12
Directed acyclical graph (Bayes net)
Arrow directions matter
a
a
c independent of a given b d independent of a
given b
a,c,d dependent when conditioned on b
b
b
c
d
c
d
P(a,b,c,d) P(cb)P(db)P(ba)P(a)
P(a,b,c,d) P(ba,c,d)P(a)P(c)P(d)
13
Directed acyclical graph (Bayes net)
  • Can model causality
  • Parameter learning
  • Decomposes learn each term separately (ML)
  • Inference
  • Simple exact inference if tree-shaped (belief
    propagation)

a
b
c
d
P(a,b,c,d) P(cb)P(db)P(ba)P(a)
14
Directed acyclical graph (Bayes net)
  • Can model causality
  • Parameter learning
  • Decomposes learn each term separately (ML)
  • Inference
  • Simple exact inference if tree-shaped (belief
    propagation)
  • Loops require approximation
  • Loopy BP
  • Tree-reweighted BP
  • Sampling

a
b
c
d
P(a,b,c,d) P(cb)P(da,b)P(ba)P(a)
15
Directed graph
  • Example Places and scenes

Place office, kitchen, street, etc.
Objects Present
Fire Hydrant
Car
Person
Toaster
Microwave
P(place, car, person, toaster, micro, hydrant)
P(place) P(car place) P(person place)
P(hydrant place)
16
Directed graph
  • Example Putting Objects in Perspective

17
Undirected graph (Markov Networks)
  • Does not model causality
  • Often pairwise
  • Parameter learning difficult
  • Inference usually approximate

x1
x2
x3
x4
18
Markov Networks
  • Example label smoothing grid

Binary nodes
Pairwise Potential
0 1 0 0 K 1 K 0
19
Factor graphs
  • A general representation

Factor Graph
a
Bayes Net
a
b
b
c
d
c
d
20
Factor graphs
  • A general representation

Factor Graph
a
b
c
d
21
Factor graphs
Write as a factor graph
22
Inference Belief Propagation
  • Very general
  • Approximate, except for tree-shaped graphs
  • Generalizing variants BP can have better
    convergence for graphs with many loops or high
    potentials
  • Standard packages available (BNT toolbox, my
    website)
  • To learn more
  • Yedidia, J.S. Freeman, W.T. Weiss, Y.,
    "Understanding Belief Propagation and Its
    Generalizations, Technical Report, 2001
    http//www.merl.com/publications/TR2001-022/

23
Inference Graph Cuts
  • Associative edge potentials penalize different
    labels
  • Associative binary networks can be solved
    optimally (and quickly) using graph cuts
  • Multilabel associative networks can be handled by
    alpha-expansion or alpha-beta swaps
  • To learn more
  • http//www.cs.cornell.edu/rdz/graphcuts.html
  • Classic paper What Energy Functions can be
    Minimized via Graph Cuts? (Kolmogorov and Zabih,
    ECCV '02/PAMI '04)

24
Inference Sampling (MCMC)
  • Metropolis-Hastings algorithm
  • Define transitions and transition probabilities
  • Make sure you can get from any state to any other
    (ergodicity)
  • Make proposal and accept if rand(1) lt P(new
    state)/P(old state) P(backward transition) /
    P(transition)
  • Note if P(state) decomposes, this is easy to
    compute
  • Example Image parsing by Tu and Zhu to find
    good segmentation

25
Learning parameters maximize likelihood
  • Simply count for Bayes network with discrete
    variables
  • Run BP and do gradient descent for Markov network
  • Often do not care about full likelihood

26
Learning parameters maximize objective
  • SPSA (simultaneous perturbation stochastic
    approximation) algorithm
  • Take two trial steps in a random direction, one
    forward and one backwards
  • Compute loss (or objective) for each and get a
    pseudo-gradient
  • Take a step according to results
  • Refs
  • Li and Huttenlocher, Learning for Optical Flow
    Using Stochastic Optimization, ECCV 2008
  • Various papers by Spall on SPSA

27
Learning parameters structured learning
See also Tsochantaridis et al.
http//jmlr.csail.mit.edu/papers/volume6/tsochant
aridis05a/tsochantaridis05a.pdf
Szummer et al. 2008
28
How to get the structure?
  • Set by hand (most common)
  • Learn (mostly for Bayes nets)
  • Maximize score (greedy search)
  • Based on independence tests
  • Logistic regression with L1 regularization for
    finding Markov blanket

For more www.autonlab.org/tutorials/bayesstruct05
.pdf
29
Graphical Models
  • Pros and cons
  • Very powerful if dependency structure is sparse
    and known
  • Modular (especially Bayesian networks)
  • Flexible representation (but not as flexible as
    feature passing)
  • Many inference methods
  • Recent development in learning Markov network
    parameters, but still tricky

30
Which techniques have I used?
  • Almost all of them
  • Feature passing (ICCV 2005, CVPR 2008)
  • Bayesian networks (CVPR 2006)
  • In factor graph form (ICCV 2007)
  • Semi-naïve Bayes (CVPR 2004)
  • Markov networks (ECCV 2008, CVPR 2007, CVPR 2005
    HMM)
  • Belief propagation (CVPR 2006, ICCV 2007)
  • Structured learning (ECCV 2008)
  • Graph cuts (CVPR 2008, ECCV 2008)
  • MCMC (IJCV 2007 didnt work well)
  • Learning Bayesian structure (2002-2003, not
    published)

31
Example faces, skin, cloth
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