learning and vision generative methods l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Learning and Vision: Generative Methods PowerPoint Presentation
Download Presentation
Learning and Vision: Generative Methods

Loading in 2 Seconds...

play fullscreen
1 / 26

Learning and Vision: Generative Methods - PowerPoint PPT Presentation


  • 217 Views
  • Uploaded on

Learning and Vision: Generative Methods. Andrew Blake, Microsoft Research Bill Freeman, MIT ICCV 2003 October 12, 2003 . Learning and vision: Generative Methods. Machine learning is an important direction in computer vision. Our goal for this class: Give overviews of useful techniques.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Learning and Vision: Generative Methods' - obelia


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
learning and vision generative methods

Learning and Vision: Generative Methods

Andrew Blake, Microsoft Research

Bill Freeman, MIT

ICCV 2003

October 12, 2003

learning and vision generative methods2
Learning and vision: Generative Methods
  • Machine learning is an important direction in computer vision.
  • Our goal for this class:
    • Give overviews of useful techniques.
    • Show how these methods can be used in vision.
    • Provide references and pointers.
  • Note afternoon companion class:

Learning and vision: Discriminative Methods,

taught by Chris Bishop and Paul Viola.

learning and vision generative models
Learning and VisionGenerative Models

Intro – roadmap for learning and inference in vision (WTF)

Probabilistic inference introduction; integration of sensory data

applications: color constancy, Bayes Matte

9:00 Basic estimation methods (WTF)

MLE, Expectation Maximization

applications: two-line fitting

Learning and inference in temporal and spatial Markov processes

Techniques:

9.25 (1) PCA, FA, TCA: (AB)

inference – linear (Wiener) filter

learning: by Expectation Maximization (EM);

applications: face simulation, denoising, Weiss’s intrinsic images

and furthermore: Active Appearance Models, Simoncelli, ICA & non-Gaussianity, filter banks

10.00 (2) Markov chain & HMM: (AB)

inference: - MAP by Dynamic Programming, Forward and Forward-Backward (FB) algorithms;

learning: by EM – Baum-Welch;

representations: pixels, patches

applications: stereo vision

and furthermore: gesture models (Bobick-Wilson)

< Break 10.30-10.45 >

10.45 (3) AR models: (AB)

Inference: Kalman-Filter, Kalman Smoother, Particle Filter;

learning: by EM-FB;

representations: patches, curves, chamfer maps, filter banks

applications: tracking (Isard-Blake, Black-Sidenbladh, Jepson-Fleet-El Maraghi); Fitzgibbon-Soatto textures

and furthermore: EP

11.30 (4) MRFs: (WTF)

Inference: ICM, LoopyBelief Propagation (BP), Generalised BP,Graph Cuts;

Parameter learning: Pseudolikelihood maximisation;

representations:color pixels, patches

applications: Texture segmentation, super resolution (Freeman-Pasztor), distinguishing shading from paint

and furthermore: Gibbs sampling, Discriminative Random Field (DRF), low level segmentation (Zhu et al.)

what is the goal of vision
What is the goal of vision?

If you are asking,

“Are there any faces in this image?”,

then you would probably want to use discriminative methods.

what is the goal of vision5
What is the goal of vision?

If you are asking,

“Are there any faces in this image?”,

then you would probably want to use discriminative methods.

If you are asking,

“Find a 3-d model that describes the runner”,

then you would use generative methods.

modeling
Modeling

So we want to look at high-dimensional visual data, and fit models to it; forming summaries of it that let us understand what we see.

how find the parameters of the best fitting gaussian

Posterior probability

Likelihood function

Prior probability

mean

data points

std. dev.

Evidence

By Bayes rule

How find the parameters of the best-fitting Gaussian?
how find the parameters of the best fitting gaussian10

Posterior probability

Likelihood function

Prior probability

mean

data points

std. dev.

Evidence

Maximum likelihood parameter estimation:

How find the parameters of the best-fitting Gaussian?
derivation of mle for gaussians
Derivation of MLE for Gaussians

Observation density

Log likelihood

Maximisation

basic maximum likelihood estimate mle of a gaussian distribution
Basic Maximum Likelihood Estimate (MLE) of a Gaussian distribution

Mean

Variance

Covariance Matrix

basic maximum likelihood estimate mle of a gaussian distribution13
Basic Maximum Likelihood Estimate (MLE) of a Gaussian distribution

Mean

Variance

For vector-valued data,

we have the Covariance Matrix

maximum likelihood estimation for the slope of a single line
Maximum likelihood estimation for the slope of a single line

Data likelihood for point n:

Maximum likelihood estimate:

where

gives regression formula

mle for fitting a line pair
MLE for fitting a line pair

(a form of mixture dist. for )

fitting two lines on the one hand

Line 1

Line 2

Fitting two lines: on the one hand…

If we knew which points went with which lines, we’d be back at the single line-fitting problem, twice.

y

x

fitting two lines on the other hand
Fitting two lines, on the other hand…

We could figure out the probability that any point came from either line if we just knew the two equations for the two lines.

y

x

mle with hidden latent variables expectation maximisation
MLE with hidden/latent variables:Expectation Maximisation

General problem:

data

parameters

hidden variables

For MLE, want to maximise the log likelihood

The sum over z inside the log gives a complicated expression for the ML solution.

the em algorithm
The EM algorithm

We don’t know the values of the

labels, zi , but let’s use its expected value under its posterior with the current parameter values, old. That gives us the “expectation step”:

“E-step”

Now let’s maximize this Q function, an expected log-likelihood, over the parameter values, giving the “maximization step”:

“M-step”

Each iteration increases the total log-likelihood log p(y|)

expectation maximisation applied to fitting the two lines
Expectation Maximisation applied to fitting the two lines

Need:

/2

and then:

and maximising that gives

associate data point

with line

Hidden variables

and probabilities of association are

:

em fitting to two lines
EM fitting to two lines

with

/2

“E-step”

and

repeat

Regression becomes:

“M-step”

experiments em fitting to two lines
Experiments: EM fitting to two lines

(from a tutorial by Yair Weiss, http://www.cs.huji.ac.il/~yweiss/tutorials.html)

Line weights

line 1

line 2

Iteration

1

2

3

applications of em in computer vision
Applications of EM in computer vision
  • Structure-from-motion with multiple moving objects
  • Motion estimation combined with perceptual grouping
  • Multiple layers/or sprites in an image.