Particle Filters and Applications in Computer Vision

Désiré Sidibé

Description

Particle Filters and Applications in Computer Vision Désiré Sidibé Maître de Conférences - Université de Bourgogne LE2I - UMR CNRS 5158 April 6th 2011 Désiré Sidibé (Le2i) Module Image - I2S April 6th 2011 1 / 110

• le2i


• state estimation


• predicting economical


• le2i umr


• maître de conférences


• tracking methods


• visual tracking


• estimation theory


• estimation estimation


• computer vision

Sujets

• Sidibé
• Bayesian
• Université de Bourgogne
• State observer
• Academic rank in France
• Estimation theory
• Computer vision

Informations

• Publié par: pefav
• Nombre de lectures: 30
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Particle Filters and Applications in Computer Vision

Désiré Sidibé (Le2i)

Désiré Sidibé

Maître de Conférences - Université de Bourgogne LE2I - UMR CNRS 5158 [e-mail]

April 6th 2011

Module Image - I2S

April 6th 2011

1 / 110

Outline

1

2

3

4

5

Introduction

General Bayesian Framework

Particle Filters

Visual Tracking

Conclusion

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

2 / 110

Outline

1

2

3

4

5

Introduction Recall on Estimation Theory What Is A Particle Filter ? Applications in Computer Vision

General Bayesian Framework Kalman Filter

Particle Filters

Visual Tracking Tracking Methods Particle Filters Based Tracking

Conclusion

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

3 / 110

Introduction

Particle Filters : two words Filter: a procedure that estimates parameters (state) of a system. Particles: a set of randomly chosen weighted samples used to approximate a pdf.

Estimation Estimationis the process by which we infer the value of a quantity of interest,x, by processing data that is in some way dependent onx.

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

4 / 110

Introduction

State estimation or filtering has many applications

Estimating communication

signals from noisy measurements Predicting economical data Tracking of aircraft positions from radar Tracking of people or cars in surveillance videos Mobile robotics etc.

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

5 / 110

Introduction

Goals of this presentation:

State the problem Introduce the key ideas Show examples of applications in computer vision

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

6 / 110

Outline

1

2

3

4

5

Introduction Recall on Estimation Theory What Is A Particle Filter ? Applications in Computer Vision

General Bayesian Framework Kalman Filter

Particle Filters

Visual Tracking Tracking Methods Particle Filters Based Tracking

Conclusion

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

7 / 110

Introduction

The problem Find thebestimsteate ˆ xfor a parameterxgiven a set ofkeasumstnemer Z 1:k ={ z 1  . . .  z k }.

State estimation is based on probability theroy. One of the’most important’results in probability theory is Bayes Rule : P ( B | A ) P ( A )

Désiré Sidibé (Le2i)

P ( A | B ) = P ( B ) likelihood × prior posterior = veenidce => simple but powerful !

Module Image - I2S

April 6th 2011

8 / 110

Introduction

Using Bayes rule, theopsteriorpdf is given by

p ( x | Z 1:k )

=

∝

p ( x | Z 1:k ) : theiorsteroppdf p ( Z 1:k | x ) : thedlhiookilefunction p ( x ) : theprioronidirtsitub

p ( Z 1:k | x ) p ( x ) p ( Z 1:k ) η× p ( Z 1:k | x ) p ( x )

"‘The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening."’ Thomas Bayes (1702-1761)

Désiré Sidibé (Le2i)

Module Image - I2S

April 6th 2011

9 / 110

Introduction

Maximum Likelihood Estimation If we have no prior knowledge about the parameterx:

p ( x | Z 1:k )∝η× p ( Z 1:k | x )

Then, the estimate ˆ xis given by the value ofxwhich maximizes the likelihood function : x ˆ ML = arg m x axp ( Z 1:k | x )

Maximum A-Posteriori Estimation In many cases we have some prior knowledge onxrepresented byp ( x ) :

p ( x | Z 1:k )∝η× p ( Z 1:k | x ) p ( x ) Then, the estimatex ˆ is given by the value ofxwhich maximizes the posterior distribution :

Désiré Sidibé (Le2i)

x ˆ MAP = arg m x axp ( Z 1:k | x ) p ( x )

Module Image - I2S

April 6th 2011

10 / 110