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Particle Filters and Applications in Computer Vision

De
110 pages
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


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Particle Filters and Applications in Computer Vision
Désiré Sidibé (Le2i)
Désiré Sidibé
Maître de Conférences - Université de Bourgogne LE2I - UMR CNRS 5158 dro-desire.sidibe@u-bourgogne.fr
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 thebestimsteateˆxfor a parameterxgiven a set ofkeasumstnemer Z1:k={z1 . . . zk}.
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
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Introduction
Using Bayes rule, theopsteriorpdf is given by
p(x|Z1:k)
=
p(x|Z1:k): theiorsteroppdf p(Z1:k|x): thedlhiookilefunction p(x): theprioronidirtsitub
p(Z1:k|x)p(x) p(Z1:k) η×p(Z1: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|Z1:k)η×p(Z1:k|x)
Then, the estimateˆxis given by the value ofxwhich maximizes the likelihood function : xˆML=arg mxaxp(Z1:k|x)
Maximum A-Posteriori Estimation In many cases we have some prior knowledge onxrepresented byp(x):
p(x|Z1:k)η×p(Z1:k|x)p(x) Then, the estimatexˆis given by the value ofxwhich maximizes the posterior distribution :
Désiré Sidibé (Le2i)
xˆMAP=arg mxaxp(Z1:k|x)p(x)
Module Image - I2S
April 6th 2011
10 / 110
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