Bayesian state estimation and application to tracking
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Bayesian state estimation and application to tracking. Jamal Saboune [email protected] VIVA Lab - SITE - University of Ottawa. Dynamic state estimation. A dynamic process described using a number of random variables (state variables) The evolution of the variables follows a model

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Bayesian state estimation and application to tracking l.jpg

Bayesian state estimation and application to tracking

Jamal Saboune

[email protected]

VIVA Lab - SITE - University of Ottawa

Jamal Saboune - CRV10 Tutorial Day


Dynamic state estimation l.jpg

Dynamic state estimation

A dynamic process described using a number of random variables (state variables)

The evolution of the variables follows a model

Indication on all or some of the variables (observation)

Evaluate at time t in a recursive manner (using t-1) the process represented by its state vector Xt , given the history of observations Yt

Jamal Saboune - CRV10 Tutorial Day

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Dynamic state estimation3 l.jpg

Dynamic state estimation

Xt= ft (Xt-1 ,Πt )

X0

The Markov process is defined by its transition model and the initial state vector:

The observation is defined by the observation model :

Yt= ht (Xt ,vt )

Jamal Saboune - CRV10 Tutorial Day


Dynamic state estimation bayesian approach l.jpg

Dynamic state estimation- Bayesian approach

Estimate the a posteriori probability density function P(Xt / Yt ) using the transition model, the observation model and the probability density function P(Xt-1 / Yt-1 )

Jamal Saboune - CRV10 Tutorial Day


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Kalman filter

Probability density propagation = Theoretical solution not an analytical one

Particular case : The observation and process noises distributions are Gaussian + The transition and observation functions are linear  The probability density functions are Gaussian mono-modal

Jamal Saboune - CRV10 Tutorial Day


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Kalman filter

A number of equations using the transition/observation functions and covariance matrices  Optimal estimation of the state vector

Minimizes the mean square error between the estimated state vector X’t andthe ‘real’ state vector Xt E[(X’t - Xt )2] given the history of observations Yt

Extended Kalman Filter (EKF) is the non linear version of the KF = The transition and observation function can be non-linear

Jamal Saboune - CRV10 Tutorial Day

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Kalman filter example

Jamal Saboune - CRV10 Tutorial Day


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Condensation algorithm (Isard, Blake 98)

Multimodal and non Gaussian probability densities

Model the uncertainty

Each possible configuration of the state vector is represented by a ‘particle'

The likelihood of a certain configuration is called ‘weight’

The posterior (a posteriori) density is represented using N ‘weighted’ particles

Jamal Saboune - CRV10 Tutorial Day


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Particles at t-1

CONDENSATION – time t

Selection

Prediction

Likelihood function

Measure

Jamal Saboune - CRV10 Tutorial Day

Chosen particle


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Condensation algorithm (Isard, Blake 98)

Tracking of a hand movement using an edge detector

Jamal Saboune - CRV10 Tutorial Day


Hands and head movement tracking using color models and optical flow tung et al 2008 l.jpg

Condensation algorithm for tracking

Hands and head movement tracking using color models and optical flow (Tung et al. 2008)

Jamal Saboune - CRV10 Tutorial Day


Head tracking with contour models zhihong et al 2002 l.jpg

Condensation algorithm for tracking

Head tracking with contour models (Zhihong et al. 2002)

Jamal Saboune - CRV10 Tutorial Day


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Interval Particle Filtering for 3D motion capture (Saboune et al. 05,07,08)

  • 3D humanoid model adapted to the height of the person

  • 32 degrees of freedom to simulate the human movement

Find the best fitting 3D model configuration

Jamal Saboune - CRV10 Tutorial Day

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Interval Particle Filtering for 3D motion capture (Saboune et al. 05,07,08)

  • Modify the Condensation algorithm and adapt it to the human motion tracking  Good estimation using a reduced number of particles

Jamal Saboune - CRV10 Tutorial Day

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Particle Filtering for multi-targets tracking et al. 05,07,08)

  • Joint state vector for all targets and joint likelihood function (Isard, MacCormick 2001, Zhao, Nevatia 2004)

  • Multiple particle filters (one/target) and combined global likelihood function (Koller-Maier 2001)

  • The Explorative particle filtering for 3D people tracking (Saboune, Laganiere 09)

Jamal Saboune - CRV10 Tutorial Day

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Q & A et al. 05,07,08)

Jamal Saboune - CRV10 Tutorial Day

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