Hoip10 presentación seguimiento de objetos_vicomtech

Marcos Nieto ([email protected]) Hands-on Image Processing 2010 (HOIP’10)

Dr.-Ing. Marcos Nieto DoncelInvestigador/Researcher

[email protected]

Probabilistic object tracking for global optimization


Outline

2

1. Introduction

2. Bayesian filtering

3. Particle filters• Human tracking• Multiple object tracking

4. MCMC• iToll project

5. Conclusions


1.- Introduction

Object tracking in video-surveillance applications

Estimate properties of the imaged objects

Propagate knowledge through time

Multiple object tracking is a challenge

3

W

H

(x0,y0)

H L

W

(x0,y0)


2.- Bayesian filtering

Model the problem as a propagation of random variablesthrough time

Each property is represented by a random variable

The set of properties define the object at time t: state vector

4

W

H

(x0,y0)

W

H

x0y0



Infererence: estimate the values of the state vector (reality)based on a sequence of observations (images) applyinguncertainty models

Observation model: how the object is expected to appear inimages

• Observation equation: p(zk|xk)

Dynamic model: what type of motion the object is expected toshow?

• Dynamic equation: p(xk|xk-1)

Find posterior distribution p(xk|z1:k) and obtain a point-estimatep(xk|z1:k) -> xk

• Mean, robust-mean, mode, median, etc.

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K-1 K K+1 TIME

MEASUREMENTS

(VISIBLE)

STATES

(HIDDEN)xk-1

zk-1

xk

zk

xk+1

zk+1

p(xk|xk-1): Dynamic model

p(zk|xk): Observation model



Bayes’ rule

Combine observation and prediction models

Under some assumptions, one can obtain the optimal solution tothis problem

• Kalman filter if distributions are Gaussians and models are linear

However, typical video-surveillance problems are highly non-linearand/or non-Gaussian

• Sub-optimal solutions need to be computed

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Observation Prior


3.- Particle filters

Particle filters

Sequential Monte Carlo (SMC) method, aka

• Condensation algorithm, bootstrap filter, survival of the fittest…

It is a technique for implementing a recursive Bayesianfilter by representing the posterior density as a set ofsamples or particles

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WEIGHTED UNWEIGHTED



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W

H

(x0,y0)

W

H

x0y0

Understanding particles

Each particle represents a hypothesis of the state-vector

The set of particles represents the “reliability” of each region of thespace

The combination of particles lead to the best estimate



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Importance sampling (weighted particles)

CONDENSATION, SIS, SIR


3.- Particle filters / Human tracking

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ELLIPTICAL MODEL

Marcos Nieto, Carlos Cuevas and Luis Salgado, “Measurement-based Reclustering for

Multiple Object Tracking with Particle Filters,” in IEEE Proc. International Conference on

Image Processing (ICIP2009).


Observation model


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Ratio between inside pixels and ellipse area

Ratio between inside and total pixels

Compactness around center of the ellipse






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Multiple objects






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Carlos R. del Blanco, Fernando Jaureguizar and Narciso García, “Visual Tracking of

Multiple Interacting Objects Through Rao-Blackwellized Data Association Particle

Filtering,” in IEEE Proc. International Conference on Image Processing (ICIP2010).



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R. Mohedano, N. García, “Robust Multi-Camera 3D Tracking from Mono-Camera 2D

Tracking using Bayesian Association”, IEEE Trans. Consumer Electronics, vol. 56, no. 1,

pp. 1-8, Feb. 2010.


4.- MCMC

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Approximation with unweighted particles

Markov Chain Monte Carlo (MCMC)

Metropolis-Hastings algorithm to generate a Markov Chain thatapproximates to the posterior

Metropolis-Hastings allows

obtaining samples for an

arbitrary distribution by making

a chain which accepts or

rejects samples


4.- MCMC

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Approximation with unweighted particles

MCMC methods improve the results obtained by importancesampling strategies for high dimensional spaces

MCMC is therefore recommended to be used when the dimensionsof the problem increase

Metropolis-Hastings is the most typically used generic samplingalgorithm for MCMC

Other alternatives

• Slice sampler

• Gibbs sampler

• Levenberg-Marquardt


4.- MCMC / Vehicle tracking

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iToll project



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iToll project

Variable perspective

Variable vehicle sizes, appearance and motion

Adverse illumination and weather conditions

Real-time operation



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Inferring 3D volume from 2D observations

There is a projective ambiguity that can not be solved analytically

MCMC-based approach

• Combination of projective geometry constraints

• Temporal coherence

• Prior knowledge about vehicle configurations


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There are 3D infinite

volumes that project onto

the same 2D shape

But only one is the right

one!



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5.- Conclusions

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Object tracking can be modelled as an probabilisticinference problem

Uncertainty is mathematically handled

Potentially any problem can be tackled like this!

Particle filters are a popular tool to solve non-linear andanalytically intractable inference problems

Importance sampling algorithms (CONDENSATION)

MCMC methods represents a step forward solving high-dimensional problems

Optimization technique could be applied to reduce thecomputational complexity and allow real-time performance

Marcos Nieto ([email protected]) Hands-on Image Processing 2010 (HOIP’10) 26

Dr.-Ing. Marcos Nieto DoncelInvestigador/Researcher

[email protected]

http://marcosnieto.zymichost.com/

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