Hoip10 presentación seguimiento de objetos_vicomtech

Probabilistic object tracking for global
optimization

Dr.-Ing. Marcos Nieto Doncel
Investigador/Researcher
mnieto@vicomtech.org

Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)

Outline

1. Introduction

2. Bayesian filtering

3. Particle filters
• Human tracking
• Multiple object tracking

4. MCMC
• iToll project

5. Conclusions

Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10) 2

1.- Introduction
 Object tracking in video-surveillance applications
 Estimate properties of the imaged objects

 Propagate knowledge through time

 Multiple object tracking is a challenge

W

W

H L
H

(x0,y0) (x0,y0)

3

2.- Bayesian filtering
 Model the problem as a propagation of random variables
through time
 Each property is represented by a random variable

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

W
W

H H

(x0,y0)
x0
y0

4

 Infererence: estimate the values of the state vector (reality)
based on a sequence of observations (images) applying
uncertainty models
 Observation model: how the object is expected to appear in
images
• Observation equation: p(zk|xk)

 Dynamic model: what type of motion the object is expected to
show?
• Dynamic equation: p(xk|xk-1)

 Find posterior distribution p(xk|z1:k) and obtain a point-estimate
p(xk|z1:k) -> xk
• Mean, robust-mean, mode, median, etc.

5


K-1 K K+1 TIME
p(zk|xk): Observation model

zk-1 zk zk+1 MEASUREMENTS
(VISIBLE)

STATES
xk-1 xk xk+1 (HIDDEN)

p(xk|xk-1): Dynamic model

6

 Bayes’ rule
 Combine observation and prediction models

Observation Prior

 Under some assumptions, one can obtain the optimal solution to
this problem
• Kalman filter if distributions are Gaussians and models are
linear

 However, typical video-surveillance problems are highly non-linear
and/or non-Gaussian
• Sub-optimal solutions need to be computed

7

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 Bayesian
filter by representing the posterior density as a set of
samples or particles

WEIGHTED UNWEIGHTED

8

 Understanding particles
 Each particle represents a hypothesis of the state-vector

 The set of particles represents the “reliability” of each region of the
space

 The combination of particles lead to the best estimate

W
W

H H

(x0,y0)
x0
y0

9

 Importance sampling (weighted particles)
 CONDENSATION, SIS, SIR

10

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).

3.- Particle filters / Human tracking

ELLIPTICAL MODEL

11


 Observation model

Ratio between inside pixels and ellipse area
Ratio between inside and total pixels
Compactness around center of the ellipse

12


 Multiple objects

13

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).


14

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.


15

4.- MCMC
 Approximation with unweighted particles
 Markov Chain Monte Carlo (MCMC)

 Metropolis-Hastings algorithm to generate a Markov Chain that
approximates to the posterior

Metropolis-Hastings allows
obtaining samples for an
arbitrary distribution by making
a chain which accepts or
rejects samples

16

4.- MCMC
 Approximation with unweighted particles
 MCMC methods improve the results obtained by importance
sampling strategies for high dimensional spaces

 MCMC is therefore recommended to be used when the dimensions
of the problem increase

 Metropolis-Hastings is the most typically used generic sampling
algorithm for MCMC

 Other alternatives
• Slice sampler
• Gibbs sampler
• Levenberg-Marquardt

17

4.- MCMC / Vehicle tracking
 iToll project

18

 iToll project
 Variable perspective

 Variable vehicle sizes, appearance and motion

 Adverse illumination and weather conditions

 Real-time operation

19


20

 Inferring 3D volume from 2D observations
 There is a projective ambiguity that can not be solved analytically

There are 3D infinite
volumes that project onto
the same 2D shape
But only one is the right
one!

 MCMC-based approach
• Combination of projective geometry constraints
• Temporal coherence
• Prior knowledge about vehicle configurations

21


22


23


24

5.- Conclusions
 Object tracking can be modelled as an probabilistic
inference problem
 Uncertainty is mathematically handled

 Potentially any problem can be tackled like this!

 Particle filters are a popular tool to solve non-linear and
analytically intractable inference problems
 Importance sampling algorithms (CONDENSATION)

 MCMC methods represents a step forward solving high-
dimensional problems
 Optimization technique could be applied to reduce the
computational complexity and allow real-time performance

25

Dr.-Ing. Marcos Nieto Doncel
Investigador/Researcher
mnieto@vicomtech.org

http://marcosnieto.zymichost.com/

26

Hoip10 presentación seguimiento de objetos_vicomtech

More Related Content

Similar to Hoip10 presentación seguimiento de objetos_vicomtech

More from TECNALIA Research & Innovation

Recently uploaded

Hoip10 presentación seguimiento de objetos_vicomtech