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Integration of shape constraints in data association filters Giambattista Gennari, Alessandro Chiuso, Fabio Cuzzolin, Ruggero Frezza University of Padova chiuso@dei.unipd.it www.dei.unipd.it/~chiuso. Outline of the Talk. Tracking and Data Association Classical solution: independent dynamics

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Integration of shape constraints in data association filtersGiambattista Gennari, Alessandro Chiuso, Fabio Cuzzolin, Ruggero FrezzaUniversity of Padovachiuso@dei.unipd.itwww.dei.unipd.it/~chiuso

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Outline of the Talk

  • Tracking and Data Association

  • Classical solution: independent dynamics

  • Our approach : integration of shape

  • Occlusions

  • Experiments

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Tracking and Data Association

  • PROBLEM:Set of targets generating UNLABELLED measurements

Associate

and

Track

  • Occlusions

  • Clutter

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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SHAPE AND COORDINATION

Motion invariant properties of targets:

  • Rigid or Articulated bodies

  • Formations of vehicles

  • (Flock of birds)

  • Deformable objects

Distances and/or angles

Connectivity – distances

Relative velocity

Group of admissible deformations (probabilistic or deterministic)

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Probabilistic Tracking and

Data Association

CLASSICALLY:

JPDAF – MHT

+

Dynamical Models

OUR APPROACH:

JPDAF- (MHT)

+

Independent Dynamical Models

+

Shape Information

Full (joint) model

-not flexible

-computationally

expensive

Model targets

Independently

-flexible and easy

-not robust

occlusions

exchange tracks

+ Flexible

+ Robust to occlusions and

track proximity

- Computation (Monte Carlo)

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Independent Motion

  • Targets are described by independent dynamics

Index of Target

  • Flexible and easy

  • Lack of robustness in presence of occlusions, false detections and closely spaced targets

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Associations

  • An association is a map matching unlabelled measurements to targets

  • Employ the overall model to compute the probability of each association

Measurements

Measurements matched to clutter

Association

Measurements matched to targets

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Description of “Shape”

Probabilistic Model

Motion Invariant

Targets positions

  • Prior Knowledge

  • Learn from Data

  • Example: pairwise distances of non perfectly rigid bodies

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Shape Integration

  • We assume the overall model can be factored into two terms describing the mutual configuration and single target dynamics

Shape constraints

Kalman filters and independent dynamical models

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Occlusions

  • To compute marginalize over the occluded :

Detected points

Missing points (occlusions)

  • Compute the integral through Monte Carlo techniques

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Monte Carlo Integration

  • Sample:

  • Weight:

  • Integrate:

  • Fair sample from the posterior

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Summary

Conditional state estimates

INDEPENDENT KALMAN FILTERS

SHAPE

….

T1

T2

TN

Association

probabilities

OVERALL MODEL

Monte Carlo fair samples for occluded points state estimation

Measurements

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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State Estimation

  • An overall state estimate can be obtained summing the conditional state estimates weighted by the corresponding association probabilities

  • Alternatively, several state estimates can be propagated over time (multi hypothesis tracker )

Necessary in the learning phase !

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Results

  • Real data from a motion capture system

  • Rapid motion

  • High numbers of false detections

  • Occlusions lasting several frames

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Results

Commercial system: looses and confuses tracks

With shape knowledge learned from data

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Conclusions

  • Algorithm for integrating shape knowledge into data association filter

  • Robust in presence of occlusions and clutter

  • Provide a framework for learning shape models (this requires use of multiple hypothesis kind of algorithms)

  • (In the example shape was learned from data)

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Shape Constraints

  • In many cases, coordinated points exhibit properties which are invariant with respect to their motion, they satisfy some sort of shape constraints:

    • pairwise distances of rigidly linked points are constant

    • the position and velocity of a point moving in group are similar to those of its neighbors

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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Coordinated Motion

  • Rigid motion

  • Articulated bodies,

  • Groups of people moving together,

  • Formations

  • Taking into account coordination improves tracking robustness

  • We describe shape and motion separately and combine them together ( more flexible than joint models )

IEEE CDC 2004 - Nassau, Bahamas, December 14-17


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