IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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Integration of shape constraints Integration of shape constraints in data association filtersin data association filters
Giambattista Gennari, Alessandro Chiuso, Fabio Cuzzolin, Ruggero Frezza
University of [email protected]
www.dei.unipd.it/~chiuso
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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Outline of the TalkOutline 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 AssociationTracking and Data Association
• PROBLEM: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 COORDINATIONSHAPE AND COORDINATION
Motion invariant properties of targets:
• Rigid or Articulated bodies
• Formations of vehicles (Flock of birds)
• Deformable objects
Distances and/or angles
Connectivity – distancesRelative velocity
Group of admissible deformations (probabilistic or deterministic)
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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Probabilistic Tracking and Probabilistic Tracking and Data AssociationData Association
CLASSICALLY:CLASSICALLY:
JPDAF – MHT JPDAF – MHT + + Dynamical ModelsDynamical Models
Full (joint) model -not flexible -computationally expensive
Model targets Independently -flexible and easy -not robust occlusions exchange tracks
OUR APPROACH:OUR APPROACH:
JPDAF- (MHT)JPDAF- (MHT)+ +
Independent Dynamical ModelsIndependent Dynamical Models++
Shape InformationShape Information
+ Flexible+ Robust to occlusions and track proximity- Computation (Monte Carlo)
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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Independent MotionIndependent Motion
• Targets are described by independent dynamics
• Flexible and easy
• Lack of robustness in presence of occlusions, false detections and closely spaced targets
Index of Target
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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AssociationsAssociations
• An association is a map matching unlabelled measurements to targets
• Employ the overall model to compute the probability of each association
Association
Measurements Measurements matched to clutter
Measurements matched to targets
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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Description of “Shape”Description of “Shape”
Probabilistic Model
• Example: pairwise distances of non perfectly rigid bodies
Motion InvariantMotion Invariant • Prior Knowledge• Learn from Data
Targets positionsTargets positions
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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Shape IntegrationShape Integration
• We assume the overall model can be factored into two terms describing the mutual configuration and single target dynamics
Kalman filters and independent dynamical models
Shape constraints
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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OcclusionsOcclusions
• 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 IntegrationMonte Carlo Integration
• Sample:
• Weight:
• Integrate:
• Fair sample from the posterior
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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SummarySummaryConditional
state estimates
SHAPEINDEPENDENT
KALMAN FILTERS
T1 TNT2 ….
Monte Carlo fair samples for
occluded points state estimation
OVERALL MODEL
Association probabilities
Measurements
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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State EstimationState 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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ResultsResults
• 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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ResultsResults
Commercial system: looses and confuses tracks
With shape knowledge learned from data
IEEE CDC 2004 - Nassau, Bahamas, December 14-17
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ConclusionsConclusions
• 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 ConstraintsShape 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 MotionCoordinated 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 )