IEEE CDC 2004 - Nassau, Bahamas, December 14-17 1 Integration of shape constraints in data association filters Integration of shape constraints in data.

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

1

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


2

Outline of the TalkOutline of the Talk

• Tracking and Data Association

• Classical solution: independent dynamics

• Our approach : integration of shape

• Occlusions

• Experiments


3

Tracking and Data AssociationTracking and Data Association

• PROBLEM:PROBLEM: Set of targets generating UNLABELLED measurements

Associate and

Track

•Occlusions•Clutter


4

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)


5

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)


6

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


7

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


8

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


9

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


10

OcclusionsOcclusions

• To compute marginalize over the occluded :

Detected points Missing points (occlusions)

• Compute the integral through Monte Carlo techniques


11

Monte Carlo IntegrationMonte Carlo Integration

• Sample:

• Weight:

• Integrate:

• Fair sample from the posterior


12

SummarySummaryConditional

state estimates

SHAPEINDEPENDENT

KALMAN FILTERS

T1 TNT2 ….

Monte Carlo fair samples for

occluded points state estimation

OVERALL MODEL

Association probabilities

Measurements


13

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 !


14

ResultsResults

• Real data from a motion capture system• Rapid motion• High numbers of false detections• Occlusions lasting several frames


15

ResultsResults

Commercial system: looses and confuses tracks

With shape knowledge learned from data


16

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)


17


18

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


19

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 )

IEEE CDC 2004 - Nassau, Bahamas, December 14-17 1 Integration of shape constraints in data association filters Integration of shape constraints in data.

Documents

ieee cdc

data slide

shape integration

deterministic slide

posterior slide

shape knowledge

example shape

shape information