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USNCCM IX, San Francisco, CA, USA, July 22-26 2007
FEUP Faculdade de Engenharia da Universidade do PortoINEGI Instituto de Mecnica e Gesto IndustrialPORTUGAL
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 2
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Contents:o Introduction;o Methodology Used:
o Kalman Filter;o Matching:
o Mahalanobis Distance;o Optimization Techniques;
o Features Management Model; o Experimental Results;o Conclusions and future work.
| IntroductionIntroduction | Methodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 3
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Introduction:o Feature tracking is a complex problem for which
computational solutions had evolved considerably in the past decade.
o Applications of motion tracking are usual: surveillance, object deformation analysis, traffic monitoring, etc.
o Some common difficulties are:o several features to be tracked simultaneously;o appearance/disappearance of features along the image
sequence;o long image sequences to be processed;o etc.
| IntroductionIntroduction | Methodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 4
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
o Existing approaches:o They try to find good compromises between the
accuracy of the motion tracking and the involved computational cost.
o Examples:o Pfinder (Wren, Azarbayejani, Darell, Pentland,1997)
A real-time system for tracking people in order to interpret their behavior. Expects only one user in the image scene and that the scene is quasi-static;
o Bayesian networks simplified by gradually discarding the influence of the past information on the current decisions.
o Tracking with Kalman Filter is a widespread technique for object tracking; although other filters have recently become more usual, they have also revealed some problems too.
| IntroductionIntroduction | Methodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 5
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Methodology adopted:o Kalman Filter is used to estimate the features
positions along the image sequence;o For the matching (data association), between
measures (real features) and filters estimates, we use Optimization of the global correspondence based on Mahalanobis Distance;
o To deal with the problem of appearance, occlusion and disappearance of the tracked features, we employ a Features Management model.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 6
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Kalman Filter:o Kalman Filter is an optimal recursive Bayesian
stochastic method, but assumes Gaussian posterior density functions at every time step;
o Erroneous estimations, for instances in problems involving non-linear motion, can be corrected overcome by using adequate approaches in the matching step.
o In this work:o the system state is composed by the positions, velocities
and accelerations of the tracked features (points);o new measurements are incorporated in the system model
whenever a new image frame is evaluated.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 7
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Matching:o For each feature estimated, there may exist, at most,
one new measurement to correct its estimated position.
o With Kalmans usual approach, the predicted search area for each tracked feature is given by an ellipse(whose area will decrease as convergence is obtained and vice-versa).
o Some problems:o there may not exist any real feature in the search area or
there might be several instead;o even if there is only one correspondence for each feature,
there is no guarantee that the best set of correspondences is achieved.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 8
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Matching:o We use optimization techniques to obtain the best
set of correspondences between predictions and measurements;
o To establish the best global set of correspondences we use the Simplex method;
o The cost of each correspondence is given by the Mahalanobis Distance.
o Simplex Method:o An iterative algebraic procedure used to determine at least
one optimal solution for each assignment problem.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 9
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Matching:o Mahalanobis Distance:
o The distance between two features is normalized by its statistical variations;
o Its values are inversely proportional to the quality of the prediction/measurement correspondence;
o To optimize the global correspondences, we minimize the cost function based on the Mahalanobis Distance.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 10
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Matching:o Occlusion/Appearance:
o Assignment restriction (1 to 1) not satisfied problem solved with addition of fictitious variables:
o Features matched with fictitious variables are considered unmatched;
o Unmatched tracked feature it is assumed that the feature has been occluded, but the tracking process is maintained by including its predicted position in the measurement vector although with higher uncertainty;
o Unmatched measurement we consider it as a new feature and initialize its tracking process.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 11
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Management Model:o When a feature disappeared of the scene: Is it just occluded? It
was removed definitively? Should we keep its tracking?o This decision is of greater importance if many features are
being tracked, if the image sequence is long, if the tracking isin real-time, etc;
o We use a management model in which a confidence value is associated to each feature:
o In each frame, if a feature is visible then its confidence value is increased, else it is decreased;
o If a minimum value of the confidence value is reached, then is considered that the feature has definitively disappeared and its tracking will cease (if it reappears, its tracking will be initialized);
o In this work, the confidence values are integers between 0 and 5, and initialized as 3.
| Introduction | MethodologyMethodology | Results | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 12
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Experimental Results:o Using synthetic data:
o Blobs A, B with horizontal translation and C, D with rotation:
| Introduction | Methodology | ResultsResults | Conclusions| Future Work |
Prediction Uncertainty Area Measurement Correspondence Results
A
B
C
D
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 13
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Experimental Results:o Using synthetic data:
o Continuation ... Blobs C, D invert their rotation direction:
| Introduction | Methodology | ResultsResults | Conclusions| Future Work |
Prediction Uncertainty Area Measurement Correspondence Results
...
A
B
C
D
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 14
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Experimental Results:o Using synthetic data:
o Management of the tracked features - blobs (dis)appearrandomly:
| Introduction | Methodology | ResultsResults | Conclusions| Future Work |
AB
C
DE
Prediction Uncertainty Area MeasurementCorrespondence Result
Confidence Values:
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 15
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Experimental Results:o Using real data:
o Tracking 5 blobs in human gait analysis:
| Introduction | Methodology | ResultsResults | Conclusions| Future Work |Prediction Uncertainty Area Measurement Correspondence Result
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 16
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Experimental Results:o Using real data:
o Tracking mice in a lab environment during 547 frames:(with very significant changes in the direction of the motion)
| Introduction | Methodology | ResultsResults | Conclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 17
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Experimental Results:o Using real data:
o Tracking persons in a shopping centre:
| Introduction| Methodology| ResultsResults| Conclusions| Future Work |
(5 frames interval)
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 18
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Conclusions:o We presented a methodology to track features along image
sequences based on:o Kalman Filter;o Optimization techniques;o Mahalanobis Distance;o A features Management Model;
o With our approach, in each image sequence frame, the best set of correspondences is guaranteed;
o Our approach also allows the incorporation of new data even if it would be out of the default Kalman search area (e.g. change in movement direction).
o The used features management model allows the tracking with the lowest computational cost possible, as the features simultaneously tracked are continuously update.
| Introduction | Methodology | Results | ConclusionsConclusions| Future Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 19
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Future Work:o Consideration of other stochastic methods in the
motion estimation; like Particle Filters and Unscented Kalman Filter;
o Adoption of matches one to several (and vice-versa);
o The automatic selection of the best dynamic model to use along the image sequence;
o The learning of the dynamic model to use from the image sequences being tracked;
o Use our tracking methodology in human clinical gait analysis.
| Introduction | Methodology | Results | Conclusions| Future WorkFuture Work |
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 20
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
Acknowledgments:o The first author would like to thank the support of the
PhD grant SFRH / BD / 12834 / 2003 from FCT -Fundao para a Cincia e a Tecnologia from Portugal;
o This work was partially done in the scope of the project Segmentation, Tracking and Motion Analysis of Deformable (2D/3D) Objects using Physical Principles, reference POSC/EEA-SRI/55386/2004, financially supported by FCT.
Raquel R. Pinho, Miguel V. Correia, Joo Manuel R. S. Tavares 21
TRACKING FEATURES WITH KALMAN FILTERING, MAHALANOBIS DISTANCE AND A MANAGEMENT MODEL
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