Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Model-based tracking of moving objects in cluttered environments


Authors: Basilis Gidas, Fernando Carvalho Gomes and Christopher Robertson
Journal: Quart. Appl. Math. 60 (2002), 737-771
MSC: Primary 68T45; Secondary 62H35
DOI: https://doi.org/10.1090/qam/1939009
MathSciNet review: MR1939009
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Abstract: We explore a coherent statistical/Bayesian framework for tracking rigid or non-rigid objects in highly cluttered environments. The procedure involves three basic models: (i) an object representation, (ii) a dynamic model, and (iii) a data or observation model. We employ two object representations -- deformable templates, and a hierarchical/syntactic model; the deformations of the template are parametrized by a finite number of global parameters viewed as generalized coordinates of the model; they determine the state space of the tracking problem. The dynamic model describes the evolution of the generalized coordinates (or the corresponding state vector); our dynamic model is a non-Gaussian Markov chain whose transition probabilities are derived from Lagrangian mechanics. We introduce two data models: one nonlinear and one linear (Gaussian); the design of the two models uses different image processing techniques. The nonlinear filtering problem induced by three models is solved both by the Extended Kalman Filter (EKF), and an iterative algorithm--to be referred to as the Monte Carlo Filter (MCF)-- introduced in the statistic literature and first employed in Computer Vision by Blake and Isard. We present several tracking experiments with real video sequences. In each experiment we implement both MCF and EKF, and their performances are compared. Overall, we find that MCF is more robust than EKF in situations with considerable clutter and/or occlusions, but EKF is comparable and sometimes more accurate than MCF in situations with less occlusion and degradation. Our studies also demonstrate that when the motion has sharp discontinuities in direction, nonlinearities in the dynamic model are key for successful tracking; put differently, the deficiencies of linear dynamics models cannot be easily compensated with more sophisticated data models.


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DOI: https://doi.org/10.1090/qam/1939009
Article copyright: © Copyright 2002 American Mathematical Society


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