A framework for spatiotemporal control in the tracking of visual contours
International Journal of Computer Vision
Computation and analysis of image motion: a synopsis of current problems and methods
International Journal of Computer Vision
The Determination of Implicit Polynomial Canonical Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Elementary geometry of algebraic curves: an undergraduate introduction
Elementary geometry of algebraic curves: an undergraduate introduction
Regular Article: On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves
Advances in Applied Mathematics
Motion Estimation Via Cluster Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking of Occluded Vehicles in Traffic Scenes
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
3L Fitting of Higher Degree Implicit Polynomials
WACV '96 Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (WACV '96)
Polynomial decompositions for shape modeling, object recognition and alignment
Polynomial decompositions for shape modeling, object recognition and alignment
The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces
Journal of Mathematical Imaging and Vision
Image and Vision Computing
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
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Tracking free form objects by fitting algebraic curve models to their boundaries in real-time is not feasible due to the computational burden of fitting algorithms. In this paper, we propose to do fitting once offline and calculate an algebraic curve space. Then, in every frame, algebraic curves from the search region of curve space are evaluated with the extracted edge points. The curve that has the smallest error according to some error metric is chosen to be the fit for that frame. The algorithm presented is for tracking a free-form shaped object, moving along an unknown trajectory, within the camera’s field of view (FOV). A discrete steady-state Kalman filter estimates the future position and orientation of the target object and provides the search area of curve space for the next frame. For initialization of the Kalman filter we used the “related points” extracted from the decomposition of algebraic curves, which represent the target’s boundary, and measured position of target’s centroid. Related points undergo the same motion with the curve, hence can be used to initialize the orientation of the target. Proposed algorithm is verified with experiments.