2D Shape Tracking Using Algebraic Curve Spaces
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.
Unable to display preview. Download preview PDF.
- 3.Unel, M., Wolovich, W.A.: A new representation for quartic curves and complete sets of geometric invariants. International Journal of Pattern Recognition and Artificial Intelligence (December 1999)Google Scholar
- 4.Taubin, G., Cooper, D.B.: 2D and 3D object recognition and positioning with algebraic invariants and covariants. In: Symbolic and Numerical Computation for Artificial Intelligence, ch. 6. Academic Press, London (1992)Google Scholar
- 5.Keren, D., et al.: Fitting curves and surfaces to data using constrained implicit polynomials. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(1) (January 1999)Google Scholar
- 7.Tasdizen, T.: Robust and Repeatable Fitting of Implicit Polynomial Curves to Point Data Sets and to Intensity Images. PhD Thesis, Brown University, Providence, RI 02912 (September 2000)Google Scholar
- 9.Frank, T., Haag, M., Kollnig, H., Nagel, H.-H.: Tracking of occluded vehicles in traffic scenes. In: 7th European Conference on Computer Vision, Cambridge, pp. 485–494. Springer, Heidelberg (April 1996)Google Scholar
- 14.Lei, Z., Blane, M.M., Cooper, D.B.: 3L Fitting of Higher Degree Implicit Polynomials. In: proceedings of 3rd IEEE Workshop on Applications of Computer Vision, Florida, pp. 148–153 (1996)Google Scholar
- 15.Corke, P.I., Good, M.C.: Dynamic effects in high performance visual servoing. In: Proc. IEEE Int. Conf. Robotics and Automation, pp. 1838–1843 (1992)Google Scholar
- 16.Unel, M.: Polynomial Decompositions for Shape Modeling, Object Recognition and Alignment. PhD Thesis, Brown University, Providence, RI 02912 (May 1999)Google Scholar