Parameter estimation of conics: Application to handwritten digits

We expose a method for modeling handwriting thanks to conic sections described by Cartesian equations under an implicit form. The parameter estimation is processed by an extended Kalman filter, taking as minimization criterion, the squared orthogonal distance between a point and the conic. The state equation is here constant, and the observation is a system of two equations: the first one characterizes the minimization of the criterion, and the second one is a normalization constraint of the parameters. The method provides a robust and invariant estimation of parameters, and an unique solution allowing the classification of modeled patterns. We apply this method to the coding of handwritten digits. A geometrical criterion allows to locate model changes. For a large interval of the used thresholds, we observe a great stability of the estimated parameters and of the instants of model changes. The method is evaluated in terms of accuracy, but equally by the data reduction rate, compared to other modeling techniques.