Efficient representation of contours using splines implemented with FIR filters

The interpolation of contour pixels, with splines, of an order greater than or equal to two, usually causes oscillations that do not fit the original shape. To overcome this we propose using a least squares filter before carrying out the interpolation. This results in a good compromise between the smoothness of the curve and the best fit to the original contour. Representing the contour with a continuous model instead of a discrete model has many advantages for carrying out calculations, as for example the contour curvature, which involves first and second order derivatives, as well as operations that are not well defined in the discrete world. We also present a new way of calculating FIR approximations to filters based on B-splines. The great advantage of this approximation in the case of least squares filter is that it does not need downsampling. This property makes it invariant to translations, and this is very important in classification tasks.