General plane curve matching under affine transformations

A unique solution to the parameters of an affine transformation with up to second order derivates is presented using differential variants as well as the available global information. The computational time on verification has been significantly reduced. In computer vision, derivatives are obtained by numerical means. Smoothing with a Gaussian filter modified by a linear combination of Hermite polynomials, can preserved the accuracy of continuous polynomials with powers up to the same order as the Hermite polynomials. The introduction of Hermite polynomials lead to a choice of large smoothing scale in order to reduce the computational errors, at the expense of a reduction of local controllability and over-smoothing of the curve. It is shown that using a large smoothing scale proportional to the order of the derivatives is more reliable in applications.