Plane curve matching under affine transformations

It is common to use an affine transformation to approximate the plane curve matching problem under a projective transformation. The plane curve itself can be used as an identity to solve the parameters of an affine transformation. The objective of the paper is to obtain a closed form solution to the transformation parameters using lower order derivatives of a plane curve. A unique solution to the parameters of an affine transformation with up to second order derivatives is presented using differential invariants as well as the available global information. In discrete space, derivatives are obtained by numerical means. Achieving accurate numerical derivatives is always a crucial application issue. Different differentiation filters were experimented with in calculating derivatives of discrete plane curves. The ICP (iterative closest point) method was employed to improve the results obtained by the proposed invariant scheme, which was believed to be an important step towards the practical use of differential invariant schemes.