An Adaptive Estimation Method for Rigid Motion Parameters of 2D Curves

A new method is presented for identifying rigid motion of free-form curves based on "related-points" extracted from the decomposition of implicit polynomials of these curves. Polynomial decomposition expresses the curve as a unique sum of products of (possibly) complex lines. We show that each real intersection point of these lines, i.e. relatedpoints, undergoes the same motion with the curve, and therefore they can be used for identifying the motion parameters of the curve. The resulting tuning algorithm is verified by experiments.