Spline approximation using Kalman filter state estimation

Curves and surfaces in computer-aided design systems are often represented using B-spline basis functions. For a given set of locations corresponding to a subset of sampled points of the curve, there are efficient algorithms which solve a normal system of equations, to compute the basis function weights which are called control vertices. However, when these knot locations are not predetermined, there is no known efficient method for determining the optimal representation of the underlying curve. In this paper, we propose a suboptimal Kalman filter algorithm which “refines” an initial set of knot locations, to provide a “good” solution to the spline approximation problem