Optimal local spline approximation of planar shape

Abstract

How to model a given planar curve by local splines defined by a number of knot points which is much smaller than the number of points defining the curve is addressed. To solve the problem an optimization technique is applied that minimizes an error norm, which reflects the discrepancy of the splines to the original curve. The error norm is defined as the total squared distance of the sample points from the local spline model. The objective function for the optimization process is the above error norm plus a term which ensures convergence to the correct solution. The objective function is minimized with respect to a set of independent variables, which are the locations of the knot points defining the local spline model. The initial locations of the knot points are selected heuristically. Experimental results show that the method converges to a solution that compares favorably with previous techniques.