Total least squares fitting of Bezier and B-spline curves to ordered data

摘要

We begin by considering the problem of fitting a single Bezier curve segment to a set of ordered data so that the error is minimized in the total least squares sense. We develop an algorithm for applying the Gauss-Newton method to this problem with a direct method for evaluating the Jacobian based on implicitly differentiating a pseudo-inverse. We then demonstrate the simple extension of this algorithm to B-spline curves. We present some experimental results for both cases.