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

Authors:
Carlos F. Borges;Tim Pastva
Affiliations:
Naval Postgraduate School, Code NA/BC, 93943 Monterey, CA;Naval Postgraduate School, Code NA/BC, 93943 Monterey, CA
Venue:
Computer Aided Geometric Design
Year:
2002

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Abstract

We begin by considering the problem of fitting a single Bézier 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.