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

✍ Scribed by Carlos F. Borges; Tim Pastva

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 518 KB
• Volume: 19
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/s0167-8396(02)00088-2

✦ Synopsis

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.