Generalized n-D Ck B-Spline Scattered Data Approximation with Confidence Values
The ability to reconstruct multivariate approximating or interpolating functions from sampled data finds many practical applications in medical image analysis. Parameterized reconstruction methods employing B-splines have typically utilized least-squares methodology for data fitting. For large sample sets, solving the resulting linear system is computationally demanding as well as susceptible to ill-conditioning. We present a generalization of a previously proposed fast surface fitting technique for cubic B-splines which avoids the pitfalls of the conventional fitting approach. Our proposed generalization consists of expanding the algorithm to n dimensions, allowing for arbitrary spline degree in the different parametric dimensions, permitting wrapping of the parametric domain, and the assignment of confidence values to the data points for more precise control over the fitting results. In addition, we implement our generalized B-spline approximation algorithm within the Insight Toolkit (ITK) for open source dissemination.
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- 1.Piegl, L., Tiller, W.: The NURBS Book. Springer, Heidelberg (1997)Google Scholar
- 2.Riesenfeld, R.F.: Applications of B-Spline Approximation to Geometric Problems of Computer-Aided Design, Ph.D. thesis, Syracuse University (1975)Google Scholar
- 4.Ibanez, L., Schroeder, W., Ng, L., Cates, J.: The ITK Software Guide. Insight Software Consortium, 2nd edn. (November 2005)Google Scholar
- 5.de Boor, C.: B-spline basics. In: Fundamental Developments of Computer-Aided Geometric Modeling, pp. 27–49. American Press (1993)Google Scholar
- 12.Hjelle, O.: Approximation of scattered data with multilevel B-splines, Tech. Rep. (2001)Google Scholar