Generalized n-D C k B-Spline Scattered Data Approximation with Confidence Values

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Abstract

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.