# N-D $C^k$ B-Spline Scattered Data Approximation

Tustison, Nicholas J., Gee, James C.

###### Published in The Insight Journal - 2005 August - December.
Submitted by Nicholas J. Tustison on 2005-11-15T20:39:45Z.

Since the 1970's B-splines have evolved to become the {\em de facto} standard for curve and surface representation due to many of their salient properties. Conventional least-squares scattered data fitting techniques for B-splines require the inversion of potentially large matrices. This is time-consuming as well as susceptible to ill-conditioning which leads to undesired results. Lee {\em et al.} proposed a novel B-spline algorithm for fitting a 2-D cubic B-spline surface to scattered data in \cite{Lee}. The proposed algorithm utilizes an optional multilevel approach for better fitting results. We generalize this technique to support N-dimensional data fitting as well as arbitrary degree of B-spline. In addition, we generalize the B-spline kernel function class to accommodate this new image filter.