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

Please use this identifier to cite or link to this publication: http://hdl.handle.net/1926/140
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.
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Comment by Nick Tustison yellow
Thanks for this. I just added a test for the ITK repository here:

http://review.source.kitware.com/#/c/20010/
Comment by Nick Tustison yellow
Thanks for this. I just added a test for the ITK repository here:

http://review.source.kitware.com/#/c/20010/
Comment by Kedar Patwardhan yellow
Has the code been tested for the case where the N-D contour (to be interpolated) is a "closed" contour? The documentation talks about this - but there are no examples provided. The closed-contour use case is not as well documented (from a quick read through) as the open-contour case.


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Keywords: B-splines, data approximation
Toolkits: ITK (moved into the sandbox)
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