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C. Harmening, H.-B. Neuner:
"Choosing the Optimal Number of B-spline Control Points (Part 2: Approximation of Surfaces and Applications)";
Journal of Applied Geodesy, 11 (2017), 2; 43 - 52.

Freeform surfaces like B-splines have proven to
be a suitable tool to model laser scanner point clouds and
to form the basis for an areal data analysis, for example an
areal deformation analysis.
A variety of parameters determine the B-spline´s appearance,
whereby the B-spline´s complexity is mostly determined
by the number of control points. Usually, this parameter
type is chosen by intuitive trial-and-error-procedures.
In [10] the problem of finding an alternative to these trialand-
error-procedures was addressed for the case of B-spline
curves: The task of choosing the optimal number of control
points was interpreted as a model selection problem. The
Akaike and the Bayesian Information Criterion were used
to identify the B-spline curve with the optimal number of
control points from a set of candidate B-spline models. In
order to overcome the drawbacks of the information criteria,
an alternative approach based on statistical learning theory
was developed. The criteria were evaluated by means of
simulated data sets.
The present paper continues these investigations. If necessary,
the methods proposed in [10] are extended to areal approaches
so that they can be used to determine the optimal
number of B-spline surface control points. Furthermore, the
methods are evaluated by means of real laser scanner data
sets rather than by simulated ones.
The application of those methods to B-spline surfaces reveals
the datum problem of B-spline surfaces. First investigations
to solve this problem are presented.

AIC, BIC, B-spline surface, structural risk