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C. Harmening, H.-B. Neuner:
"Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)";
Journal of Applied Geodesy, 10 (2016), 3; 139 - 157.

Due to the establishment of terrestrial laser
scanner, the analysis strategies in engineering geodesy
change from pointwise approaches to areal ones. These
areal analysis strategies are commonly built on the modelling
of the acquired point clouds.
Freeform curves and surfaces like B-spline curves/
surfaces are one possible approach to obtain space continuous
information. A variety of parameters determines
the B-spline´s appearance; the B-spline´s complexity
is mostly determined by the number of control points.
Usually, this number of control points is chosen quite
arbitrarily by intuitive trial-and-error-procedures. In this
paper, the Akaike Information Criterion and the Bayesian
Information Criterion are investigated with regard to a
justified and reproducible choice of the optimal number
of control points of B-spline curves. Additionally, we
develop a method which is based on the structural risk
minimization of the statistical learning theory. Unlike the
Akaike and the Bayesian Information Criteria this method
doesn´t use the number of parameters as complexity
measure of the approximating functions but their Vapnik-
Chervonenkis-dimension.
Furthermore, it is also valid for
non-linear models. Thus, the three methods differ in their
target function to be minimized and consequently in their
definition of optimality.
The present paper will be continued by a second paper
dealing with the choice of the optimal number of control
points of B-spline surfaces.

AIC, BIC, B-spline Curves, Structural Risk

http://dx.doi.org/10.1515/jag-2016-0003