C. Harmening, H.-B. Neuner:

"Choosing the Optimal Number of B-spline Control Points (Part 2: Approximation of Surfaces and Applications)";

accepted for publication in Journal of Applied Geodesy11(2017), 2; # - ?.

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

Created from the Publication Database of the Vienna University of Technology.