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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 11, Issue 1


Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)

Corinna Harmening
  • Corresponding author
  • Department of Geodesy and Geoinformation, TU Wien, Gusshausstr. 25-29 / E120, 1040 Vienna, Austria
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  • Other articles by this author:
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/ Hans Neuner
Published Online: 2017-02-13 | DOI: https://doi.org/10.1515/jag-2016-0036


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, the B-spline's complexity being 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 trial-and-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. Two model selection criteria, 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 those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.

Keywords: AIC; BIC; B-spline Surface; Structural Risk Minimization; VC-dimension


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About the article

Received: 2016-08-03

Accepted: 2016-11-22

Published Online: 2017-02-13

Published in Print: 2017-03-01

Funding Source: Austrian Science Fund

Award identifier / Grant number: 1706-N29

The presented paper shows results developed during the research project “Integrierte raumzeitliche Modellierung unter Nutzung korrelierter Messgrößen zur Ableitung von Aufnahmekonfiguationen und Beschreibung von Deformationsvorgängen” (IMKAD) (1706-N29), which is funded by the Austrian Science Fund (FWF).

Citation Information: Journal of Applied Geodesy, Volume 11, Issue 1, Pages 43–52, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2016-0036.

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