On the impact of correlations on the congruence test: a bootstrap approach
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On the impact of correlations on the congruence test: a bootstrap approach Case study: B-spline surface fitting from TLS observations Kermarrec Gaël1 · Kargoll Boris2 · Alkhatib Hamza1 Received: 10 January 2020 / Accepted: 19 June 2020 © The Author(s) 2020
Abstract The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terrestrial laser scanners, allowing the setting of a specific congruence test based on the B-spline surfaces. Such tests are known to be strongly influenced by the underlying stochastic model chosen for the observation errors. The latter has to be correctly specified, which includes accounting for heteroscedasticity and correlations. In this contribution, we justify and make use of a parametric correlation model called the Matérn model to approximate the variance covariance matrix (VCM) of the residuals by performing their empirical mode decomposition. The VCM obtained is integrated into the computation of the congruence test statistics for a more trustworthy test decision. Using a real case study, we estimate the distribution of the test statistics with a bootstrap approach, where no parametric assumptions are made about the underlying population that generated the random sample. This procedure allows us to assess the impact of neglecting correlations on the critical value of the congruence test, highlighting their importance. Keywords Terrestrial laser scanner · Deformation · Statistical test · Congruency test · Correlation · Matérn covariance function · Variance component estimation · Bootstrap
* Kermarrec Gaël [email protected]‑hannover.de Kargoll Boris kargoll@hs‑anhalt.de Alkhatib Hamza [email protected]‑hannover.de 1
Geodetic Institute, Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, Germany
2
Institut für Geoinformation und Vermessung Dessau, Anhalt University of Applied Sciences, Seminarplatz 2a, 06846 Dessau, Germany
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Vol.:(0123456789)
Acta Geodaetica et Geophysica
1 Introduction Statistical tests for deformation provide a way to detect potential risks linked with natural hazards or the collapse of artificial objects, such as bridges. One of their main applications in geodesy is the estimation and minimization of risks. Combined with, for example, the concept of utility theory, they allow their consequences and costs to be estimated (Zhang and Neumann 2014). Terrestrial laser scanners (TLS) capture a large amount of three-dimensional (3D) points rapidly, with high precision and spatial resolution. In addition to the visualization of 3D topography or buildings, TLS are, thus, increasingly used to detect and quantify displacements or deformations. Software such as CloudCompare (www.danielgm.net/cc), 3DReshaper (Hexagon Metrology) or Geomagic Studio (3DSystems) provide ma
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