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Open AccessArticle

Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

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
*
Author to whom correspondence should be addressed.
Remote Sens. 2020, 12(5), 829; https://doi.org/10.3390/rs12050829
Received: 6 February 2020 / Revised: 27 February 2020 / Accepted: 2 March 2020 / Published: 4 March 2020
The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces. View Full-Text
Keywords: correlations; terrestrial laser scanning; deformation; B-splines; surface modelling; bootstrapping; Matérn covariance function; Hausdorff distance; averaged Hausdorff distance correlations; terrestrial laser scanning; deformation; B-splines; surface modelling; bootstrapping; Matérn covariance function; Hausdorff distance; averaged Hausdorff distance
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MDPI and ACS Style

Kermarrec, G.; Kargoll, B.; Alkhatib, H. Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load. Remote Sens. 2020, 12, 829.

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