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C. Harmening, H.-B. Neuner:
"A spatio-temporal deformation model for laser scanning point clouds";
Journal of Geodesy, 94 (2020), 26; 1 - 26.

The establishment of the terrestrial laser scanner changed the analysis strategies in engineering geodesy from point-wise
approaches to areal ones. During recent years, a multitude of developments regarding a laser scanner-based geometric state
description were made. However, the areal deformation analysis still represents a challenge. In this paper, a spatio-temporal
deformation model is developed, combining the estimation of B-spline surfaces with the stochastic modelling of deformations.
The approach´s main idea is to model the acquired measuring object by means of three parts, similar to a least squares
collocation: a deterministic trend, representing the undistorted object, a stochastic signal, describing a locally homogeneous
deformation process, and the measuring noise, accounting for uncertainties caused by the measuring process. Due to the
stochastic modelling of the deformations in the form of distance-depending variograms, the challenge of defining identical
points within two measuring epochs is overcome. Based on the geodetic datum defined by the initial trend surface, a pointto-
surface- and a point-to-point-comparison of the acquired data sets is possible, resulting in interpretable and meaningful
deformation metrics. Furthermore, following the basic ideas of a least squares collocation, the deformation model allows
a time-related space-continuous description as well as a space- and time-continuous prediction of the deformation. The
developed approach is validated using simulated data sets, and the respective results are analysed and compared with respect
to nominal surfaces.

B-spline surfaces · Deformation modelling · Laser scanning · Locally homogeneous stochastic processes ·

http://dx.doi.org/10.1007/s00190-020-01352-0

https://publik.tuwien.ac.at/files/publik_289953.pdf