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A flexible approach for geometric modelling of point clouds obtained from Terrestrial Laser Scanning (TLS) is by means of B-splines. These functions have gained some popularity in the engineering geodesy as they provide a suitable basis for a spatially continuous and parametric deformation analysis. In the predominant studies on geometric modelling of point clouds by B-splines, uncorrelated and equally weighted measurements are assumed. Trying to overcome this, the elementary errors theory is applied for establishing fully populated covariance matrices of TLS observations that consider correlations in the observed point clouds. In this article, a systematic approach for establishing realistic synthetic variance–covariance matrices (SVCMs) is presented and afterward used to model TLS point clouds by B-splines. Additionally, three criteria are selected to analyze the impact of different SVCMs on the functional and stochastic components of the estimation results. Plausible levels for variances and covariances are obtained using a test specimen of several dm—dimension. It is used to identify the most dominant elementary errors under laboratory conditions. Starting values for the variance level are obtained from a TLS calibration. The impact of SVCMs with different structures and different numeric values are comparatively investigated. Main findings of the paper are that for the analyzed object size and distances, the structure of the covariance matrix does not significantly affect the location of the estimated surface control points, but their precision in terms of the corresponding standard deviations. Regarding the latter, properly setting the main diagonal terms of the SVCM is of superordinate importance compared to setting the off-diagonal ones. The investigation of some individual errors revealed that the influence of their standard deviation on the precision of the estimated parameters is primarily dependent on the scanning distance. When the distance stays the same, one-sided influences on the precision of the estimated control points can be observed with an increase in the standard deviations., Deutsche Forschungsgemeinschaft, Austrian Science Fund

This contribution presents a B-spline-based approach of area-wise deformation analysis applied on elements of a double curved wooden tower. The monitored object is the Urbach Tower with a height of 14 m. Terrestrial laser scans from two epochs acquired under real-world conditions are used for approximating two jointly parametrized B-spline surfaces of the tower’s outer shell. The stochastic model of the observations used within the surface approximation is based on elementary error theory and is defined by a synthetic variance-covariance matrix (SVCM). In addition to previous work on this topic, the object’s dimension is extended from a few dm to a few m and the measurement distance ranges from 20 to 60 m. Moreover, environment specific error sources are addressed in the SVCM, revealing the effect of the object’s dimension as well as of additional elementary errors on the estimated B-spline surfaces and the subsequent deformation analysis. Based on constructed points pairs using a grid of surface parameters, rigid body movements of the object under investigation are estimated while at the same time distorted regions of the wooden tower are detected. All results of the deformation analysis are statistically verified using hypothesis tests based on the elementary error model propagated through the processing algorithms of surface estimation and deformation analysis. The results demonstrate that during the modelling and deformation analysis, the measurement noise is reduced and therefore distorted regions are detectable in a statistically correct way.

The present paper deals with the derivation of roughness parameters of soil from laser scanning point clouds, allowing to draw conclusions about properties of the soil (e. g. soil aggregation, soil sealing) and related to this its vulnerability to soil erosion. For this purpose, soil erosion scenes with agricultural cultivation are acquired in five measuring epochs under field conditions. For geo-referencing of the acquired time series of point clouds, a target-based and a data-driven approach are compared. In order to derive roughness parameters, the point clouds are cleaned of vegetation and then modelled to reduce the measurement noise. For this purpose, a collocation-based approach is used, in which a trend surface roughly approximates the point clouds. Remaining systematic deviations, which are caused by the insufficient functional approximation, are caught with the help of a stochastic signal, the variances and correlations lengths of which simultaneously provide information about the soil’s roughness.

[EN] The Cluster of Excellence Integrative Computational Design and Construction for Architecture at the University of Stuttgart brings together various disciplines to jointly develop amongst other things a better understanding of processes in the manufacturing and construction domain. One of the cluster’s aims is to create new solutions for the construction of lightweight fibrous structures using coreless winding of lightweight fiber composite systems. For this purpose, a precise geometry and an understanding of the fibers’ behavior during the production process are of major importance. The fibers’ production process is monitored by repeatedly scanning the fibers during different stages of the process using a terrestrial laser scanner. In order to determine the geometry of the fibers’ axes as well as their cross-sections, two different strategies are used. The first strategy focuses on the segmentation of several straight lines between two intersection points. For the comparison of the individual fabrication steps, the positions of the intersection points are contrasted. For the cross-sectional areas of the fibers, orthogonal planes of intersection are then defined and all points within a predefined area are projected onto this plane. Then the area is calculated using a convex hull. In the second strategy, the fibers‘ main axes are represented by best-fitting B-spline curves. The borders of the cross-sections of interest are also approximated by best-fitting B-spline curves, forming the basis for the final determination of the cross-sectional areas. In this case study two epochs are analyzed with a deformation of the size of around 1cm. For both epochs the cross-sections are calculated in cm steps., The research published in this article is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC 2120/1 – 390831618. The authors cordially thank the DFG. A part of the research was realized within a one-month research stay of the second author at the University of Stuttgart within the IntCDC incoming programme.

In den letzten Jahren hat sich das terrestrische Laserscanning zu einem der Standard-Messverfahren für ingenieurgeodätische Anwendungen entwickelt. Aufgrund der kontaktlosen und schnellen Datenerfassung sowie der resultierenden quasi-kontinuierlichen Beschreibung des Messobjektes verfügt das Laserscanning über eine Reihe von Vorteilen gegenüber den klassischen punktbasierten Messverfahren. Gleichzeitig entstehen neue Herausforderungen, vor allem in Hinblick auf die Deformationsanalyse. So erfordert beispielsweise die Tatsache, dass das Messverfahren des Laserscanners keine Punktreproduktion in unterschiedlichen Messepochen erlaubt, eine Abkehr von den klassischen punktbasierten Auswerteverfahren hin zu flächenhaften Ansätzen.Einer flächenhaften Deformationsanalyse wird häufig eine Punktwolkenmodellierung mit mathematischen Funktionen vorangestellt. Im Rahmen dieser Arbeit werden verbesserte B-Spline Modelle für die raum-kontinuierliche Modellierung von Laserscanning-Punktwolken entwickelt. Diese Untersuchungen beinhalten die Entwicklung einer iterativen Reparametrisierungsstrategie mit Bedingungsgleichungen für Laserscanning-Punktwolken sowie die Entwicklung eines B-Spline-Klassifikators, der es erlaubt, die VC-Dimension von B-Splines zu schätzen. Mit dieser Entwicklung wird die strukturelle Risikominimierung anwendbar um B-Spline-Kurven und -Flächen mit optimaler Komplexität auszuwählen. Die verbesserten B-Spline Modelle bilden die Grundlage für die Entwicklung eines raum-zeitlichen Deformationsmodells. Die Grundidee des Ansatzes ist es, ähnlich einer Kollokation nach kleinsten Quadraten, das erfasste und sich deformierende Objekt mit Hilfe dreier Anteile zu modellieren. Ein deterministischer Trend, der mit Hilfe einer B-Spline-Fläche beschrieben wird, repräsentiert das nicht-deformierte Objekt. Die Deformation wird als Realisierung eines lokal homogenen stochastischen Prozesses interpretiert und mit Hilfe eines stochastischen Signals modelliert. Das Messrauschen als dritter Anteil berücksichtigt die durch den Messprozess verursachten Unsicherheiten. Der entwickelte Ansatz wird erfolgreich auf simulierte Datensätze angewandt., In recent years, terrestrial laser scanning has become a standard measuring technique for engineering geodetic applications. Due to its contact-less and fast data acquisition as well as the resulting quasi-continuous description of the object under investigation, laser scanning has a number of advantages over classical point-based measuring techniques. However, a variety of challenges arises, in particular regarding the scope of deformation analyses. Among other things, it is impossible to acquire identical data points in different measuring epochs by means of a laser scanner. Hence, a movement from classical point-based analysis strategies to area-based strategies is necessary. An areal deformation analysis is often preceded by a modelling of the point clouds with mathematical functions. Within this thesis, enhanced B-spline models are developed with regard to a space-continuous modelling of laser scanning point clouds. These investigations include the development of a constraint iterative reparameterization strategy for laser scanning point clouds, as well as the development of a B-spline classifier, allowing for the estimation of the VC-dimension of B-splines. With this development, structural risk minimization becomes applicable for choosing B-spline curves and surfaces with optimal complexity. The enhanced B-spline models provide the basis for the development of a spatio-temporal deformation model. The developed approach’s main idea is to model the acquired and deforming object by means of three parts, similar to least squares collocation. A deterministic trend, which is described by means of a B-spline surface, represents the undistorted object. The deformation is interpreted to be a realization of a locally homogeneous stochastic process and is modelled by means of a stochastic signal. The third part, the measuring noise, accounts for uncertainties caused by the measuring process. The developed approach is successfully applied to simulated data sets.