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.
Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds.Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline’s appearance; the B-spline’s complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn’t use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality.The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.
The paper presents a review of testing methods and a classification of strategies and tools in terms of technologies and techniques applied to the monitoring of tunnels. In particular, the topic is contextualized through a brief introduction in Chapter 1, followed by defect taxonomy and degradation mechanisms in Chapters 2 and 3, respectively. Chapters 4 and 5 are related to monitoring strategies and technologies. The former consists of purpose‐based categorization of monitoring policies, while the latter consists of classification of monitoring methods including nondestructive and semidestructive techniques as well as of classification of various types of sensors also based on the physical or chemical quantity measured. General rules of implementation and operation of tunnel monitoring systems are presented taking into account international expert knowledge as well as contemporary practical experience in Austria. Considered issues are related to the fib Model Code 2020 (MC2020) focused on evaluation of structural performance assisted by monitoring and testing. Chapter 6 presents challenges related to the monitoring implementation and operation. Chapter 7 discusses about monitoring characteristics in new tunnel, including data acquisition‐transmission and specific monitoring techniques. Chapter 8 instead treats a particular topic related to considerations related to monitoring characteristics of existing tunnel under investigation. Concluding remarks and references finally close the paper.
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 [The present paper continues these investigations. If necessary, the methods proposed in [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.
Plant phenotyping deals with the metrological acquisition of plants in order to investigate the impact of environmental factors and a plant’s genotype on its appearance. Phenotyping methods that are used as standard in crop science are often invasive or even destructive. Due to the increase of automation within geodetic measurement systems and with the development of quasi-continuous measurement techniques, geodetic techniques are perfectly suitable for performing automated and non-invasive phenotyping and, hence, are an alternative to standard phenotyping methods. In this contribution, sequentially acquired point clouds of cucumber plants are used to determine the plants’ phenotypes in terms of their leaf areas. The focus of this contribution is on the spatio-temporal segmentation of the acquired point clouds, which automatically groups and tracks those sub point clouds that describe the same leaf. The application on example data sets reveals a successful segmentation of 93% of the leafs. Afterwards, the segmented leaves are approximated by means of B-spline surfaces, which provide the basis for the subsequent determination of the leaf areas. In order to validate the results, the determined leaf areas are compared to results obtained by means of standard methods used in crop science. The investigations reveal consistency of the results with maximal deviations in the determined leaf areas of up to 5%.
Deformation analysis is one of the classical tasks in engineering geodesy. The development of the laser scanner has changed the data acquisition as well as the analysis strategy; instead of point-based approaches, areal ones move into focus. In this paper, a project is presented which aims to develop a spatiotemporal continuous collocation in order to describe areal deformations.The collocation requires among other things the modelling of a deterministic trend which is realized by the estimation of B-spline surfaces in the present study. One of the main challenges in the estimation of such freeform surfaces is the definition of an appropriate parameter form which is in the focus of this contribution. An initial parameterization is obtained by projecting the acquired point cloud onto a base surface called Coons patch. By means of a reparameterization, these initial parameters are improved iteratively. In order to handle irregular point densities, several strategies to introduce boundary constraints into the adjustment are developed, compared and evaluated.
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.
Due to the increased use of areal measurement techniques, such as laser scanning in geodetic monitoring tasks, areal analysis strategies have considerably gained in importance over the last decade. Although a variety of approaches that quasi-continuously model deformations are already proposed in the literature, there are still a multitude of challenges to solve. One of the major interests of engineering geodesy within monitoring tasks is the detection of absolute distortions with respect to a stable reference frame. Determining distortions and simultaneously establishing the joint geodetic datum can be realised by modelling the differences between point clouds acquired in different measuring epochs by means of a rigid body movement that is superimposed by distortions. In a previous study, we discussed the possibility of estimating these rigid body movements from the control points of B-spline surfaces approximating the acquired point clouds. Alternatively, we focus on estimating them by means of constructed points on B-spline surfaces in this study. This strategy has the advantage of larger redundancy compared to the control point–based strategy. Furthermore, the strategy introduced allows for the detection of rigid body movements between point clouds of different epochs and for the simultaneous localisation of areas in which the rigid body movement is superimposed by distortions. The developed approach is based on B-spline models of epoch-wise acquired point clouds, the surface parameters of which define point correspondences on different B-spline surfaces. Using these point correspondences, a RANSAC-approach is used to robustly estimate the parameters of the rigid body movement. The resulting consensus set initially defines the non-distorted areas of the object under investigation, which are extended and statistically verified in a second step. The developed approach is applied to simulated data sets, revealing that distorted areas can be reliably detected and that the parameters of the rigid body movement can be precisely and accurately determined by means of the strategy.
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