scholarly journals How Significant Are Differences Obtained by Neglecting Correlations When Testing for Deformation: A Real Case Study Using Bootstrapping with Terrestrial Laser Scanner Observations Approximated by B-Spline Surfaces

Sensors ◽  
2019 ◽  
Vol 19 (17) ◽  
pp. 3640 ◽  
Author(s):  
Kermarrec ◽  
Paffenholz ◽  
Alkhatib
Keyword(s):  
Stochastic Model ◽  
Statistical Tests ◽  
Point Clouds ◽  
Least Square ◽  
Test Statistics ◽  
B Spline ◽  
3D Point Clouds ◽  
Spline Surfaces ◽  
Propagation Law ◽  
The Impact

B-spline surfaces possess attractive properties such as a high degree of continuity or the local support of their basis functions. One of the major applications of B-spline surfaces in engineering geodesy is the least-square (LS) fitting of surfaces from, e.g., 3D point clouds obtained from terrestrial laser scanners (TLS). Such mathematical approximations allow one to test rigorously with a given significance level the deformation magnitude between point clouds taken at different epochs. Indeed, statistical tests cannot be applied when point clouds are processed in commonly used software such as CloudCompare, which restrict the analysis of deformation to simple deformation maps based on distance computation. For a trustworthy test decision and a resulting risk management, the stochastic model of the underlying observations needs, however, to be optimally specified. Since B-spline surface approximations necessitate Cartesian coordinates of the TLS observations, the diagonal variance covariance matrix (VCM) of the raw TLS measurements has to be transformed by means of the error propagation law. Unfortunately, this procedure induces mathematical correlations, which can strongly affect the chosen test statistics to analyse deformation, if neglected. This may lead potentially to rejecting wrongly the null hypothesis of no-deformation, with risky and expensive consequences. In this contribution, we propose to investigate the impact of mathematical correlations on test statistics, using real TLS observations from a bridge under load. As besides TLS, a highly precise laser tracker (LT) was used, the significance of the difference of the test statistics when the stochastic model is misspecified can be assessed. However, the underlying test distribution is hardly tractable so that only an adapted bootstrapping allows the computation of trustworthy p-values. Consecutively, the extent to which heteroscedasticity and mathematical correlations can be neglected or simplified without impacting the test decision is shown in a rigorous way, paving the way for a simplification based on the intensity model.

scholarly journals On the impact of correlations on the congruence test: a bootstrap approach

2020 ◽  
Vol 55 (3) ◽  
pp. 495-513 ◽  
Author(s):  
Kermarrec Gaël ◽  
Kargoll Boris ◽  
Alkhatib Hamza
Keyword(s):  
Statistical Significance ◽  
Spline Approximation ◽  
Point Clouds ◽  
Test Statistics ◽  
B Spline ◽  
Mode Decomposition ◽  
Spline Surfaces ◽  
Bootstrap Approach ◽  
The Impact ◽  
Congruence Test

AbstractThe 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.

scholarly journals A Fully Automated Three-Stage Procedure for Spatio-Temporal Leaf Segmentation with Regard to the B-Spline-Based Phenotyping of Cucumber Plants

2020 ◽  
Vol 13 (1) ◽  
pp. 74
Author(s):  
Corinna Harmening ◽  
Jens-André Paffenholz
Keyword(s):  
Measurement Techniques ◽  
Point Clouds ◽  
Plant Phenotyping ◽  
Data Sets ◽  
Temporal Segmentation ◽  
B Spline ◽  
Crop Science ◽  
Spline Surfaces ◽  
Spatio Temporal ◽  
The Impact

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%.

Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis

2019 ◽  
Vol 13 (3) ◽  
pp. 199-214 ◽  
Author(s):  
Xin Zhao ◽  
Gaël Kermarrec ◽  
Boris Kargoll ◽  
Hamza Alkhatib ◽  
Ingo Neumann
Keyword(s):  
Stochastic Model ◽  
Stochastic Models ◽  
Null Hypothesis ◽  
Point Clouds ◽  
Deformation Monitoring ◽  
B Splines ◽  
3D Point Clouds ◽  
Relative Standard ◽  
Deformation Area ◽  
The Impact

Abstract Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Compared with approximating surfaces with predetermined geometric primitives, such as plane or sphere, the B-splines surface approximation offers a great flexibility and can be used to fit nearly every object scanned with TLS. However, a variance-covariance matrix (VCM) of the observations involved in approximating the scattered points to B-spline surfaces impact the results of a congruency test, which is the uniformly most powerful invariant (UMPI) test for discriminating between the null hypothesis of zero deformation and its alternative hypotheses. Consequently, simplified stochastic models may weaken the UMPI property. Based on Monte Carlo simulations, the impact of the heteroscedasticity and mathematical correlations often neglected in B-splines approximation are investigated. These correlations are specific in approximating TLS measurements when the raw measurements are transformed into Cartesian coordinates. The rates of rejecting the null hypothesis in a congruency test is employed to reflect the impact of unspecified VCMs on the power of the congruency test. The rejection rates are not sensitive to the simplification of the stochastic models, in the larger deformation area with higher point accuracy, while they are obviously influenced in the smaller deformation area with unfavourable geometries, i. e. larger uncertainties. A threshold ratio of estimated differences to the relative standard deviation highlights whereas the results of congruency test are reliable when using simplified VCMs. It is concluded that the simplification of the stochastic model has a significant impact on the power of the congruency test, especially in the smaller deformation area with larger uncertainties.

scholarly journals GEOMETRIC FEATURES ANALYSIS FOR THE CLASSIFICATION OF CULTURAL HERITAGE POINT CLOUDS

2019 ◽  
Vol XLII-2/W15 ◽  
pp. 541-548 ◽  
Author(s):  
E. Grilli ◽  
E. M. Farella ◽  
A. Torresani ◽  
F. Remondino
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Cultural Heritage ◽  
Point Clouds ◽  
Geometric Features ◽  
3D Point Clouds ◽  
3D Data ◽  
3D Documentation ◽  
The Impact

<p><strong>Abstract.</strong> In the last years, the application of artificial intelligence (Machine Learning and Deep Learning methods) for the classification of 3D point clouds has become an important task in modern 3D documentation and modelling applications. The identification of proper geometric and radiometric features becomes fundamental to classify 2D/3D data correctly. While many studies have been conducted in the geospatial field, the cultural heritage sector is still partly unexplored. In this paper we analyse the efficacy of the geometric covariance features as a support for the classification of Cultural Heritage point clouds. To analyse the impact of the different features calculated on spherical neighbourhoods at various radius sizes, we present results obtained on four different heritage case studies using different features configurations.</p>

Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Corinna Harmening ◽  
Hans Neuner
Keyword(s):  
Data Analysis ◽  
Laser Scanner ◽  
Point Clouds ◽  
Optimal Number ◽  
Deformation Analysis ◽  
Control Points ◽  
Trial And Error ◽  
B Spline ◽  
B Splines ◽  
Spline Surfaces

AbstractFreeform 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.

scholarly journals Tunnel Deformation Inspection via Global Spatial Axis Extraction from 3D Raw Point Cloud

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6815
Author(s):  
Cheng Yi ◽  
Dening Lu ◽  
Qian Xie ◽  
Jinxuan Xu ◽  
Jun Wang
Keyword(s):  
Cross Sections ◽  
Point Cloud ◽  
Large Scale ◽  
Spline Approximation ◽  
Point Clouds ◽  
Driving Safety ◽  
Inspection Method ◽  
B Spline ◽  
3D Point Clouds ◽  
Spatial Axis

Global inspection of large-scale tunnels is a fundamental yet challenging task to ensure the structural stability of tunnels and driving safety. Advanced LiDAR scanners, which sample tunnels into 3D point clouds, are making their debut in the Tunnel Deformation Inspection (TDI). However, the acquired raw point clouds inevitably possess noticeable occlusions, missing areas, and noise/outliers. Considering the tunnel as a geometrical sweeping feature, we propose an effective tunnel deformation inspection algorithm by extracting the global spatial axis from the poor-quality raw point cloud. Essentially, we convert tunnel axis extraction into an iterative fitting optimization problem. Specifically, given the scanned raw point cloud of a tunnel, the initial design axis is sampled to generate a series of normal planes within the corresponding Frenet frame, followed by intersecting those planes with the tunnel point cloud to yield a sequence of cross sections. By fitting cross sections with circles, the fitted circle centers are approximated with a B-Spline curve, which is considered as an updated axis. The procedure of “circle fitting and B-SPline approximation” repeats iteratively until convergency, that is, the distance of each fitted circle center to the current axis is smaller than a given threshold. By this means, the spatial axis of the tunnel can be accurately obtained. Subsequently, according to the practical mechanism of tunnel deformation, we design a segmentation approach to partition cross sections into meaningful pieces, based on which various inspection parameters can be automatically computed regarding to tunnel deformation. A variety of practical experiments have demonstrated the feasibility and effectiveness of our inspection method.

scholarly journals Estimating Control Points for B-Spline Surfaces Using Fully Populated Synthetic Variance–Covariance Matrices for TLS Point Clouds

2021 ◽  
Vol 13 (16) ◽  
pp. 3124
Author(s):  
Jakob Raschhofer ◽  
Gabriel Kerekes ◽  
Corinna Harmening ◽  
Hans Neuner ◽  
Volker Schwieger
Keyword(s):  
Laser Scanning ◽  
Point Clouds ◽  
Covariance Matrices ◽  
Geometric Modelling ◽  
Deformation Analysis ◽  
Control Points ◽  
B Splines ◽  
Spline Surfaces ◽  
Standard Deviations ◽  
The Impact

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.

scholarly journals MORPHOLOGICAL CHANGES ALONG A DIKE LANDSIDE SLOPE SAMPLED BY 4D HIGH RESOLUTION TERRESTRIAL LASER SCANNING

2016 ◽  
Vol XLI-B3 ◽  
pp. 227-232 ◽  
Author(s):  
Mónica Herrero-Huertaa ◽  
Roderik Lindenbergh ◽  
Luc Ponsioen ◽  
Myron van Damme
Keyword(s):  
High Resolution ◽  
Laser Scanning ◽  
Morphological Changes ◽  
Terrestrial Laser Scanning ◽  
Emergency Situation ◽  
Point Clouds ◽  
Data Sampling ◽  
Wave Overtopping ◽  
3D Point Clouds ◽  
The Impact

Emergence of light detection and ranging (LiDAR) technology provides new tools for geomorphologic studies improving spatial and temporal resolution of data sampling hydrogeological instability phenomena. Specifically, terrestrial laser scanning (TLS) collects high resolution 3D point clouds allowing more accurate monitoring of erosion rates and processes, and thus, quantify the geomorphologic change on vertical landforms like dike landside slopes. Even so, TLS captures observations rapidly and automatically but unselectively. &lt;br&gt;&lt;br&gt; In this research, we demonstrate the potential of TLS for morphological change detection, profile creation and time series analysis in an emergency simulation for characterizing and monitoring slope movements in a dike. The experiment was performed near Schellebelle (Belgium) in November 2015, using a Leica Scan Station C10. Wave overtopping and overflow over a dike were simulated whereby the loading conditions were incrementally increased and 14 successful scans were performed. The aim of the present study is to analyse short-term morphological dynamic processes and the spatial distribution of erosion and deposition areas along a dike landside slope. As a result, we are able to quantify the eroded material coming from the impact on the terrain induced by wave overtopping which caused the dike failure in a few minutes in normal storm scenarios (Q = 25 l/s/m) as 1.24 m&lt;sup&gt;3&lt;/sup&gt;. As this shows that the amount of erosion is measurable using close range techniques; the amount and rate of erosion could be monitored to predict dike collapse in emergency situation. &lt;br&gt;&lt;br&gt; The results confirm the feasibility of the proposed methodology, providing scalability to a comprehensive analysis over a large extension of a dike (tens of meters).

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

2020 ◽  
Vol 12 (5) ◽  
pp. 829 ◽  
Author(s):  
Gaël Kermarrec ◽  
Boris Kargoll ◽  
Hamza Alkhatib
Keyword(s):  
Laser Scanner ◽  
Point Clouds ◽  
Testing Procedure ◽  
Local Deformation ◽  
Measurement Noise ◽  
Deformation Analysis ◽  
Terrestrial Laser Scanner ◽  
B Spline ◽  
Set Up ◽  
The Impact

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.

scholarly journals Accuracy Assessment of Cultural Heritage Models Extracting 3D Point Cloud Geometric Features with RPAS SfM-MVS and TLS Techniques

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 145
Author(s):  
Alessandra Capolupo
Keyword(s):  
Cultural Heritage ◽  
Point Cloud ◽  
Accuracy Assessment ◽  
Laser Scanner ◽  
Point Clouds ◽  
Geometric Features ◽  
3D Point Cloud ◽  
3D Point Clouds ◽  
Research Activities ◽  
The Impact

A proper classification of 3D point clouds allows fully exploiting data potentiality in assessing and preserving cultural heritage. Point cloud classification workflow is commonly based on the selection and extraction of respective geometric features. Although several research activities have investigated the impact of geometric features on classification outcomes accuracy, only a few works focused on their accuracy and reliability. This paper investigates the accuracy of 3D point cloud geometric features through a statistical analysis based on their corresponding eigenvalues and covariance with the aim of exploiting their effectiveness for cultural heritage classification. The proposed approach was separately applied on two high-quality 3D point clouds of the All Saints’ Monastery of Cuti (Bari, Southern Italy), generated using two competing survey techniques: Remotely Piloted Aircraft System (RPAS) Structure from Motion (SfM) and Multi View Stereo (MVS) techniques and Terrestrial Laser Scanner (TLS). Point cloud compatibility was guaranteed through re-alignment and co-registration of data. The geometric features accuracy obtained by adopting the RPAS digital photogrammetric and TLS models was consequently analyzed and presented. Lastly, a discussion on convergences and divergences of these results is also provided.

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