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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 13, Issue 3


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

Xin ZhaoORCID iD: https://orcid.org/0000-0001-5265-6659 / Gaël KermarrecORCID iD: https://orcid.org/0000-0001-5986-5269 / Boris Kargoll / Hamza Alkhatib / Ingo Neumann
Published Online: 2019-04-12 | DOI: https://doi.org/10.1515/jag-2019-0002


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.

Keywords: Terrestrial laser scanning; B-spline approximation; variance-covariance matrix; deformation analysis; congruency test


  • [1]

    Alkhatib, H., Kargoll, B., Paffenholz, J., and Bureick, J. Terrestrial laser scanning for deformation monitoring. In Proceedings of the XXVI FIG congress (Istanbul, Turkey, 6–11 May, 2018).

  • [2]

    Alkhatib, H., Neumann, I., and Kutterer, H. Uncertainty modeling of random and systematic errors by means of Monte-Carlo and fuzzy techniques. J. Appl. Geod. 3, 2 (2009), 67–79.Google Scholar

  • [3]

    Baselga, S., García-Asenjo, L., and Garrigues, P. Deformation monitoring and the maximum number of stable points method. Measurement 70 (2015), 27–35.CrossrefGoogle Scholar

  • [4]

    Bureick, J., Alkhatib, H., and Neumann, I. Robust spatial approximation of laser scanner point clouds by means of free-form curve approaches in deformation analysis. J. Appl. Geod. 10, 1 (2016), 27–35.Google Scholar

  • [5]

    Bureick, J., Neuner, H., Harmening, C., and Neumann, I. Curve and surface approximation of 3D point clouds. avn. 123, 11–12 (2016), 315–327.Google Scholar

  • [6]

    Denli, H. H., and Deniz, R. Global congruency test methods for GPS networks. J. Surv. Eng. 129, 3 (2003), 95–98.CrossrefGoogle Scholar

  • [7]

    Farin, G. From conics to NURBS: A tutorial and survey. IEEE Comput. Graph. 12, 5 (1992), 78–86.CrossrefGoogle Scholar

  • [8]

    Girardeau-Montaut, D., Roux, M., Marc, R., and Thibault, G. Change detection on points cloud data acquired with a ground laser scanner. ISPRS J. Photogramm. Remote Sens. 36, part 3 (2005), 30–35.Google Scholar

  • [9]

    Gotthardt, E. Die Auswirkung unrichtiger Annahmen über Gewichte und Korrelationen auf die Genauigkeit von Ausgleichungen. Z. Vermess. 87 (1962), 65–68.Google Scholar

  • [10]

    Harmening, C., and Neuner, H. A constraint-based parameterization technique for B-spline surfaces. J. Appl. Geod. 9, 3 (2015), 143–161.Google Scholar

  • [11]

    Hoffmann, M., Li, Y., and Wang, G. Paths of C-Bézier and CB-spline curves. Comput. Aided Geom. Des. 23, 5 (2006), 463–475.CrossrefGoogle Scholar

  • [12]

    Holst, C., and Kuhlmann, H. Challenges and present fields of action at laser scanner based deformation analyses. J. Appl. Geod. 10, 1 (2016), 17–25.Google Scholar

  • [13]

    Holst, C., Nothnagel, A., Blome, M., Becker, P., Eichborn, M., and Kuhlmann, H. Improved area-based deformation analysis of a radio telescopes main reflector based on terrestrial laser scanning. J. Appl. Geod. 9, 1 (2015), 1–14.CrossrefGoogle Scholar

  • [14]

    JCGM. Uncertainty of measurement–Part 3: Guide to the expression of uncertainty in measurement (GUM:1995 with minor corrections). 2008.

  • [15]

    Jurek, T., Kuhlmann, H., and Holst, C. Impact of spatial correlations on the surface estimation based on terrestrial laser scanning. J. Appl. Geod. 11, 3 (2017), 143–155.Google Scholar

  • [16]

    Kargoll, B. On the theory and application of model misspecification tests in geodesy. PhD thesis, Deutsche Geodätische Kommission, 2012.Google Scholar

  • [17]

    Kauker, S., and Schwieger, V. A synthetic covariance matrix for monitoring by terrestrial laser scanning. J. Appl. Geod. 11, 2 (2017), 77–87.Google Scholar

  • [18]

    Kermarrec, G., and Schön, S. Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix. J. Geod. 90, 9 (2016), 793–805.CrossrefGoogle Scholar

  • [19]

    Kermarrec, G., and Schön, S. A priori fully populated covariance matrices in least-squares adjustment-case study: GPS relative positioning. J. Geod. 91, 5 (2017), 465–484.CrossrefGoogle Scholar

  • [20]

    Koch, K.-R. Introduction to Bayesian Statistics. Springer Science & Business Media, 2007.Google Scholar

  • [21]

    Koch, K.-R. Determining uncertainties of correlated measurements by Monte-Carlo simulations applied to laserscanning. J. Appl. Geod. 2, 3 (2008), 139–147.Google Scholar

  • [22]

    Koch, K.-R. Evaluation of uncertainties in measurements by Monte-Carlo simulations with an application for laserscanning. J. Appl. Geod. 2, 2 (2008), 67–77.Google Scholar

  • [23]

    Koch, K.-R. NURBS surface with changing shape. avn. 117 (2010), 83–89.Google Scholar

  • [24]

    Koch, K.-R. Parameter Estimation and Hypothesis Testing in Linear Models. Springer Science & Business Media, 2013.Google Scholar

  • [25]

    Lague, D., Brodu, N., and Leroux, J. Accurate 3D comparison of complex topography with terrestrial laser scanner: Application to the Rangitikei canyon (N-Z). ISPRS J. Photogramm. Remote Sens. 82 (2013), 10–26.CrossrefGoogle Scholar

  • [26]

    Lehmann, R., and Lösler, M. Congruence analysis of geodetic networks-hypothesis tests versus model selection by information criteria. J. Appl. Geod. 11, 4 (2017), 271–283.Google Scholar

  • [27]

    Lindenbergh, R., and Pfeifer, N. A statistical deformation analysis of two epochs of terrestrial laser data of a lock. In Proceedings of the 7th Conference on Optical 3D Measurement Techniques (Vienna, Austria, 3–5 October 2005).

  • [28]

    Linkwitz, K. Über den Einfluß verschiedener Gewichtsannahmen auf das Ausgleichungsergebnis bei bedingten Beobachtungen. Z. Vermess. 86 (1961), 179–186.Google Scholar

  • [29]

    Meagher, D. J. Octree encoding: A new technique for the representation, manipulation and display of arbitrary 3D objects by computer. Tech. Rep. IPL-TR-80-111, Rensselaer Polytechnic Institute, Image Processing Laboratory, 1980.

  • [30]

    Neumann, I., and Kutterer, H. Congruence tests and outlier detection in deformation analysis with respect to observation imprecision. J. Appl. Geod. 1, 1 (2007), 1–7.CrossrefGoogle Scholar

  • [31]

    Neumann, I., and Kutterer, H. The probability of type I and type II errors in imprecise hypothesis testing with an application to geodetic deformation analysis. Int. J. Reliab. Saf. 3, 1–3 (2009), 286–306.CrossrefGoogle Scholar

  • [32]

    Neuner, H., Schmitt, C., and Neumann, I. Zur Bestimmung der verkehrsseitig verursachten Dehnung an einem Brückentragwerk mittels terrestrischem Laserscanning. In A. Wieser (ed.): Ingenieurvermessung’ 14. Beiträge zum 17. Internationalen Ingenieurvermessungskurs (Zürich, Switzerland, 2014).

  • [33]

    Niemeier, W. Statistical tests for detecting movements in repeatedly measured geodetic networks. Tectonophysics 71, 1–4 (1981), 335–351.CrossrefGoogle Scholar

  • [34]

    Niemeier, W. Ausgleichungsrechnung: Statistische Auswertemethoden. Walter de Gruyter, 2008.Google Scholar

  • [35]

    Ohlmann-Lauber, J., and Schäfer, T. Ansätze zur Ableitung von Deformationen aus TLS-Daten. In DVW Seminal Terrestrisches Laserscanning-TLS 2011 mit TLS-Challenge (Fulda, Germany, 2011).

  • [36]

    Pelzer, H. Zur Analyse geodatischer Deformations-messungen. Reihe c, Deutsche Geodätische Kommission, 1971.

  • [37]

    Piegl, L., and Tiller, W. The NURBS Book. Springer Science & Business Media, 2012.Google Scholar

  • [38]

    Schneider, D. Terrestrial laser scanning for area based deformation analysis of towers and water damns. In Proceedings of 3rd IAG/12th FIG Symposium (Baden, Austria, 22–24 May, 2006).

  • [39]

    Setan, H., and Singh, R. Deformation analysis of a geodetic monitoring network. Geomatica 55, 3 (2001), 333–346.Google Scholar

  • [40]

    Taşccedil, L. Analysis of dam deformation measurements with the robust and non-robust methods. Sci. Res. Essays 5, 14 (2010), 1770–1779.Google Scholar

  • [41]

    Teza, G., Galgaro, A., Zaltron, N., and Genevois, R. Terrestrial laser scanner to detect landslide displacement fields: a new approach. Int. J. Remote Sens. 28, 16 (2007), 3425–3446.CrossrefGoogle Scholar

  • [42]

    Tsakiri, M., Lichti, D., and Pfeifer, N. Terrestrial laser scanning for deformation monitoring. In Proceedings of 3rd IAG/12th FIG Symposium (Baden, Austria, 22–24 May, 2006).

  • [43]

    Velsink, H. On the deformation analysis of point fields. J. Geod. 89, 11 (2015), 1071–1087.CrossrefGoogle Scholar

  • [44]

    Vezočnik, R., Ambrožič, T., Sterle, O., Bilban, G., Pfeifer, N., Stopar, B., et al. Use of terrestrial laser scanning technology for long term high precision deformation monitoring. Sensors 9, 12 (2009), 9873–9895.CrossrefGoogle Scholar

  • [45]

    Wang, J. Block-to-point fine registration in terrestrial laser scanning. Remote Sens. 5, 12 (2013), 6921–6937.CrossrefGoogle Scholar

  • [46]

    Wolf, H. Der Einfluss von Gewichtsänderungen auf die Ausgleichungsergebnisse. Z. Vermess. 86 (1961), 361–362.Google Scholar

  • [47]

    Wujanz, D., Burger, M., Mettenleiter, M., and Neitzel, F. An intensity-based stochastic model for terrestrial laser scanners. ISPRS J. Photogramm. Remote Sens. 125 (2017), 146–155.CrossrefGoogle Scholar

  • [48]

    Xu, P. The effect of incorrect weights on estimating the variance of unit weight. Stud. Geophys. Geod. 57, 3 (2013), 339–352.CrossrefGoogle Scholar

  • [49]

    Xu, X., Kargoll, B., Bureick, J., Yang, H., Alkhatib, H., and Neumann, I. TLS-based profile model analysis of major composite structures with robust B-spline method. Compos. Struct. 184 (2018), 814–820.CrossrefGoogle Scholar

  • [50]

    Zhao, X., Alkhatib, H., Kargoll, B., and Neumann, I. Statistical evaluation of the influence of the uncertainty budget on B-spline curve approximation. J. Appl. Geod. 11, 4 (2017), 215–230.Google Scholar

  • [51]

    Zhao, X., Kargoll, B., Omidalizarandi, M., Xu, X., and Alkhatib, H. Model selection for parametric surfaces approximating 3D point clouds for deformation analysis. Remote Sens. 10, 4 (2018), 634.CrossrefGoogle Scholar

About the article

Received: 2019-01-08

Accepted: 2019-03-18

Published Online: 2019-04-12

Published in Print: 2019-07-26

Citation Information: Journal of Applied Geodesy, Volume 13, Issue 3, Pages 199–214, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2019-0002.

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