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.
References
[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).Search in Google Scholar
[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), 67–79.10.1515/JAG.2009.008Search in Google Scholar
[3] Baselga, S., García-Asenjo, L., and Garrigues, P. Deformation monitoring and the maximum number of stable points method. Measurement 70 (2015), 27–35.10.1016/j.measurement.2015.03.034Search in Google 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), 27–35.10.1515/jag-2015-0020Search in 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.Search in Google Scholar
[6] Denli, H. H., and Deniz, R. Global congruency test methods for GPS networks. J. Surv. Eng. 129, 3 (2003), 95–98.10.1061/(ASCE)0733-9453(2003)129:3(95)Search in Google Scholar
[7] Farin, G. From conics to NURBS: A tutorial and survey. IEEE Comput. Graph. 12, 5 (1992), 78–86.10.1109/38.156017Search in Google 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.Search in Google Scholar
[9] Gotthardt, E. Die Auswirkung unrichtiger Annahmen über Gewichte und Korrelationen auf die Genauigkeit von Ausgleichungen. Z. Vermess. 87 (1962), 65–68.Search in Google Scholar
[10] Harmening, C., and Neuner, H. A constraint-based parameterization technique for B-spline surfaces. J. Appl. Geod. 9, 3 (2015), 143–161.10.1515/jag-2015-0003Search in 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), 463–475.10.1016/j.cagd.2006.03.001Search in Google 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), 17–25.10.1515/jag-2015-0025Search in 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), 1–14.10.1515/jag-2014-0018Search in Google Scholar
[14] JCGM. Uncertainty of measurement–Part 3: Guide to the expression of uncertainty in measurement (GUM:1995 with minor corrections). 2008.Search in Google Scholar
[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), 143–155.10.1515/jag-2017-0006Search in Google Scholar
[16] Kargoll, B.On the theory and application of model misspecification tests in geodesy. PhD thesis, Deutsche Geodätische Kommission, 2012.Search in Google Scholar
[17] Kauker, S., and Schwieger, V. A synthetic covariance matrix for monitoring by terrestrial laser scanning. J. Appl. Geod. 11, 2 (2017), 77–87.10.1515/jag-2016-0026Search in 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), 793–805.10.1007/s00190-016-0911-zSearch in Google 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), 465–484.10.1007/s00190-016-0976-8Search in Google Scholar
[20] Koch, K.-R.Introduction to Bayesian Statistics. Springer Science & Business Media, 2007.Search in Google Scholar
[21] Koch, K.-R. Determining uncertainties of correlated measurements by Monte-Carlo simulations applied to laserscanning. J. Appl. Geod. 2, 3 (2008), 139–147.10.1515/JAG.2008.016Search in 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), 67–77.10.1515/JAG.2008.008Search in Google Scholar
[23] Koch, K.-R. NURBS surface with changing shape. avn. 117 (2010), 83–89.Search in Google Scholar
[24] Koch, K.-R.Parameter Estimation and Hypothesis Testing in Linear Models. Springer Science & Business Media, 2013.Search in 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), 10–26.10.1016/j.isprsjprs.2013.04.009Search in Google 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), 271–283.10.1515/jag-2016-0049Search in 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).Search in Google Scholar
[28] Linkwitz, K. Über den Einfluß verschiedener Gewichtsannahmen auf das Ausgleichungsergebnis bei bedingten Beobachtungen. Z. Vermess. 86 (1961), 179–186.Search in 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.Search in Google Scholar
[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), 1–7.10.1515/jag.2007.001Search in Google 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), 286–306.10.1504/IJRS.2009.026847Search in Google 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).Search in Google Scholar
[33] Niemeier, W. Statistical tests for detecting movements in repeatedly measured geodetic networks. Tectonophysics 71, 1–4 (1981), 335–351.10.1016/0040-1951(81)90076-7Search in Google Scholar
[34] Niemeier, W.Ausgleichungsrechnung: Statistische Auswertemethoden. Walter de Gruyter, 2008.10.1515/9783110206784Search in 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).Search in Google Scholar
[36] Pelzer, H.Zur Analyse geodatischer Deformations-messungen. Reihe c, Deutsche Geodätische Kommission, 1971.Search in Google Scholar
[37] Piegl, L., and Tiller, W.The NURBS Book. Springer Science & Business Media, 2012.Search in 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).Search in Google Scholar
[39] Setan, H., and Singh, R. Deformation analysis of a geodetic monitoring network. Geomatica 55, 3 (2001), 333–346.Search in 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.Search in 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), 3425–3446.10.1080/01431160601024234Search in Google 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).Search in Google Scholar
[43] Velsink, H. On the deformation analysis of point fields. J. Geod. 89, 11 (2015), 1071–1087.10.1007/s00190-015-0835-zSearch in Google 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), 9873–9895.10.3390/s91209873Search in Google Scholar PubMed PubMed Central
[45] Wang, J. Block-to-point fine registration in terrestrial laser scanning. Remote Sens. 5, 12 (2013), 6921–6937.10.3390/rs5126921Search in Google Scholar
[46] Wolf, H. Der Einfluss von Gewichtsänderungen auf die Ausgleichungsergebnisse. Z. Vermess. 86 (1961), 361–362.Search in 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), 146–155.10.1016/j.isprsjprs.2016.12.006Search in Google Scholar
[48] Xu, P. The effect of incorrect weights on estimating the variance of unit weight. Stud. Geophys. Geod. 57, 3 (2013), 339–352.10.1007/s11200-012-0665-xSearch in Google 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), 814–820.10.1016/j.compstruct.2017.10.057Search in Google 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), 215–230.10.1515/jag-2017-0018Search in 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), 634.10.3390/rs10040634Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- Using direct transformation approach as an alternative technique to fuse global digital elevation models with GPS/levelling measurements in Egypt
- Empirical stochastic model of detected target centroids: Influence on registration and calibration of terrestrial laser scanners
- Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis
- Accuracy assessment of relative and precise point positioning online GPS processing services
- Monitoring of extreme land hydrology events in central Poland using GRACE, land surface models and absolute gravity data
- Occurrences of counter electrojets and possible ionospheric TEC variations round new Moon and full Moon days across the low latitude Indian region
- Control survey for a 6.7 km immersed tunnel in Chinese Lingding ocean
- Geometric and statistical interpretation of correlation between fault tests in integrated GPS/INS systems
Articles in the same Issue
- Frontmatter
- Research Articles
- Using direct transformation approach as an alternative technique to fuse global digital elevation models with GPS/levelling measurements in Egypt
- Empirical stochastic model of detected target centroids: Influence on registration and calibration of terrestrial laser scanners
- Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis
- Accuracy assessment of relative and precise point positioning online GPS processing services
- Monitoring of extreme land hydrology events in central Poland using GRACE, land surface models and absolute gravity data
- Occurrences of counter electrojets and possible ionospheric TEC variations round new Moon and full Moon days across the low latitude Indian region
- Control survey for a 6.7 km immersed tunnel in Chinese Lingding ocean
- Geometric and statistical interpretation of correlation between fault tests in integrated GPS/INS systems