Abstract
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.
Acknowledgments
This article presents the results developed during the research project “Integrierte raumzeitliche Modellierung unter Nutzung korrelierter Messgrößen zur Ableitung von Aufnahmekonfigurationen und Beschreibung von Deformationsvorgängen” (IMKAD) (1706–N29), which is funded by the Austrian Science Fund (FWF).
References
[1] Mario Alba, Luigi Fregonese, Federico Prandi, Marco Scaioni and Paolo Valgoi, Structural Monitoring of a Large Dam by Terrestrial Laserscanning, The ISPRS International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Dresden, Deutschland (2006).Search in Google Scholar
[2] Danny L. Anderson, Daniel P. Ames and Ping Yang, Quantitative Methods for Comparing Different Polyline Stream Network Models, Journal of Geographic Information System06 (2014), 88–98.10.4236/jgis.2014.62010Search in Google Scholar
[3] Carl de Boor, On calculating with B-splines, Journal of Approximation Theory6 (1972), 50–62.10.1016/0021-9045(72)90080-9Search in Google Scholar
[4] Maurice G. Cox, The Numerical Evaluation of B-Splines, IMA Journal of Applied Mathematics10 (1972), 134–149.10.1093/imamat/10.2.134Search in Google Scholar
[5] Dirk Eling, Terrestrisches Laserscanning für die Bauwerksüberwachung, Ph.D. thesis, Wiss. Arb. GuG Leibniz Universität Hannover, Nr. 282, Hannover (2009).Search in Google Scholar
[6] Gerald E. Farin, Curves and surfaces for CAGD: A practical guide, 5th ed, The Morgan Kaufmann series in computer graphics and geometric modeling, Morgan Kaufmann and Academic Press, San Francisco, CA and London (2002).Search in Google Scholar
[7] Stuart Gordon, Derek Lichti, Mike Stewart and Jochen Franke, Structural deformation measurement using terrestrial laser scanners, Proceedings of the 11th FIG Symposium on Deformation Measurements (2003).Search in Google Scholar
[8] Jean-Francois Hangouet, Computation of the Hausdorff distance between plane vector polylines, Twelfth International Symposium on Computer-Assisted Cartography (1995).Search in Google Scholar
[9] Corinna Harmening, Raum-zeitliche Segmentierung von natürlichen Objekten in stark verdeckten Szenen, Master thesis (unpublished), Leibniz Universität Hannover (2013).Search in Google Scholar
[10] Otto Heunecke, Heiner Kuhlmann, Walter Welsch, Andreas Eichhorn and Hans Neuner, Handbuch Ingenieurgeodäsie: Auswertung geodätischer Überwachungsmessungen, 2. ed, Wichmann, H, Heidelberg, Neckar, 2008.Search in Google Scholar
[11] Christoph Holst, Jan Dupuis, Stefan Paulus and Heiner Kuhlmann, Flächenhafte Deformationsanalysen mit terrestrischen und Nahbereichslaserscannern - eine Gegenüberstellung anhand von Beispielen, Allgemeine Vermessungsnachrichten (2014), 260–272.Search in Google Scholar
[12] Christoph Holst, Philipp Zeimetz, Axel Nothnagel, Wolfgang Schauerte and Heiner Kuhlmann, Estimation of Focal Length Variations of a 100-m Radio Telescope’s Main Reflector by Laser Scanner Measurements, Journal of Surveying Engineering138 (2012), 126–135.10.1061/(ASCE)SU.1943-5428.0000082Search in Google Scholar
[13] Stephanie Kauker and Volker Schwieger, Approach for a Synthetic Covariance Matrix for Terrestrial Laser Scanner, Proceedings of the 2nd International Workshop: Integration of point- and area-wise geodetic monitoring for structures and natural objects, March 23–24, 2015, Stuttgart (2015).Search in Google Scholar
[14] Karl-Rudolf Koch, Parameter estimation and hypothesis testing in linear models, 2nd ed, Springer, Berlin and New York (1999).Search in Google Scholar
[15] Karl-Rudolf Koch, Identity of simultaneous estimates of control points and of their estimates by the lofting method for NURBS surface fitting, The International Journal of Advanced Manufacturing Technology44 (2009), 1175–1180.10.1007/s00170-009-1934-xSearch in Google Scholar
[16] Karl-Rudolf Koch, NURBS surface with changing shape, Allgemeine Vermessungsnachrichten (2010), 83–89.Search in Google Scholar
[17] Weiyin Ma and Jean-Pierre Kruth, Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces, Computer-Aided Design27 (1995), 663–675.10.1016/0010-4485(94)00018-9Search in Google Scholar
[18] Facundo Mémoli and Guillermo Sapiro, Comparing point clouds, in: The 2004 Eurographics/ACM SIGGRAPH symposium (Jean-Daniel Boissonnat and Pierre Alliez, eds.), p. 32 (2004).Search in Google Scholar
[19] Kurt Meyberg and Peter Vachenauer, Differential- und Integralrechnung, Vektor- und Matrizenrechnung, 6. ed, Springer-Lehrbuch 1, Springer, Berlin [u.a.] (2003).Search in Google Scholar
[20] Oriol Monserrat and Michele Crosetto, Deformation measurement using terrestrial laser scanning data and least squares 3D surface matching, ISPRS Journal of Photogrammetry and Remote Sensing63 (2008), 142–154.10.1016/j.isprsjprs.2007.07.008Search in Google Scholar
[21] Wolfgang Niemeier, Ausgleichungsrechnung: Statistische Auswertemethoden, 2. ed, De Gruyter Lehrbuch, De Gruyter, Berlin [u.a.] (2008).Search in Google Scholar
[22] Johannes Ohlmann-Lauber and Thomas Schafer, Ansätze zur Ableitung von Deformationen aus TLS-Daten, Terrestrisches Laserscanning - TLS 2011 mit TLS-Challenge (2011), 147–158.Search in Google Scholar
[23] Les A. Piegl, On NURBS: a survey, IEEE Computer Graphics and Applications11 (1991), 55–71.10.1109/38.67702Search in Google Scholar
[24] Les A. Piegl and Wayne Tiller, The NURBS Book, Monographs in Visual Communications, Springer, Berlin, Heidelberg (1995).10.1007/978-3-642-97385-7Search in Google Scholar
[25] Les A. Piegl and Wayne Tiller, Parametrization for surface fitting in reverse engineering, Computer-Aided Design33 (2001), 593–603.10.1016/S0010-4485(00)00103-2Search in Google Scholar
[26] Michael Schmidt, Denise Dettmering and Florian Seitz, Using B-Spline Expansions for Ionosphere Modeling, Handbook of Geomathematics (Willi Freeden, M. Zuhair Nashed and Thomas Sonar, eds.), Springer, Berlin, Heidelberg (2014) pp. 1–40.Search in Google Scholar
[27] Claudius Schmitt, Hans Neuner and Ingo Neumann, Strain detection on bridge constructions with kinematic laser scanning, Proceedings of the 2nd Joint international Symposium on Deformation Monitoring (2013).Search in Google Scholar
[28] Rinske van Gosliga, Roderik Lindenbergh and Norbert Pfeifer, Deformation Analysis of a bored tunnel by means of Terrestrial Laserscanning, Proceedings on ISPRS Commission V Symposium, Dresden (2006).Search in Google Scholar
[29] Remco C. Veltkamp and Michiel Hagedoorn, State of the Art in Shape Matching, Principles of Visual Information Retrieval (Sameer Singh and Michael S. Lew, eds.), Advances in Pattern Recognition, Springer London, London (2001) pp. 87–119.Search in Google Scholar
© 2015 Walter de Gruyter GmbH, Berlin/Munich/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- A constraint-based parameterization technique for B-spline surfaces
- Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems
- Monitoring of Civil Engineering Structures using a State-of-the-art Image Assisted Total Station
- The Impact of Vehicle Maneuvers on the Attitude Estimation of GNSS / INS for Mobile Mapping
- InKoPoMoVer – Cooperative Positioning for Real-time User Assistance and Guidance at Multi-modal Public Transit Junctions
Articles in the same Issue
- Frontmatter
- Research Articles
- A constraint-based parameterization technique for B-spline surfaces
- Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems
- Monitoring of Civil Engineering Structures using a State-of-the-art Image Assisted Total Station
- The Impact of Vehicle Maneuvers on the Attitude Estimation of GNSS / INS for Mobile Mapping
- InKoPoMoVer – Cooperative Positioning for Real-time User Assistance and Guidance at Multi-modal Public Transit Junctions