Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis
-
,
Abstract
In many geodetic engineering applications it is necessary to solve the problem of describing a measured data point cloud, measured, e. g. by laser scanner, by means of free-form curves or surfaces, e. g., with B-Splines as basis functions. The state of the art approaches to determine B-Splines yields results which are seriously manipulated by the occurrence of data gaps and outliers.
Optimal and robust B-Spline fitting depend, however, on optimal selection of the knot vector. Hence we combine in our approach Monte-Carlo methods and the location and curvature of the measured data in order to determine the knot vector of the B-Spline in such a way that no oscillating effects at the edges of data gaps occur. We introduce an optimized approach based on computed weights by means of resampling techniques. In order to minimize the effect of outliers, we apply robust M-estimators for the estimation of control points.
The above mentioned approach will be applied to a multi-sensor system based on kinematic terrestrial laserscanning in the field of rail track inspection.
Acknowledgement
A large part of the shown results were developed in the research project “Advanced Rail Track Inspection System (ARTIS)” supported by the Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag.
References
[1] Cox, M. G., 1972. The Numerical Evaluation of B -Splines. IMA J Appl Math 10 (2), 134–149. doi:10.1093/imamat/10.2.134.Search in Google Scholar
[2] de Boor, C., 1972. On calculating with B-splines. Journal of Approximation Theory 6 (1), 50–62. doi:10.1016/0021-9045(72)90080-9.Search in Google Scholar
[3] Gálvez, A., Iglesias, A., Avila, A., Otero, C., Arias, R., Manchado, C., 2015. Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting. Applied Soft Computing 26, 90–106. doi:10.1016/j.asoc.2014.09.030.Search in Google Scholar
[4] Hartung, J., Elpelt, B., Klösener, K.-H., 2009. Statistik: Lehr- und Handbuch der angewandten Statistik, 15th ed. Oldenbourg, München, XXXIII, 1145.10.1524/9783486710540Search in Google Scholar
[5] Huber, P. J., 1981. Robust statistics. Wiley, New York, ix, 308.10.1002/0471725250Search in Google Scholar
[6] Jupp, D.L., 1978. Approximation to Data by Spline with Free Knots. SIAM Journal on Numerical Analysis 15 (2), 328–343.10.1137/0715022Search in Google Scholar
[7] Koch, K.-R., 2009. Fitting Free-Form Surfaces to Laserscan Data by NURBS. Allgemeine Vermessungs-Nachrichten (AVN) (4), 134–140.Search in Google Scholar
[8] Lai, J. -Y., Lu, C. -Y., 1996. Reverse Engineering of Composite Sculptured Surfaces. Int J Advanced Manufacturing Technology (12), 180–189.10.1007/BF01351197Search in Google Scholar
[9] Liu, A., Wang, Y., 2004. Hypothesis testing in smoothing spline models. Journal of Statistical Computation and Simulation 74 (8), 581–597. doi:10.1080/00949650310001623416.Search in Google Scholar
[10] Park, H., Lee, J. -H., 2007. B-spline curve fitting based on adaptive curve refinement using dominant points. Computer-Aided Design 39 (6), 439–451. doi:10.1016/j.cad.2006.12.006.Search in Google Scholar
[11] Piegl, L., Tiller, W., 1997. The NURBS book, 2nd ed. Springer, Berlin, New York, xiv, 646.10.1007/978-3-642-59223-2Search in Google Scholar
[12] Rice, J. R., 1969. The Approximation of Function, 2nd ed. Addison-Wesley Publishing Company, Reading, MA.Search in Google Scholar
[13] Sarfraz, M., Raza, S. A., 2001. Capturing outline of fonts using genetic algorithm and splines, in: Proceedings. IEEE Computer Soc., Los Alamitos, Calif. [et al.], pp. 738–743.Search in Google Scholar
[14] Schmitt, C., Neuner, H., 2015. Knot estimation on B-Spline curves. Österreichische Zeitschrift für Vermessung & Geoinformation 103 (2 + 3), 188–197.Search in Google Scholar
[15] Simon, D., 2006. Optimal state estimation: Kalman, H [infinity] and nonlinear approaches. Wiley-Interscience, Hoboken, N. J., xxvi, 526.10.1002/0470045345Search in Google Scholar
[16] Ülker, E., Arslan, A., 2009. Automatic knot adjustment using an artificial immune system for B-spline curve approximation. Information Sciences 179 (10), 1483–1494. doi:10.1016/j.ins.2008.11.037.Search in Google Scholar
[17] Wicki, F., 1998. Robuste Schätzverfahren für die Parameterschätzung in geodätischen Netzen. Institut für Geodäsie und Photogrammetrie, Eidgenössische Technische Hochschule, Zürich, 185.Search in Google Scholar
[18] Yoshimoto, F., Moriyama, M., Harada, T., 1999. Automatic knot placement by a genetic algorithm for data fitting with a spline, in: Proceedings of the international conference on shape modeling and applications, pp. 162–169.10.1109/SMA.1999.749336Search in Google Scholar
[19] Zhao, X., Zhang, C., Yang, B., Li, P., 2011. Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation. Computer-Aided Design 43 (6), 598–604. doi:10.1016/j.cad.2011.01.015.Search in Google Scholar
© 2016 Walter de Gruyter GmbH, Berlin/Munich/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- Editorial to the Special Edition on Deformation Monitoring
- Research Articles
- Time Series Analysis of 3D Coordinates Using Nonstochastic Observations
- Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses
- Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis
- Laser Scanning Based Growth Analysis of Plants as a New Challenge for Deformation Monitoring
- Potential of GPS Common Clock Single-differences for Deformation Monitoring
- Investigations on the Influence of Antenna Near-field Effects and Satellite Obstruction on the Uncertainty of GNSS-based Distance Measurements
- Deformation Measurement of a Driven Pile Using Distributed Fibre-optic Sensing
- Measurement of Deflection in Concrete Beams During Fatigue Loading Test Using the Microsoft Kinect 2.0
- Design and Implementation of a Modern Automatic Deformation Monitoring System
- Deck and Cable Dynamic Testing of a Single-span Bridge Using Radar Interferometry and Videometry Measurements
Articles in the same Issue
- Frontmatter
- Editorial
- Editorial to the Special Edition on Deformation Monitoring
- Research Articles
- Time Series Analysis of 3D Coordinates Using Nonstochastic Observations
- Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses
- Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis
- Laser Scanning Based Growth Analysis of Plants as a New Challenge for Deformation Monitoring
- Potential of GPS Common Clock Single-differences for Deformation Monitoring
- Investigations on the Influence of Antenna Near-field Effects and Satellite Obstruction on the Uncertainty of GNSS-based Distance Measurements
- Deformation Measurement of a Driven Pile Using Distributed Fibre-optic Sensing
- Measurement of Deflection in Concrete Beams During Fatigue Loading Test Using the Microsoft Kinect 2.0
- Design and Implementation of a Modern Automatic Deformation Monitoring System
- Deck and Cable Dynamic Testing of a Single-span Bridge Using Radar Interferometry and Videometry Measurements
