Prof. Dr.-Ing. Rüdiger Lehmann
Research / Forschung
- IN DUBIO PRO GEO - Geodetic Cloud Computing
- Outlier detection in geodetic observations
- Robust geodetic methods
- Detection of significant frequencies in geodetic time series
Researchgate Score: 22.3 h-index: 9 (excluding self-citations)
My main scientific interests are directed towards developing new estimation techniques for ever more complex geodetic observation models, to enhance the retrieval of valuable information from the measurements in terms of accuracy, reliability, and computational efficiency. Such novel techniques include outlier detection, robust estimation, advanced methods of hypothesis testing and model selection in geodetic adjustment models as well as Monte Carlo techniques for geodetic data analysis.
18th century: C.F. Gauß invented the geodetic adjustment by least squares, which is solvable by pencil and paper (Gaussian algorithm).
19th century: F.W. Bessel and others realized that the stochastic model of least squares adjustment often does not describe practical observations well. However, better models could not be established due to lack of computing power.
20th century: K. Zuse and others developped the electronic computer
21st century: Geodesists continue to use primarily Gaussian least squares.
Currently in print / Momentan im Druck:
Type-Constrained Total Least Squares Fitting of Curved Surfaces to 3D Point Clouds
co-authored by: none
abstract: We present a unified approach to curved surface fitting in the framework of total least squares. Compared to algebraic and geometric fitting of surface models to 3D point cloud, this approach is relatively new. It has the largest degree of generality, such that any conceivable surface fitting problem can be formulated within this framework. In our contribution we consider quadric surfaces, which represent a very large and most popular class of curved surfaces. We discuss aspects of parametrizations and the use of constraints to restrict the set of solutions to special types of quadrics, like planes, spheres, ellipsoids, hyperboloids, cubes, cuboids, toroids, cylinders, cones, pyramids etc. Then we propose an iterative solution using Lagrange multipliers and the Newton method. The choice of an initial guess is discussed. Finally, we present a numerical example: fitting an elliptic cylinder with oblique axis to 20 data points. The results show that the total least squares fitting using type-constraints can be generally recommended to fit curved surfaces to point clouds.
keywords: Quadric Surfaces; Point Cloud Fitting; Newton Method; Total Least Squares; Lagrange Multipliers
to appear in: Journal of Mathematical and Statistical Analysis
doi: not yet assigned