Biased and Unbiased Estimates Based on Laser Scans of Surfaces with Unknown Deformations

Abstract

The estimates based on laser scans of surfaces with unknown deformations are biased and not reproducible when changing the scanning geometry. While the existence of a bias is only disadvantageous at some applications, non-reproducible estimates are never desired. Hence, this varying bias and its origin need to be investigated -since this situation has not been examined suciently in the literature. Analyzing this situation, the dependence of the estimation on the network con guration is highlighted: the network con guration -studied similarly to geodetic networks -rules about the impact of the deformation. As pointed out, this impact can be altered by manipulating the network con guration. Therefore, several strategies are proposed. These include manipulations of the leastsquares adjustment as well as robust estimation. It is revealed that the reproducibility of the estimates can indeed be signi cantly increased by some of the proposed leastsquares manipulations. However, the bias can only be signi cantly reduced by robust estimation.

Improved area-based deformation analysis of a radio telescope’s main reflector based on terrestrial laser scanning

“…This has been shown theoretically by [10] and it can be con rmed by the present study when analyzing the measurements of the year 2010 [31]. For approximating the whole point cloud of about million points, the adjustment had to be implemented in C++ on a highperformance processor using parallel computing.…”

“…This is a consequence of the progress in knowledge regarding the measurement and processing of laser scanner point clouds that took place in recent years. This especially holds for data reduction of point clouds [10,14] and the calibration of TLS [13]. Additionally, new measurements of the E elsberg radio telescope have been performed in the year 2013 using the laser scanner Leica Scan Station P20.…”

“…For numerical reasons due to the large number of observations when approximating laser scans, the GHM is transformed to a Gauß-Markov model (GMM) [44]. This transformation is valid when working with TLS measurements [10].…”

“…Usually, the aim is to improve the manageability of the data memory and processing time by reducing the data volume when the object was over-sampled initially [19,20,45]. Only in the recent past, data reduction has been analyzed regarding its potential for rigorously achieving unbiased results in area-based surface analysis [10,14].…”

Measuring Leaf Thickness with 3D Close-Up Laser Scanners: Possible or Not?

“…Both point clouds were approximated by the best fitting plane using an established least-squares adjustment approach [18,27]. The mean distance between the two measured surfaces, i.e., the thickness, is calculated from the distance of each point of side A to the plane of side B and vice versa.…”