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Correlations at Terrestrial Laser Scanning

 

Using terrestrial laser scanners (TLS) to acquire geometric properties of surfaces has been proven to be a solid procedure in tasks of industrial and classical survey. New TLS measure with a rate of up to one million points per second and generate a highly dense three-dimensional point cloud. Accordingly, they have a high spatio-temporal resolution.

 

In terms of deformation analyses, the results depend on the stochastic characteristics of the point cloud. They are defined by the covariance matrix of the observations, which consists of variances and covariances. Yet, the correlations and, thus, the covariances are unknown and therefore neglected (Holst & Kuhlmann 2016). Determining the stochastic model is complex and there is no common approach to detect the unknown correlations in the observations, yet.

Correlations

Figure 1 – Increasing the correlation in between simulated scan points. Correlations have a formative influence on the scanned object.

First investigations show that correlations have a formative effect on the observations (Figure 1). On the basis of a simulation environment, correlated observations of a plane were generated. If these correlations are not considered in parameter estimations, the adjustment is inconsistent and the estimated parameters are biased (Jurek et al., 2017). Consequently, the formative effect of correlations and the deformations might not be distinguishable.

 

The systematic effects which cause correlations (stochastic dependencies) in between the points of the point cloud are segmented as (Figure 2):

  • Scanner mechanism (calibration, settings),
  • Atmospheric conditions (temperature, pressure),
  • Object properties (color, reflection),
  • Scanning geometry (incidence angle).

 

The correlations in the measurements (distance, vertical angle, horizontal angle) are not known due to the complexity of the instrument and the physical processes.

 

Systematic Influences

Figure 2 - Systematic influences on a laser scan

Accordingly, the stochastic model is not known and, hence, a parameter estimation of the scanned object leads to unsatisfying results.

Thus, further experimental investigations are needed to quantify the effects of correlations and, moreover, to reveal methods to handle correlations in laser scan’s analyses.

 

 Contacts:

Publications:

  • Jurek, T., Holst Ch., Kuhlmann, H. (2017) Impact of spatial correlations on the surface estimation based on terrestrial laser scanning, J. Appl. Geodesy, 11 (3), 143-155, doi:10.1515/jag-2017-0006
  • Holst, Ch., Kuhlmann, H. (2016) Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses, J. Appl. Geodesy, 10 (1), S. 17-25 (identical with: Holst, Ch., Kuhlmann, H. (2016) Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses, 3rd Joint International Symposium on Deformation Monitoring (JISDM), 30th March - 1st April 2016, Vienna) 
  • Holst, Ch., Artz, T., Kuhlmann, H. (2014) Biased and unbiased estimates based on laser scans of surfaces with unknown deformations, J. Appl. Geodesy, 8 (3), S. 169-184.
 
 

 

 
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