Details
| Original language | English |
|---|---|
| Pages (from-to) | 199-214 |
| Number of pages | 16 |
| Journal | Journal of Applied Geodesy |
| Volume | 13 |
| Issue number | 3 |
| Publication status | Published - 12 Apr 2019 |
Abstract
Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Compared with approximating surfaces with predetermined geometric primitives, such as plane or sphere, the B-splines surface approximation offers a great flexibility and can be used to fit nearly every object scanned with TLS. However, a variance-covariance matrix (VCM) of the observations involved in approximating the scattered points to B-spline surfaces impact the results of a congruency test, which is the uniformly most powerful invariant (UMPI) test for discriminating between the null hypothesis of zero deformation and its alternative hypotheses. Consequently, simplified stochastic models may weaken the UMPI property. Based on Monte Carlo simulations, the impact of the heteroscedasticity and mathematical correlations often neglected in B-splines approximation are investigated. These correlations are specific in approximating TLS measurements when the raw measurements are transformed into Cartesian coordinates. The rates of rejecting the null hypothesis in a congruency test is employed to reflect the impact of unspecified VCMs on the power of the congruency test. The rejection rates are not sensitive to the simplification of the stochastic models, in the larger deformation area with higher point accuracy, while they are obviously influenced in the smaller deformation area with unfavourable geometries, i. e. larger uncertainties. A threshold ratio of estimated differences to the relative standard deviation highlights whereas the results of congruency test are reliable when using simplified VCMs. It is concluded that the simplification of the stochastic model has a significant impact on the power of the congruency test, especially in the smaller deformation area with larger uncertainties.
Keywords
- B-spline approximation, congruency test, deformation analysis, Terrestrial laser scanning, variance-covariance matrix
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Earth and Planetary Sciences(all)
- Earth and Planetary Sciences (miscellaneous)
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In: Journal of Applied Geodesy, Vol. 13, No. 3, 12.04.2019, p. 199-214.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis
AU - Zhao, Xin Fu
AU - Kermarrec, Gaël
AU - Kargoll, Boris
AU - Alkhatib, Hamza
AU - Neumann, Ingo
PY - 2019/4/12
Y1 - 2019/4/12
N2 - Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Compared with approximating surfaces with predetermined geometric primitives, such as plane or sphere, the B-splines surface approximation offers a great flexibility and can be used to fit nearly every object scanned with TLS. However, a variance-covariance matrix (VCM) of the observations involved in approximating the scattered points to B-spline surfaces impact the results of a congruency test, which is the uniformly most powerful invariant (UMPI) test for discriminating between the null hypothesis of zero deformation and its alternative hypotheses. Consequently, simplified stochastic models may weaken the UMPI property. Based on Monte Carlo simulations, the impact of the heteroscedasticity and mathematical correlations often neglected in B-splines approximation are investigated. These correlations are specific in approximating TLS measurements when the raw measurements are transformed into Cartesian coordinates. The rates of rejecting the null hypothesis in a congruency test is employed to reflect the impact of unspecified VCMs on the power of the congruency test. The rejection rates are not sensitive to the simplification of the stochastic models, in the larger deformation area with higher point accuracy, while they are obviously influenced in the smaller deformation area with unfavourable geometries, i. e. larger uncertainties. A threshold ratio of estimated differences to the relative standard deviation highlights whereas the results of congruency test are reliable when using simplified VCMs. It is concluded that the simplification of the stochastic model has a significant impact on the power of the congruency test, especially in the smaller deformation area with larger uncertainties.
AB - Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Compared with approximating surfaces with predetermined geometric primitives, such as plane or sphere, the B-splines surface approximation offers a great flexibility and can be used to fit nearly every object scanned with TLS. However, a variance-covariance matrix (VCM) of the observations involved in approximating the scattered points to B-spline surfaces impact the results of a congruency test, which is the uniformly most powerful invariant (UMPI) test for discriminating between the null hypothesis of zero deformation and its alternative hypotheses. Consequently, simplified stochastic models may weaken the UMPI property. Based on Monte Carlo simulations, the impact of the heteroscedasticity and mathematical correlations often neglected in B-splines approximation are investigated. These correlations are specific in approximating TLS measurements when the raw measurements are transformed into Cartesian coordinates. The rates of rejecting the null hypothesis in a congruency test is employed to reflect the impact of unspecified VCMs on the power of the congruency test. The rejection rates are not sensitive to the simplification of the stochastic models, in the larger deformation area with higher point accuracy, while they are obviously influenced in the smaller deformation area with unfavourable geometries, i. e. larger uncertainties. A threshold ratio of estimated differences to the relative standard deviation highlights whereas the results of congruency test are reliable when using simplified VCMs. It is concluded that the simplification of the stochastic model has a significant impact on the power of the congruency test, especially in the smaller deformation area with larger uncertainties.
KW - B-spline approximation
KW - congruency test
KW - deformation analysis
KW - Terrestrial laser scanning
KW - variance-covariance matrix
UR - http://www.scopus.com/inward/record.url?scp=85066338929&partnerID=8YFLogxK
U2 - 10.1515/jag-2019-0002
DO - 10.1515/jag-2019-0002
M3 - Article
AN - SCOPUS:85066338929
VL - 13
SP - 199
EP - 214
JO - Journal of Applied Geodesy
JF - Journal of Applied Geodesy
SN - 1862-9016
IS - 3
ER -