Details
| Original language | English |
|---|---|
| Article number | 3640 |
| Journal | Sensors |
| Volume | 19 |
| Issue number | 17 |
| Early online date | 21 Aug 2019 |
| Publication status | Published - 1 Sept 2019 |
Abstract
B-spline surfaces possess attractive properties such as a high degree of continuity or the local support of their basis functions. One of the major applications of B-spline surfaces in engineering geodesy is the least-square (LS) fitting of surfaces from, e.g., 3D point clouds obtained from terrestrial laser scanners (TLS). Such mathematical approximations allow one to test rigorously with a given significance level the deformation magnitude between point clouds taken at different epochs. Indeed, statistical tests cannot be applied when point clouds are processed in commonly used software such as CloudCompare, which restrict the analysis of deformation to simple deformation maps based on distance computation. For a trustworthy test decision and a resulting risk management, the stochastic model of the underlying observations needs, however, to be optimally specified. Since B-spline surface approximations necessitate Cartesian coordinates of the TLS observations, the diagonal variance covariance matrix (VCM) of the raw TLS measurements has to be transformed by means of the error propagation law. Unfortunately, this procedure induces mathematical correlations, which can strongly affect the chosen test statistics to analyse deformation, if neglected. This may lead potentially to rejecting wrongly the null hypothesis of no-deformation, with risky and expensive consequences. In this contribution, we propose to investigate the impact of mathematical correlations on test statistics, using real TLS observations from a bridge under load. As besides TLS, a highly precise laser tracker (LT) was used, the significance of the difference of the test statistics when the stochastic model is misspecified can be assessed. However, the underlying test distribution is hardly tractable so that only an adapted bootstrapping allows the computation of trustworthy p-values. Consecutively, the extent to which heteroscedasticity and mathematical correlations can be neglected or simplified without impacting the test decision is shown in a rigorous way, paving the way for a simplification based on the intensity model.
Keywords
- 3D point clouds, B-spline surface approximation, Bootstrap, Deformation analysis, Intensity model, Laser tracker, Mathematical correlation, Terrestrial laser scanner, Test statistics
ASJC Scopus subject areas
- Chemistry(all)
- Analytical Chemistry
- Biochemistry, Genetics and Molecular Biology(all)
- Biochemistry
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Instrumentation
- Engineering(all)
- Electrical and Electronic Engineering
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In: Sensors, Vol. 19, No. 17, 3640, 01.09.2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - How Significant Are Differences Obtained by Neglecting Correlations When Testing for Deformation: A Real Case Study Using Bootstrapping with Terrestrial Laser Scanner Observations Approximated by B-Spline Surfaces
AU - Kermarrec, Gaël
AU - Paffenholz, Jens André
AU - Alkhatib, Hamza
N1 - Funding information: The publication of this article was funded by the Open Access Fund of the Leibniz Universität Hannover.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - B-spline surfaces possess attractive properties such as a high degree of continuity or the local support of their basis functions. One of the major applications of B-spline surfaces in engineering geodesy is the least-square (LS) fitting of surfaces from, e.g., 3D point clouds obtained from terrestrial laser scanners (TLS). Such mathematical approximations allow one to test rigorously with a given significance level the deformation magnitude between point clouds taken at different epochs. Indeed, statistical tests cannot be applied when point clouds are processed in commonly used software such as CloudCompare, which restrict the analysis of deformation to simple deformation maps based on distance computation. For a trustworthy test decision and a resulting risk management, the stochastic model of the underlying observations needs, however, to be optimally specified. Since B-spline surface approximations necessitate Cartesian coordinates of the TLS observations, the diagonal variance covariance matrix (VCM) of the raw TLS measurements has to be transformed by means of the error propagation law. Unfortunately, this procedure induces mathematical correlations, which can strongly affect the chosen test statistics to analyse deformation, if neglected. This may lead potentially to rejecting wrongly the null hypothesis of no-deformation, with risky and expensive consequences. In this contribution, we propose to investigate the impact of mathematical correlations on test statistics, using real TLS observations from a bridge under load. As besides TLS, a highly precise laser tracker (LT) was used, the significance of the difference of the test statistics when the stochastic model is misspecified can be assessed. However, the underlying test distribution is hardly tractable so that only an adapted bootstrapping allows the computation of trustworthy p-values. Consecutively, the extent to which heteroscedasticity and mathematical correlations can be neglected or simplified without impacting the test decision is shown in a rigorous way, paving the way for a simplification based on the intensity model.
AB - B-spline surfaces possess attractive properties such as a high degree of continuity or the local support of their basis functions. One of the major applications of B-spline surfaces in engineering geodesy is the least-square (LS) fitting of surfaces from, e.g., 3D point clouds obtained from terrestrial laser scanners (TLS). Such mathematical approximations allow one to test rigorously with a given significance level the deformation magnitude between point clouds taken at different epochs. Indeed, statistical tests cannot be applied when point clouds are processed in commonly used software such as CloudCompare, which restrict the analysis of deformation to simple deformation maps based on distance computation. For a trustworthy test decision and a resulting risk management, the stochastic model of the underlying observations needs, however, to be optimally specified. Since B-spline surface approximations necessitate Cartesian coordinates of the TLS observations, the diagonal variance covariance matrix (VCM) of the raw TLS measurements has to be transformed by means of the error propagation law. Unfortunately, this procedure induces mathematical correlations, which can strongly affect the chosen test statistics to analyse deformation, if neglected. This may lead potentially to rejecting wrongly the null hypothesis of no-deformation, with risky and expensive consequences. In this contribution, we propose to investigate the impact of mathematical correlations on test statistics, using real TLS observations from a bridge under load. As besides TLS, a highly precise laser tracker (LT) was used, the significance of the difference of the test statistics when the stochastic model is misspecified can be assessed. However, the underlying test distribution is hardly tractable so that only an adapted bootstrapping allows the computation of trustworthy p-values. Consecutively, the extent to which heteroscedasticity and mathematical correlations can be neglected or simplified without impacting the test decision is shown in a rigorous way, paving the way for a simplification based on the intensity model.
KW - 3D point clouds
KW - B-spline surface approximation
KW - Bootstrap
KW - Deformation analysis
KW - Intensity model
KW - Laser tracker
KW - Mathematical correlation
KW - Terrestrial laser scanner
KW - Test statistics
UR - http://www.scopus.com/inward/record.url?scp=85071515807&partnerID=8YFLogxK
U2 - 10.3390/s19173640
DO - 10.3390/s19173640
M3 - Article
C2 - 31438564
AN - SCOPUS:85071515807
VL - 19
JO - Sensors
JF - Sensors
SN - 1424-8220
IS - 17
M1 - 3640
ER -