Details
| Original language | English |
|---|---|
| Pages (from-to) | 495-513 |
| Number of pages | 19 |
| Journal | Acta Geodaetica et Geophysica |
| Volume | 55 |
| Issue number | 3 |
| Early online date | 6 Jul 2020 |
| Publication status | Published - Sept 2020 |
Abstract
The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terrestrial laser scanners, allowing the setting of a specific congruence test based on the B-spline surfaces. Such tests are known to be strongly influenced by the underlying stochastic model chosen for the observation errors. The latter has to be correctly specified, which includes accounting for heteroscedasticity and correlations. In this contribution, we justify and make use of a parametric correlation model called the Matérn model to approximate the variance covariance matrix (VCM) of the residuals by performing their empirical mode decomposition. The VCM obtained is integrated into the computation of the congruence test statistics for a more trustworthy test decision. Using a real case study, we estimate the distribution of the test statistics with a bootstrap approach, where no parametric assumptions are made about the underlying population that generated the random sample. This procedure allows us to assess the impact of neglecting correlations on the critical value of the congruence test, highlighting their importance.
Keywords
- Bootstrap, Congruency test, Correlation, Deformation, Matérn covariance function, Statistical test, Terrestrial laser scanner, Variance component estimation
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Geology
- Earth and Planetary Sciences(all)
- Geophysics
- Engineering(all)
- Building and Construction
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In: Acta Geodaetica et Geophysica, Vol. 55, No. 3, 09.2020, p. 495-513.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the impact of correlations on the congruence test: a bootstrap approach
T2 - Case study: B-spline surface fitting from TLS observations
AU - Kermarrec , Gaël
AU - Kargoll, Boris
AU - Alkhatib, Hamza
PY - 2020/9
Y1 - 2020/9
N2 - The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terrestrial laser scanners, allowing the setting of a specific congruence test based on the B-spline surfaces. Such tests are known to be strongly influenced by the underlying stochastic model chosen for the observation errors. The latter has to be correctly specified, which includes accounting for heteroscedasticity and correlations. In this contribution, we justify and make use of a parametric correlation model called the Matérn model to approximate the variance covariance matrix (VCM) of the residuals by performing their empirical mode decomposition. The VCM obtained is integrated into the computation of the congruence test statistics for a more trustworthy test decision. Using a real case study, we estimate the distribution of the test statistics with a bootstrap approach, where no parametric assumptions are made about the underlying population that generated the random sample. This procedure allows us to assess the impact of neglecting correlations on the critical value of the congruence test, highlighting their importance.
AB - The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terrestrial laser scanners, allowing the setting of a specific congruence test based on the B-spline surfaces. Such tests are known to be strongly influenced by the underlying stochastic model chosen for the observation errors. The latter has to be correctly specified, which includes accounting for heteroscedasticity and correlations. In this contribution, we justify and make use of a parametric correlation model called the Matérn model to approximate the variance covariance matrix (VCM) of the residuals by performing their empirical mode decomposition. The VCM obtained is integrated into the computation of the congruence test statistics for a more trustworthy test decision. Using a real case study, we estimate the distribution of the test statistics with a bootstrap approach, where no parametric assumptions are made about the underlying population that generated the random sample. This procedure allows us to assess the impact of neglecting correlations on the critical value of the congruence test, highlighting their importance.
KW - Bootstrap
KW - Congruency test
KW - Correlation
KW - Deformation
KW - Matérn covariance function
KW - Statistical test
KW - Terrestrial laser scanner
KW - Variance component estimation
UR - http://www.scopus.com/inward/record.url?scp=85087618037&partnerID=8YFLogxK
U2 - 10.1007/s40328-020-00302-8
DO - 10.1007/s40328-020-00302-8
M3 - Article
VL - 55
SP - 495
EP - 513
JO - Acta Geodaetica et Geophysica
JF - Acta Geodaetica et Geophysica
SN - 2213-5812
IS - 3
ER -