A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds

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The fitting of a plane to data points is essential to the geosciences. However, it is recognized that the reliability of these best fit planes depends upon the point set distribution and geometry, evaluated in terms of the eigen-based parameters derived from the moment of inertia analysis. Despite i...

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Detalles Bibliográficos
Autores principales: Gallo, L.C., Cristallini, E.O., Svarc, M.
Formato: JOUR
Materias:
best fit plane
bootstrap statistics
moment of inertia analysis
Monte Carlo simulation
orientation of structural heterogeneities
bootstrapping
inertia
Monte Carlo analysis
precision
simulation
threshold
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_21699313_v123_n11_p10,297_Gallo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_21699313_v123_n11_p10,297_Gallo
record_format dspace
spelling todo:paper_21699313_v123_n11_p10,297_Gallo2023-10-03T16:39:58Z A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds Gallo, L.C. Cristallini, E.O. Svarc, M. best fit plane bootstrap statistics moment of inertia analysis Monte Carlo simulation orientation of structural heterogeneities bootstrapping inertia Monte Carlo analysis precision simulation threshold The fitting of a plane to data points is essential to the geosciences. However, it is recognized that the reliability of these best fit planes depends upon the point set distribution and geometry, evaluated in terms of the eigen-based parameters derived from the moment of inertia analysis. Despite its significance, few studies have addressed the uncertainties of the analysis, which can adversely affect the reproduction of results one of the cornerstones of scientific endeavor. Aiming to contribute toward the neglected issue of the moment of inertia precision, we have developed a bootstrap resampling scheme to empirically discover the distribution of uncertainties in the orientation of best fit planes. Dispersion of the bootstrapped normal vectors to the best fit plane is regarded as a measure of precision, evaluated with the maximum angular distance from the optimal solution. This rationale was tested using Monte Carlo-generated samples covering a comprehensive range of shape parameters to assess the dependence between eigen parameters and their inherent bias. Our results show that the oblateness of the point cloud is a robust parameter to assess the reliability of the best fit plane. Given this, the method was then applied to a publicly available lidar data set. We argue that georeferenced point clouds with an oblateness parameter greater than 3 and 1.5 may be placed at 95% confidence levels of 5° and 10°, respectively. We propose using these values as thresholds to obtain robust best fit planes, guaranteeing reproducible results for scientific research. ©2018. American Geophysical Union. All Rights Reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_21699313_v123_n11_p10,297_Gallo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic best fit plane
bootstrap statistics
moment of inertia analysis
Monte Carlo simulation
orientation of structural heterogeneities
bootstrapping
inertia
Monte Carlo analysis
precision
simulation
threshold
spellingShingle best fit plane
bootstrap statistics
moment of inertia analysis
Monte Carlo simulation
orientation of structural heterogeneities
bootstrapping
inertia
Monte Carlo analysis
precision
simulation
threshold
Gallo, L.C.
Cristallini, E.O.
Svarc, M.
A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds
topic_facet best fit plane
bootstrap statistics
moment of inertia analysis
Monte Carlo simulation
orientation of structural heterogeneities
bootstrapping
inertia
Monte Carlo analysis
precision
simulation
threshold
description The fitting of a plane to data points is essential to the geosciences. However, it is recognized that the reliability of these best fit planes depends upon the point set distribution and geometry, evaluated in terms of the eigen-based parameters derived from the moment of inertia analysis. Despite its significance, few studies have addressed the uncertainties of the analysis, which can adversely affect the reproduction of results one of the cornerstones of scientific endeavor. Aiming to contribute toward the neglected issue of the moment of inertia precision, we have developed a bootstrap resampling scheme to empirically discover the distribution of uncertainties in the orientation of best fit planes. Dispersion of the bootstrapped normal vectors to the best fit plane is regarded as a measure of precision, evaluated with the maximum angular distance from the optimal solution. This rationale was tested using Monte Carlo-generated samples covering a comprehensive range of shape parameters to assess the dependence between eigen parameters and their inherent bias. Our results show that the oblateness of the point cloud is a robust parameter to assess the reliability of the best fit plane. Given this, the method was then applied to a publicly available lidar data set. We argue that georeferenced point clouds with an oblateness parameter greater than 3 and 1.5 may be placed at 95% confidence levels of 5° and 10°, respectively. We propose using these values as thresholds to obtain robust best fit planes, guaranteeing reproducible results for scientific research. ©2018. American Geophysical Union. All Rights Reserved.
format JOUR
author Gallo, L.C.
Cristallini, E.O.
Svarc, M.
author_facet Gallo, L.C.
Cristallini, E.O.
Svarc, M.
author_sort Gallo, L.C.
title A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds
title_short A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds
title_full A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds
title_fullStr A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds
title_full_unstemmed A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds
title_sort nonparametric approach for assessing precision in georeferenced point clouds best fit planes: toward more reliable thresholds
url http://hdl.handle.net/20.500.12110/paper_21699313_v123_n11_p10,297_Gallo
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