On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation
For a trustworthy least-squares (LS) solution, a good description of the stochastic properties of the measurements is indispensable. For a terrestrial laser scanner (TLS), the range variance can be described by a power law function with respect to the intensity of the reflected signal. The power and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | Sensors |
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| Online Access: | http://www.mdpi.com/1424-8220/18/9/2964 |
| _version_ | 1811306834031542272 |
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| author | Gaël Kermarrec Hamza Alkhatib Ingo Neumann |
| author_facet | Gaël Kermarrec Hamza Alkhatib Ingo Neumann |
| author_sort | Gaël Kermarrec |
| collection | DOAJ |
| description | For a trustworthy least-squares (LS) solution, a good description of the stochastic properties of the measurements is indispensable. For a terrestrial laser scanner (TLS), the range variance can be described by a power law function with respect to the intensity of the reflected signal. The power and scaling factors depend on the laser scanner under consideration, and could be accurately determined by means of calibrations in 1d mode or residual analysis of LS adjustment. However, such procedures complicate significantly the use of empirical intensity models (IM). The extent to which a point-wise weighting is suitable when the derived variance covariance matrix (VCM) is further used in a LS adjustment remains moreover questionable. Thanks to closed loop simulations, where both the true geometry and stochastic model are under control, we investigate how variations of the parameters of the IM affect the results of a LS adjustment. As a case study, we consider the determination of the Cartesian coordinates of the control points (CP) from a B-splines curve. We show that a constant variance can be assessed to all the points of an object having homogeneous properties, without affecting the a posteriori variance factor or the loss of efficiency of the LS solution. The results from a real case scenario highlight that the conclusions of the simulations stay valid even for more challenging geometries. A procedure to determine the range variance is proposed to simplify the computation of the VCM. |
| first_indexed | 2024-04-13T08:51:48Z |
| format | Article |
| id | doaj.art-d0444dca9a8d4df394d1e5d178beafcb |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-13T08:51:48Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-d0444dca9a8d4df394d1e5d178beafcb2022-12-22T02:53:27ZengMDPI AGSensors1424-82202018-09-01189296410.3390/s18092964s18092964On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline ApproximationGaël Kermarrec0Hamza Alkhatib1Ingo Neumann2Geodetic Institute, Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, GermanyGeodetic Institute, Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, GermanyGeodetic Institute, Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, GermanyFor a trustworthy least-squares (LS) solution, a good description of the stochastic properties of the measurements is indispensable. For a terrestrial laser scanner (TLS), the range variance can be described by a power law function with respect to the intensity of the reflected signal. The power and scaling factors depend on the laser scanner under consideration, and could be accurately determined by means of calibrations in 1d mode or residual analysis of LS adjustment. However, such procedures complicate significantly the use of empirical intensity models (IM). The extent to which a point-wise weighting is suitable when the derived variance covariance matrix (VCM) is further used in a LS adjustment remains moreover questionable. Thanks to closed loop simulations, where both the true geometry and stochastic model are under control, we investigate how variations of the parameters of the IM affect the results of a LS adjustment. As a case study, we consider the determination of the Cartesian coordinates of the control points (CP) from a B-splines curve. We show that a constant variance can be assessed to all the points of an object having homogeneous properties, without affecting the a posteriori variance factor or the loss of efficiency of the LS solution. The results from a real case scenario highlight that the conclusions of the simulations stay valid even for more challenging geometries. A procedure to determine the range variance is proposed to simplify the computation of the VCM.http://www.mdpi.com/1424-8220/18/9/2964terrestrial laser scannerstochastic modelB-spline approximationcontrol pointintensity-based model |
| spellingShingle | Gaël Kermarrec Hamza Alkhatib Ingo Neumann On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation Sensors terrestrial laser scanner stochastic model B-spline approximation control point intensity-based model |
| title | On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation |
| title_full | On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation |
| title_fullStr | On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation |
| title_full_unstemmed | On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation |
| title_short | On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner. Case Study: B-Spline Approximation |
| title_sort | on the sensitivity of the parameters of the intensity based stochastic model for terrestrial laser scanner case study b spline approximation |
| topic | terrestrial laser scanner stochastic model B-spline approximation control point intensity-based model |
| url | http://www.mdpi.com/1424-8220/18/9/2964 |
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