TY - JOUR

T1 - On the Sensitivity of the Parameters of the Intensity-Based Stochastic Model for Terrestrial Laser Scanner

T2 - Case Study: B-Spline Approximation

AU - Kermarrec, Gaël

AU - Alkhatib, Hamza

AU - Neumann, Ingo

N1 - Funding Information: Funding: The publication of this article was funded by the Open Access fund of Leibniz Universität Hannover.

PY - 2018/9

Y1 - 2018/9

N2 - 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.

AB - 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.

KW - B-spline approximation

KW - Control point

KW - Intensity-based model

KW - Stochastic model

KW - Terrestrial laser scanner

KW - intensity-based model

KW - terrestrial laser scanner

KW - control point

KW - stochastic model

UR - http://www.scopus.com/inward/record.url?scp=85053079516&partnerID=8YFLogxK

U2 - 10.3390/s18092964

DO - 10.3390/s18092964

M3 - Article

C2 - 30189695

AN - SCOPUS:85053079516

VL - 18

JO - Sensors (Switzerland)

JF - Sensors (Switzerland)

SN - 1424-8220

IS - 9

M1 - 2964

ER -