Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling †
Abstract
:1. Introduction
2. Mathematical Background
2.1. Least-Squares
2.2. Surface Approximation Using T-Splines
2.2.1. General Principle of Surface Approximation
2.2.2. T-Splines Surface
2.2.3. Residual Analysis
3. Data Analysis
3.1. Simulated Point Clouds
3.1.1. Reference Point Cloud
3.1.2. Noise Generation
- to the X- and Y-components: a Gaussian noise with a standard deviation of 1 × 10−4 m–generated with the Matlab function randn;
- to the Z-component: an fGn or a combination of fGn and WN. We use the MATLAB function ffgn [19].
3.1.3. Surface Approximation
3.1.4. Residual Analysis
3.2. Real Data Set
3.2.1. Using a 3D Printer
3.2.2. Scanning
3.2.3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Slope/std [m] | Case 1 | Case 2 |
---|---|---|
Original noise | 0.9/1 × 10−3 | 0.88/1 × 10−3 |
Residuals | 0.89/0.95 × 10−4 | 0.86/0.91 × 10−4 |
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Kermarrec, G.; Schild, N.; Hartmann, J. Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling. Eng. Proc. 2021, 5, 59. https://doi.org/10.3390/engproc2021005059
Kermarrec G, Schild N, Hartmann J. Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling. Engineering Proceedings. 2021; 5(1):59. https://doi.org/10.3390/engproc2021005059
Chicago/Turabian StyleKermarrec, Gaël, Niklas Schild, and Jan Hartmann. 2021. "Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling" Engineering Proceedings 5, no. 1: 59. https://doi.org/10.3390/engproc2021005059