STUBA_TLS: improving Statistical Test for deformation Using B-spline Approximation from Terrestrial Laser Scanner observations

• Applicant: Dr. Gael Kermarrec
• Subject Area: Geodesy, Photogrammetry, Remote Sensing, Geoinformatics, Cartography
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 436402386

An accurate and realistic knowledge of the stochastic properties of Terrestrial Laser Scanner (TLS) errors is of main importance to avoid inappropriate test decisions when analysing deformation, as well as to specify the precision of the TLS point clouds. However, stochastic models are often obtained from the residuals of least squares (LS) adjustments for ideal objects, scanned under optimum conditions. Consequently, the derived models may not be optimal for real case applications, where breaklines or object inhomogeneities may occur. It follows that the conclusions of statistical tests for deformation are less trustworthy: risks may be underestimated with unpredictable and expensive consequences. When correctly interpreted, LS residuals from B-spline approximation of TLS point clouds provide the needed information about the stochastic properties of TLS range and angle errors “in situ”, i.e. without having to be dependent from any calibration. To that aim, a filtering of the LS residuals from any functional misspecifications that may occur due to inaccurate B spline parameters, such as the number of control points, or the knot vector, is necessary. The second-generation wavelets provide an ideal basis to filter these specific residuals, as they come from unequispaced and scattered TLS observations for which such wavelets are optimally designed. This innovative method opens the door for the estimation and analysis of the parameters from a general variance and correlation model. Thus, the development of an innovative and trustworthy procedure to test for deformation between B-spline approximations of TLS point clouds is made possible, using the derived stochastic information. The new testing strategy include the refinement of the concept of distance, the study of the impact of stochastic misspecification with bootstrapping, up to the simplification of fully populated variance covariance matrices in easy-to-handle diagonal matrices.

• DFG Programme: Research Grants
• International Connection: Belgium
• Cooperation Partner: Professor Dr. Maarten Jansen