Abstract
The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces.
Highlights
Computing the distance between two objects is an important task in domains such as shape registration [1], shape approximation and simplification [2] or pattern recognition [3]
Accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the Hausdorff distance (HD) and AHD between two raw point clouds (PC) or between their mathematical approximations regarding reference values
When a mathematical approximation of the PC is performed, the best stochastic model should be used in the LS adjustment to assess a trustworthy distance
Summary
Computing the distance between two objects is an important task in domains such as shape registration [1], shape approximation and simplification [2] or pattern recognition [3]. In the field of engineering geodesy, the distance between objects recorded at different times allows the estimation of deformation magnitudes [4] and their associated risks (see, e.g., Reference [5] for bridges, Reference [6] for dams and Reference [7] for risk management). The raw point clouds (PC) from a static or kinematic terrestrial laser scanner (TLS) can be analyzed in commercial software. Provided that a registration of the PC is performed (e.g., Reference [8]), maps of deformation magnitudes are formed by building the difference between the PC recorded at two different epochs and allows visualization of the corresponding strength of deformation.
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