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Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observationsa??A Bridge Under Load
摘要： 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 Hausdor? 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 a?ected by measurement 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.
关键词： B-splines,Matérn covariance function,Hausdor? distance,surface modelling,terrestrial laser scanning,bootstrapping,deformation,averaged Hausdor? distance,correlations
更新于2025-09-23 15:19:57
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[Lecture Notes in Computer Science] Shape in Medical Imaging Volume 11167 (International Workshop, ShapeMI 2018, Held in Conjunction with MICCAI 2018, Granada, Spain, September 20, 2018, Proceedings) || Global Divergences Between Measures: From Hausdorff Distance to Optimal Transport
摘要： The data ?delity term is a key component of shape registration pipelines: computed at every step, its gradient is the vector ?eld that drives a deformed model towards its target. Unfortunately, most classical formulas are at most semi-local: their gradients saturate and stop being informative above some given distance, with appalling consequences on the robustness of shape analysis pipelines. In this paper, we build on recent theoretical advances on Sinkhorn entropies and divergences [6] to present a uni?ed view of three ?delities between measures that alleviate this problem: the Energy Distance from statistics; the (weighted) Hausdor? distance from computer graphics; the Wasserstein distance from Optimal Transport theory. The ε-Hausdor? and ε-Sinkhorn divergences are positive ?delities that interpolate between these three quantities, and we implement them through e?cient, freely available GPU routines. They should allow the shape analyst to handle large deformations without hassle.
关键词： Kernel,Optimal Transport,Energy Distance,Shape registration,Hausdor? distance,GPU
更新于2025-09-10 09:29:36