From tensor-product to truncated hierarchical B-splines: Enhancing spatial resolution in space-continuous deformation analysis based on 3D point clouds

Abstract. The quasi-continuous capturing of our environment by terrestrial laser scanning (TLS) in form of 3D point clouds provides the basis for numerous spatial analyses, including space-continuous deformation analysis. In times of aging infrastructure and climate change-induced, cumulative mass movements, statistically-sound methods for determining areal deformations are becoming increasingly important. However, the lack of reproducibility of absolute point positions between consecutive scans and the presence of measurement noise demand approaches that retrieve credible comparison statements. The representation of point clouds by geometric surfaces supports noise reduction and serves as basis for successive analysis. Tensor-product B-spline surfaces have proven to be particularly versatile geometric representations to derive spatially consistent deformation estimates. This paper extends this concept by investigating the use of truncated hierarchical B-splines for statistically sound deformation analysis. We show that deformation is detectable when partition of unity is preserved through truncation. In a simulated environment, significant deformations between two point clouds were successfully detected. Results indicate that coarse surface representations lead to type-1 errors and underestimated deformation magnitudes, whereas more refined surface representations yield consistent deformation estimates, providing a potential termination criterion for adaptive model refinement.