Visual Analysis of Point Cloud Neighborhoods via Multi-Scale Geometric Measures

Abstract

Point sets are a widely used spatial data structure in computational and observational domains, e.g. in physics particle simulations, computer graphics or remote sensing. Algorithms typically operate in local neighborhoods of point sets, for computing physical states, surface reconstructions, etc. We present a visualization technique based on multi-scale geometric features of such point clouds. We explore properties of different choices on the underlying weighted co-variance neighborhood descriptor, illustrated on different point set geometries and for varying noise levels. The impact of different weighting functions and tensor centroids, as well as point set features and noise levels becomes visible in the rotation-invariant feature images. We compare to a curvature based scale space visualization method and, finally, show how features in real-world LiDAR data can be inspected by images created with our approach in an interactive tool. In contrast to the curvature based approach, with our method line structures are highlighted over growing scales, with clear border regions to planar or spherical geometric structures.