Analytical and numerical investigations on the accuracy and robustness of geometric features extracted from 3D point cloud data

In photogrammetry, remote sensing, computer vision and robotics, a topic of major interest is represented by the automatic analysis of 3D point cloud data. This task often relies on the use of geometric features amongst which particularly the ones derived from the eigenvalues of the 3D structure tensor
(e.g. the three dimensionality features of linearity, planarity and sphericity) have proven to be descriptive and are therefore commonly involved for classification tasks. Although these geometric features are meanwhile considered as standard, very little attention has been paid to their accuracy and robustness.
In this paper, we hence focus on the influence of discretization and noise on the most commonly used geometric features. More specifically, we investigate the accuracy and robustness of the eigenvalues of the 3D structure tensor and also of the features derived from these eigenvalues. Thereby, we provide both analytical and numerical considerations which clearly reveal that certain features are more susceptible to discretization and noise whereas others are more robust.