Studies on deformation analysis of TLS point clouds using B-splines – A control point based approach (Part I)

Abstract

Abstract This paper presents a method to overlay laser scan data from at least two different epochs using B-splines. Here, an approach is described in which the laser scan points are directly taken as control points for the B-spline curves or surfaces. In combination with a second part of the publication, the presented technique should be able to detect small deformations compared to the object size based on the curvature parameter. However, the method does not aim at detecting object movements, rotations or translations. Before the epoch-wise laser scan acquisition of an object, a sampling rate adjustment according to the object properties has to be performed. By means of a defining algorithm, control polygons with different numbers of points are defined from the point clouds, whose points are available in scanning order, however not in a uniform grid structure, but an irregular distributed form. As a basis for a bidirectional grid structure of tensor product B-spline surfaces a knot insertion algorithm (Boehm’s algorithm) is to be applied. While the previous process steps are implemented for both B-spline curves and surfaces, the following process steps are only available for B-spline curves so far. In a correlation analysis where the ranks of the curvatures of the B-spline curve points are used, one shift position of the curve can be generated in both epochs. This forms the foundation for the determination of identical curve points, which are iteratively improved to provide the basis for a Helmert transformation to epoch 0. The rotation and translation parameters calculated with the Helmert transformation are only used to map the B-spline curve of an epoch n to epoch 0. A determination of an object rotation is not possible, because the laser scans are not georeferenced. The transformation applied allows the representation of coordinate differences between the laser scan data of different epochs. An implementation of the process steps is available for B-spline curves so far and has to be completed for B-spline surfaces. The finalization of the implementation for B-spline surfaces will be done in a second part of the publication. The calculation process of the standard deviations of the laser scan data up to the standard deviations of the curve and surface points for detecting deformations by means of a significance test will also be listed in more detail in the second part of the publication.