Approximation of 3D Point Clouds by Means of B-Splines in Natural and Anthropogenic Object Monitoring

In this thesis, we present a method for surface approximation and monitoring of two different types of 3D point cloud data, namely natural and anthropogenic. The natural point cloud
data was obtained from an experimental setup in TU Clausthal, while the anthropogenic data was obtained from the Okertalsperre using a laser scanner.

For the natural point cloud data, we propose a method for approximating the surface of a curved object using B-spline curves. The method is evaluated by calculating the distance between the approximated surface and the original point cloud data using the M3C2 algorithm. The results show a mean absolute error of 1.7 mm for the height difference methodand 2.4 mm for the M3C2 distance calculating the B-spline points.

For the anthropogenic point cloud data, we use the open uniform knot vector to calculate the B-spline curves and present the results from blue to red in reference to the ground of the dam.
The approximated curves are compared to the data from the next monitoring of the Okertalsperre. We calculate the distance between the original point cloud and the approximated surface using two methods, height differencing and M3C2 distance calculation. The results show that the M3C2 distance ca lculation of the B-spline points is smoother than the height difference method, with a mean absolute error of 2.4 mm.

The proposed methods in this thesis provide accurate and efficient solutions for surface approximation and monitoring of natural and anthropogenic point cloud data, respectively. The results demonstrate the importance of utilizing appropriate methods and algorithms for analyzing 3D point cloud data and the potential for further applications in various fields.