Segmentierung und Approximation großer Punktwolken

In my PhD thesis Segmentation and Approximation of large point clouds I created an new approach for the automation of the point cloud segmentation process. Surface reconstruction or Reverse Engineering describes the process to get a mathematical representation of a measured object ( based on B-Spline surfaces ) from an unorganized set of 3D points ( point cloud ). This process is nowadays interactively done in Computer Aided Design ( CAD ) Systems and will take a long time of interactive work for the correct selection of a net of curves ( Segmentation ) where the surface curvature changes. Therefore in this thesis I developed new algorithms and methods for an automatic segmentation of point clouds based on geometrically criteria. The user has to determine some intuitive thresholds and the algorithm creates automatically regions with similar curvature behaviour. The boundary lines of this regions are called feature lines and may be reused in CAD-systems for the creation of approximation surfaces. This methods leads to better surface approximation quality and strongly accelerates the surface reconstruction process. The first step of the automatic surface reconstruction of an unorganized point cloud is the piecewise linear approximation of the points with a set of connected triangles. Therefore I developed two new Triangulation algorithm which computes automatically an triangulation of arbitrary 3D point clouds ( scattered data ) in a very short time. Theses triangulations may be treated as input for post-processing steps like Rapid Prototyping and the direct calculation of tool pathes. This triangulation may also be used as input for applications in the Virtual Reality area. For these three applications the surface reconstruction is finished with the complete triangulation of the point cloud. Moreover I use the neighbouring information between the points which is implicit given by the triangulation to caculate an effective and robust estimation of the surface curvature on the measured point cloud. At first there were filters applied for finding points with measurement errors and projecting these points a step in the best fit plane to the points from all neighboured triangles ( fairing the point cloud). Afterwards we have to inspect the triangulated cloud whether it contains points which may be removed from the triangulation without loosing accuracy ( data reduction ). In flat areas of the object there are less triangles needed for an accurate surface description as in curved areas of the object or at sharp corners. These, for the surface structure unnecessary points, will be removed from the triangulation. The last step is an attempt to find automatically edges and natural segment boundaries ( feature lines ) on the triangulation. The feature lines are curves on the triangulation where the curvature behaviour of the underlying surfaces changes. For the determination of this feature line curves I expanded an Region Growing algorithm for 2D-Image segmentation to work on the segmentation of 3D triangulated point clouds. With these feature lines and some user defined continuity constrains between the neighboured regions of the feature line it is possible to make another automatic step for the surface reconstruction process of the point cloud. Examples for the surface reconstruction workflow with the developed methods are shown on measured point clouds from car models.