Covariance Based Differential Geometry Segmentation Techniques for Surface Representation Using Vector Field Framework

Abstract

In this paper, the concepts of differential geometry traditionally applied to the segmentation of range maps is revisited in the context of implicit surface representation of unorganized point clouds. The paper shows that it is possible to combine covariance-based differential geometry and implicit surface representation methods to perform the segmentation of an unorganized point cloud (and not just a range map) into seven surface types. The acquisition of the point cloud data is achieved with handheld scanners used in metrology applications. The advantages of combining covariance-based differential geometry and implicit surface representation are that the segmentation does not require surface fitting nor does it require that all points be processed, thus reducing computational complexity. The segmentation approach is validated on synthetic data as well as point clouds borrowed from common datasets. Scans obtained from commercial metrologic handheld 3D sensors are also used for validation. The paper first presents the workflow commonly used for 3D scanning using handheld 3D scanners in the context of metrology. This is followed by a discussion on the different methods that are used for surface representation including the vector field, the implicit representation method exploited in this paper. Basic concepts of classical differential geometry for surface segmentation are presented. This is followed by the presentation of covariance-based differential geometry. The concepts of handheld 3D scanning, covariance-based differential geometry and implicit surface representation are then combined to achieve efficient segmentation of a point cloud into seven different surface types. Experimental results obtained on synthetic 3D data as well as real data demonstrate the segmentation approach.