Recognition of one class of quadric surfaces from unstructured point cloud

Abstract

Critical elements of the state of the art three-dimensional (3D) point cloud processing software are the algorithms for retrieval of high level geometric primitives from raw data. This paper presents a method for recognition of a class of quadric surfaces, in particular for recognition of cylinders, elliptical cylinders, and ellipsoids from 3D point clouds. The method is based on direct least squares fitting of ellipsoids, and it exploits the closeness of scatter matrix to singular in the case when data are sampled for an approximate ellipsoid. This method belongs to the class of region growing methods, and the region is expanded using region growing strategy that is also proposed in this paper. Presented recognition procedure is suitable for segmentation of regions with G1 or higher continuality, and this is its advantage when compared to similar methods. Besides, recognition of quadric surfaces can be performed on unstructured, as well as on structured point clouds. The applicability of the method is illustrated and experimentally verified using two examples that contain G1 continuous surfaces from the considered class. The first example represents synthesized, and the second real-world scanned point cloud.