Identification and Characterization of Regular Surfaces from Unorganized Points by Normal Sensitivity Analysis

Abstract

In this paper, the concept of free motion subspace is introduced and utilized to characterize the special kinematic properties of regular surfaces, including planes, natural quadrics, and regular swept surfaces. Based on the concept, a general approach is developed to automatically identify the surface type and calculate the associated geometric parameters of an unknown surface from unorganized measurement points. In the approach, a normal sensitivity matrix, that characterizes the normal perturbation of surface points under differential motions, is derived. With the normal sensitivity matrix, it is shown that the free motion subspace of a surface can be determined through a regular eigen analysis. From the identified free motion subspace, the surface type of a regular surface can be determined and its geometric parameters can be simultaneously computed. An algorithm that identifies the free motion subspace of an unknown surface from its unorganized sample points has been implemented. Experiments are carried out to investigate the robustness and efficiency of the developed algorithm. The developed algorithm can be used to solve various problems including geometric primitive classification and parameter estimation, regular swept surface reconstruction, geometric constraint recognition and multi-view data registration. Integrated with state-of-art segmentation techniques, the proposed method can be used for object recognition, robot vision, and reverse engineering.