GEOMETRIC PARAMETERS EXTRACTION

OF SPHERE, CYLINDER AND CONE

Liu Yuanpeng  Zhang Dinghua  Ao Bo  Zhang Lining

(Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Northwestern Polytechnical University, Xi’an 710072)

Abstract: Extracting geometric parameters of spheres, cylinders and cones in space has extensive engineering applications practically, such as reverse engineering and object recognition. A new approach is presented to solve this kind of problems based on the L-BFGS-B algorithm, where L-BFGS-B is a limited memory algorithm for solving large-scale nonlinear optimization problems subjected to simple bound-constrained or unconstrained on the variables. The method aims to discuss the geometric parameters extraction of the quadric surfaces under the bound-constrained or unconstrained, by taking the mean- squared geometric distance between a set of points and quadric surfaces as objective function. For the objective function of a cylinder or cone, its axis direction vectors are expressed in terms of spherical coordinates. This can make its objective function into a multi-variables, non-linear and bound-constrained optimization problem. Finally, the L-BFGS-B algorithm is used to iteratively minimize the objective function. Experimental results show this method is effectively and easy to use for the geometric parameters extraction of spheres, cylinders and cones.

Key words: Sphere  Cylinder  Cone  Geometric parameters  L-BFGS-B algorithm  Bound-constrained

CLC No: TP391

国家自然科学基金资助项目(50375126). Received 20041117, received in revised form 20050130