Geometric parameters extraction of sphere, cylinder and cone

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.