Least-squares-based fitting of paraboloids

摘要

A technique for reconstructing a class of quadric surfaces from 3D data is presented. The technique is driven by a linear least-squares-based fitting mechanism. Previously, such fitting was restricted to recovery of central quadrics; here, extension of that basic mechanism to allow recovery of one commonly-occurring class of non-central quadric, the elliptic paraboloids, is described. The extension uses an indirect solution approach that involves introducing a variable to the basic mechanism that is a function of a quadric surface invariant. Results from fitting real and synthetic data are also exhibited.