Geometric invariant of noncoplanar lines in a single view

Abstract

The importance of geometric invariants to many machine vision tasks, such as model-based recognition, has been recognized. A number of studies on geometric invariants in a single view concentrate on coplanar objects: coplanar points, coplanar lines, coplanar conics, etc. Therefore, it is essentially only to 2-D objects that we can apply methods using geometric invariants. This paper presents a study on geometric invariants of noncoplanar objects, i.e., 3-D objects. A new geometric invariant is derived from six lines on three planes in a single view. The condition under which the invariant is nonsingular is also described. In addition, we present some experimental results with real images and find that the values of the invariant over a number of viewpoints remain stable even for noisy images.