Akihiro SUGIMOTO
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 since an object generically has its own value for an invariant.
A number of recent studies on geometric invariants in a single view concentrate on coplanar objects: coplanar points, coplanar lines, coplanar points and lines, coplanar conics, etc.
Therefore, it is essentially only to 2-D objects that we can apply a method 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 distribution of the six lines is clarified and 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. We can apply a method using geometric invariants to 3-D objects as well.
Key Words: geometric invariant, noncoplanar lines, nonsingularity, 3-D object recognition.