Akihiro SUGIMOTO
Projective Invariants of Noncoplanar Lines
Derived from a Single View
Abstract:The importance of projective invariants to many machine vision tasks, such as model-based recognition, has been emphasized because an object generically has its own value for an invariant. A number of recent studies on projective 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 methods using invariants. This paper presents a study on projective invariants of noncoplanar objects, that is. 3-D objects. Two new projective invariants are derived from noncoplanar lines in a single view: one from five lines on two planes and the other from six lines on three planes. The conditions under which they are nonsingular are also described. In addition, we present some experimental results with real images and we find that the values of the invariants over a number of viewpoints remain stable even for noisy images. Hence, we no longer need assume coplanar objects; we can directly treat 3-D objects to calculate invariants.
Key Words: projective invariants, noncoplanar lines, nonsingularity, 3-D object recognition.