Joint Invariants of a Triplet of Coplanar Conics: Stability and Discriminating Power for Object Recognition

摘要

Joint invariants of a pair of coplanar conics have played a central role in the initial work on the application of invariants to object recognition. In this paper, we are concerned with the invariants of a triplet of coplanar conics. It will be shown that, in addition to the invariants associated to all pairs of three conics, there exists one new invariant which is only associated to the triplet of conics. This new invariant of the three conics can therefore be used to discriminate triplets of conics which might be pair-wise similar. All joint invariants of a triplet of coplanar conics will first be derived based on the invariant algebra of a net of ternary quadratic forms. Then, experimentations for discriminating power, accuracy, and stability of joint invariants are conducted both for simulated and real images. Finally, it is also shown that the method developed for a triplet of coplanar conics can be extended to any number of coplanar conics.