JOINT INVARIANTS OF A TRIPLET OF COPLANAR CONICS - STABILITY AND DISCRIMINATING POWER FOR OBJECT RECOGNITION

Joint invariants of a pair of coplanar conics have played a central ro le in the initial work on the application of invariants to object reco gnition. In this paper, we are concerned with the invariants of a trip let of coplanar conics. It will be shown that, in addition to the inva riants associated to all pairs of three conics, there exists one new i nvariant which is only associated to the triplet of conics. This new i nvariant of the three conics can therefore be used to discriminate tri plets of conics which might be pair-wise similar. All joint invariants of a triplet of coplanar conics will first be derived based on the in variant algebra of a net of ternary quadratic forms. Then, experimenta tions for discriminating power, accuracy, and stability of joint invar iants 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. (C) 1998 Academic P ress.