L. Quan et F. Veillon, JOINT INVARIANTS OF A TRIPLET OF COPLANAR CONICS - STABILITY AND DISCRIMINATING POWER FOR OBJECT RECOGNITION, Computer vision and image understanding, 70(1), 1998, pp. 111-119
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.