Joint invariant signatures (Q5944038)

The power of the moving frame method established in [\textit{M. Fels} and \textit{P. J. Olver}, Acta Appl. Math. 55, No. 2, 127-208 (1999; Zbl 0937.53013)], is used here for classifying joint invariants and joint differential invariants of transformation groups. Equivalence and symmetry properties of submanifolds are completley determined by their joint signatures which are parametrized by a suitable collection of joint invariants. Several interesting examples are given. Application to object recognition problems in computer vision and the design of invariant numerical approximations are provided.