A General Method to Determine Invariants

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known: Hu's moment invariants are invariant to shifts, to changes of scale, and to rotations [Hu62]; Burkhardt's Fourier descriptors to shifts, to changes of scale and to rotations [Bu79]; Arbter's Fourier descriptors to a ne transformations [Ar90]; Wang's invariant moments to a ne transformations [Wa77]; the two well-known 5-points invariants to projective transformations [MZ92], etc. This paper shows that all these results, which were obtained independently and by di erent methods, derive from a common basic principle that allows the determination of new invariants as well.