The method of normalization to determine invariants

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known, which have been obtained either by normalization [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] or by other methods [11], [12], [13], [14], [15], [16]. This paper shows that the method of normalization is much more general and allows to derive a lot of sets of invariants from the second list as well. To this end, the normalization method is generalized and is presented in such a way that it is easy to apply, thus unifying and simplifying the determination of invariants. Furthermore, this paper discusses the advantages and disadvantages of the invariants obtained by normalization. Their main advantage is that the normalization process provides us with a standard position of the object. Because of the generality of the method, also new invariants are obtained such as normalized moments more stable than known ones, Legendre descriptors and Zernike descriptors to affine transformations, two-dimensional Fourier descriptors and affine moment invariants obtained by combining Hu's moment invariants and normalized moments.