Generalized dual Hahn moment invariants

In this work we introduce a generalized expression of the weighted dual Hahn moment invariants up to any order and for any value of their parameters. In order for the proposed invariants to be formed, the weighted dual Hahn moments (up to any order and for any value of their parameters) are expressed as a linear combination of geometric ones. For this reason a formula expressing the nth degree dual Hahn polynomial, for any value of its parameters, as a linear combination of monomials ( c r · x r ), is proved. In addition, a recurrent relation for the fast computation of the aforementioned monomials coefficients (cr) is also given. Moreover, normalization aspects of the generalized weighted dual Hahn moment invariants are discussed, while a modification of them is proposed in order to avoid their numerical instabilities. Finally, experimental results and classification scenarios, including datasets of natural scenes, evaluate the proposed methodology.