Refined translation and scale Legendre moment invariants

Orthogonal Legendre moments are used in several pattern recognition and image processing applications. Translation and scale Legendre moment invariants were expressed as a combination of the approximate original Legendre moments. The shifted and scaled Legendre polynomials were expressed in terms of the original Legendre polynomials according to complicated and time-consuming algebraic relations. In this paper, refined translation-scale Legendre moment invariants are obtained through the exact computation of original Legendre moments which completely remove approximation. Fast straightforward computation of central Legendre moments significantly reduces the computational time. According to the tremendous reduction of the computational complexity, the refined set of Legendre invariants is suitable for large size images. The performance of descriptors is evaluated by using a set of standard images.