Image Analysis By Discrete Orthogonal Moments

A new discrete orthogonal moment—Hahn moment based on the discrete classical Hahn polynomials is introduced. In order to ensure numerical stability, the Hahn polynomials are normalized, thus creating a set of weighted orthonormal Hahn polynomials, to define the so-called Hahn moments. The recurrence relations of the Hahn polynomials are derived. These relations, combining with the symmetry property, are used to evaluate the Hahn polynomial values. Such a strategy permits us to reduce the accumulation of numerical errors in the computation of high order polynomial values so that the original image can be accurately reconstructed.1 The image reconstruction ability using Hahn moment is compared with that using Tchebichef moment, and the experimental results demonstrate the effectiveness of the proposed method.A novel set of discrete orthogonal moments based on these polynomials which are built on the nonuniform lattices are introduced--Racah polynomials and Dual Hahn polynomials. In order to ensure numerical stability, the Racah polynomials are normalized, thus creating a set of weighted orthonormal Racah polynomials, to define the so-called Racah moments--the same to Dual Hahn polynomials. The recurrence relations of the both polynomials are derived. And the experiments about the reconstruction of the original images have been done. The experimental results demonstrate the effectiveness of the proposed method. At last the series of discrete orthogonal polynomials used to be the base sets of the discrete orthogonal moment have been discussed.