Generic Orthogonal Moments and Applications

We present a detailed analysis of the Jacobi-Fourier moments and their applications in digital image processing. In order to reach numerical stability during the computation of the Jacobi radial polynomials a recursive approach is described. Also, some discussions are done about the best values of the parameters α and β in terms of its performance. Moreover, the digital image applications studied here are divided in low or high orders n of the polynomials. Typically, the pattern recognition applications are based in low order polynomials whilst image reconstruction can be achieved by using high order polynomials. On the other hand, the polar pixel approach is taken into account, in order to increase the numerical accuracy in the calculation of the moments, also some ad hoc cases using this polar geometry are studied. Experiments and results are presented.