3D Image Representation Using Separable Discrete Orthogonal Moments

This paper introduces a new sets of separable three-dimensional moments, called Racah-Tchebichef-Krawtchouk Moments (RTKM), Racah-Krawtchouk-Krawtchouk Moments (RKKM) and Racah-Racah-Krawtchouk Moments (RRKM), for the field of 3D image representation. First, we will provide the detailed mathematical framework of the proposed separable 3D moments. Second, we outline the main applications of the newly introduced moments. Where, the global feature extraction capability is evaluated by measuring reconstruction quality of 3D image, under noisy and noise-free conditions. While, the ability to extract local feature is also demonstrated by adjusting the polynomials parameters value according to the desired Region of Interest (ROI). The obtained results show that the proposed separable moments perform better than the classical moments in terms of image representation capability.