New 3D Fractional-Order Zernike Moments for Shape Analysis

This paper introduces the new three-dimensional (3D) fractional-order Zernike moments obtained by extending the radial component of classical Zernike polynomials to admit fractional exponents. This formulation provides a mathematically consistent extension of integer-order Zernike moments to fractional orders while preserving their orthogonality in the unit ball. A reformulation of the fractional Zernike functions and a recurrence relation are also presented for efficient computation of the fractional-order moments. Rotationally invariant descriptors are further derived to allow orientation-independent shape representation. Numerical experiments demonstrate that the proposed fractional-order moments improve the accuracy of shape reconstruction and representation compared to their integer-order counterparts, highlighting their effectiveness for 3D shape analysis.