Digital Filter Implementation of Orthogonal Moments

The importance of geometric moment (GM) invariants first received research attention when Hu [1] introduced them in his study. As they capture global features have been widely used in applications such as object classification, image and shape analysis and edge detection [2-8]. However, since GMs are non-orthogonal, a set of continuous orthogonal moments including Zernike and Legendre moments was introduced by Teague [9]. Their desirable qualities of orthogonality, speed of computation and robustness have found a wider range of applications such as character recognition, two-dimensional (2D) direction-of-arrival estimation, and trademark segmentation and retrieval [10-13]. However, these continuous moments pose certain problems in computation: they require coordinate transformation and suitable approximation of the continuous moment integrals. The transformation and approximation they require create additional opportunities for the occurrence of error in the computation of the feature descriptors. This recognition of the error potential in continuous orthogonal moments led to a new set of discrete orthogonal moments such as Tchebichef, Krawtchouk and Hahn moments as these do not require coordinate transformation and the discretization step in the moment computation [14-18].