Moment invariants in the space and frequency domains

Moment invariants of the Fourier transform of an image are introduced. It is found that a feature set composed of moment invariants from both the space domain and the Fourier domain gives better performance for a wide range of classification tasks than does the same number of moment invariants from either domain alone. Redundancy among moments of the two domains is examined by using the correlation coefficient between the feature kernels as a measure. Examples are used to compare the feature sets and to assess their performance in classification tasks. Moment invariants of the magnitude of the Fourier transform and, by inference, some popular features, such as the spectral ring-wedge detector, are found to fall far short in performance compared with those in which the phase of the Fourier transform is also utilized. Coherent optical systems to compute the dual-domain moment invariants are proposed.