Abstract

The scale-invariant and rotation-invariant Fourier-Mellin transform depends on the position of the object. This limits its field of use. We propose filters of the form r^s–2 exp(jmθ) with complex-valued s = v + jw. The filter contains no object information. The correlation function of the filter with an input object at every point (x', y') in the output plane is the Fourier-Mellin transform of the object developed about the origin (x', y') of a polar coordinate system. The shift-invariant features are then extracted: these are the distances between the correlation maxima from the filters with different orders s and m and the intensities of those maxima. The logpolar coordinate transform normally used for the optical Fourier-Mellin transform is not required. The method is invariant under changes of position, scale, orientation, rotation, and intensity. It also allows input containing multiple objects simultaneously. The invariant features can be used for image classification or as inputs to neural networks for invariant associative and adaptive pattern recognition.

© 1988 Optical Society of America