Spatially inhomogeneous scaled transforms for vision and pattern recognition

Scale invariance and data compression are two desirable attributes for spatial transforms to be used for pattern recognition. We have found that the requirement of a form of scale invariance leads to a natural reduction in the information to be processed. Such scaled transforms exhibit spatial inhomogeneity similar to that of the human visual system. That is, scaled transforms provide a global view of low resolution while maintaining a detailed view of the image at the transform center (which can be moved to points of interest). Like the visual system, scaled transforms can have rotational invariance, but, in general, translational invariance is lost. The conventional Fourier transform is a limiting case of the general class of scaled transforms.