In both the Laplacian and Gaussian pyramids, the lowest level of the pyramid is constructed from the original image. Academic Press, 1990. Moments Integrals can also be used to compute geometrical moments of the image. It should be noted, however, that the phases of the spatial frequency components can be varied independently. There are thus many possible images of greatly varying visual appearance which have the same amplitude spectrum.
Projective transformations preserve neither lengths, nor ratios of lengths.
Such a ratio is known as a cross ratio. Since projective transformations are many to one, matching cross ratios are a necessary, but not sufficient, condition for feature matching. Computational Vision . Sixth Avenue, San Diego, CA 92101, 1990. The resulting frequency spectrum can be analyzed for a variety of qualities, including homogeneity of regions and boundaries between regions.