Positional, rotational and scale invariant optical correlation method

Abstract

A method and electro-optical apparatus for correlating two functions, f.sub.1 (x,y) and f.sub.2 (x,y) which are shifted, scaled and rotated versions of each other without loss of signal-to-noise and signal-to-clutter ratios as compared to the autocorrelation case. The coordinates of two correlation peaks provide an indication of the scale and orientation differences between the two functions. In performing the method, the magnitudes of the Fourier transforms of the functions are obtained, .vertline.F.sub.1 (.omega..sub.x, .omega..sub.y).vertline. and .vertline.F.sub.2 (.omega..sub.x,.omega..sub.y).vertline. and then a polar coordinate conversion is performed, and the resultant functions F.sub.1 (r,.theta.) and F.sub.2 (r,.theta.) are logarithmically scaled in the r coordinate. The functions thus produced F.sub.1 (e.sup..rho.,.theta.) and F.sub.2 (e.sup..rho.,.theta.) are Fourier transformed to produce the Mellin transforms M.sub.1 (.omega..sub..rho., .omega..sub..theta.) and M.sub.2 (.omega..sub..rho.,.omega..sub..theta.). The conjugate of one of these Mellin transforms is obtained, and the product of this conjugate with the other Mellin transform is produced and, subsequently, Fourier transformed to complete the correlation process.