Rotationally invariant correlation filtering for multiple images

Abstract

A method is presented for designing translation-invariant optical correlation filters that have a specified rotational response for each of several input images. The correlation filter is postulated to have the form of an infinite linear combination of the angular Fourier harmonics of the input images. The corresponding response of the optical system to rotations of the multiple input images is described by a vector–matrix convolution equation. The solution of this equation for the unknown correlation filter is presented in terms of Fourier series. Use of one term in the Fourier series gives the multiple circular-harmonic filter that provides a specified rotationally invariant response for each of the multiple input images. Applications to rotationally invariant discrimination are described, and examples are given.