Synthesis of distortion invariant optical correlation filters

Abstract

A method is presented for synthesizing optical correlation filters that will detect a target image independent of position and other general kinds of image distortion. The various distortions can be rotation, scale, and perspective, or any combination of these. Most generally, any linear coordinate distortion is allowed. Since these filters do not require energy normalization, they are also intensity invariant. The design technique starts by finding a set of eigenfunctions and eigenimages for the specified target and distortion. Because these modes completely describe the target image, the correlation filter is formed from their linear combination. The spatial orthogonality of the eigenimages preserves the target information when the modes are combined. The linear combination coefficients are required to have unit amplitude, and their phases are found so that the optical system outputs a constant amplitude. Filters meeting these criteria are successfully designed by iterating between the spatial domain and the eigenfunction domain. All the target information can be extracted by the optical system if the distortion is introduced as a temporal variation of the filter. Detection of a constant intensity signature will uniquely locate input targets in parallel. We illustrate this technique with several examples.