Correlation filters with controlled scale response

Correlation filtering methods are becoming increasingly popular for image recognition and location. The recent introduction of optimal tradeoff circular harmonic function filters allowed the user to specify the response of a correlation filter to in-plane rotation distortion. In this paper we introduce a new correlation filter design that can provide a user-specified response to in-plane scale distortion. The design is based on the Mellin radial harmonic (MRH) transform and incorporates multiple harmonics into the correlation filter for improved discrimination capability. Additionally, the filter design minimizes the average correlation energy in order to achieve sharp correlation peaks, and thus we refer to these filters as minimum average correlation energy Mellin radial harmonic (MACE-MRH) filters. We present underlying theory, a MACE-MRH filter design method, and numerical simulation results.