Multiple circular-harmonic-function correlation filter providing specified response to in-plane rotation

The circular-harmonic-function correlation filter originally proposed by Hsu and Arsenault [Appl. Opt. 21, 4016 (1982)] for in-plane rotation invariance uses only one harmonic, which results in poor discrimination capability of the filter. Various methods to use multiple harmonics were explored previously by different researchers. We present a new method to combine multiple circular harmonics into a single filter that can provide the desired correlation response to in-plane rotation while minimizing the correlation-plane energy. Since multiple harmonics are included, the filter can discriminate well, and since correlation-plane energy is minimized, correlation peaks tend to be sharp. Since the designer can specify the desired in-plane rotation response, a variety of filter behaviors (including complete invariance to input rotations) can be obtained. Underlying theory is discussed, and simulation results are presented.