Theory and optical implementation of the geometrical approach of multiple circular harmonic filters.

The circular harmonic filter contains only one component of the image. Its discrimination capability has been questionable. The geometrical approach of multiple circular harmonic filters uses relative locations of the correlation peaks as the rotation-, shift-, and intensity-invariant features for pattern recognition. Each feature depends on the entire image. This approach has a good discrimination capability. Optical real-time implementation of the on-axis continuous phase-only circular harmonic filters by the use of a commercial liquid-crystal television is shown. A harmonic analysis shows that the phase-mostly filter can tolerate coupled amplitude modulation at the acceptable expense of the output signal-to-noise ratio. An optical experiment of the geometrical approach of multiple circular harmonic filters for a multiple-image input is described. The cross-correlation peaks between the individual filters and the clutter are eliminated, because they are not in good locations.