Coordinate-transformed filter for shift-invariant and scale-invariant pattern recognition

A variable radial coordinate transformation of the phase-only filter (POF) that is dependent on the energy's angular distribution of the target spectrum is used to perform shift- and scale-invariant pattern recognition. The POF of a basic size target and the cumulative energy of its angular distribution are calculated. The filter function is then transformed by means of stretching along the radial coordinate so that the same energy contribution to the correlation peak is provided for any size target. The maximum ratio for recognizing scaled objects is 1:1.5. Computer simulations and optical experiments showing the performances of the filter are presented. (C) 1997 Optical Society America.