Shift- and scale-invariant recognition of contour objects with logarithmicradial harmonic filters

The phase-only logarithmic radial harmonic (LRH) filter has been shown to b e suitable for scale-invariant block object recognition. However, an import ant set of objects is the collection of contour functions that results from a digital edge extraction of the original block objects. Therefore, since the energy of the contour objects decreases more slowly with the scale fact or than does the energy of the block objects, the phase-only LRH filter has difficulties in the recognition tasks when these contour objects are used. We propose a modified LRH filter that permits the realization of a shift- and scale-invariant optical recognition of contour;objects. The modified LR H filter is a complex filter that compensates the energy variation resultin g from the scaling of contour objects. Optical results validate the theory and show the utility of the newly proposed method. (C) 2000 Optical Society of America. OCIS code: 100.5010.