ROTATION AND SCALE-INVARIANCE WITH POLAR AND LOG-POLAR COORDINATE TRANSFORMATIONS

The optical implementation by means of holographic optical elements of polar and log-polar coordinate transformations (CTs) for rotation and scale invariant pattern recognition is attractive to achieve real-time processing of input scenes. The quality of the CTs realized so far and the image wrapping problem have limited this method to the processing of the most simple objects. We propose a new CT implementation with computer generated holograms partioned into non-uniform facets. The hologram recording is done with a commercial photo-typesetter at a very low cost. The image wrapping problem is alleviated by means of juxtaposed CTs. The intensity of the Fourier transform of the CTs is used to correctly classify the objects, and only this classification step was done numerically in our experiment. Optical results are presented and demonstrate the quality of our CTs.