Abstract

In recent years, efforts to expand the capabilities of conventional VanderLugt filters so that an invariant capability could be added have been made. These are based on matching the filter to only a part of the input information, one of its harmonics, so that an invariant parameter feature could be added to the already existing lateral shift invariances. A projection invariant filter requires the correlation to be invariant to the tilt of the input object with respect to a fixed axis. As a result, the most general projection invariant system contains two parameters, the tilting direction and the tilting ratio which leads to a coordinate reduction factor, perpendicular to the tilt axis. In this work we present a novel approach for a shift and 1-D projection invariant filter, where the projection direction is a variant parameter and thus has to be known a priori. This approach is based on decomposing the object into an orthogonal and complete set of logarithmic harmonics, the harmonics being computed for a 1-D image contraction. Analysis of the correlation properties of these harmonics shows that they provide shift and projection invariant pattern recognition for a given range when using only one harmonic.

© 1989 Optical Society of America