Abstract

The geometric notion of an N-dimensional linear vector space provides a useful framework in which to understand the operation and limitations of correlation techniques for pattern recognition. In general, correlators classify patterns according to a hyperplane decision surface whose orientation is determined by the filter and whose distance from the origin is determined by the threshold level that the correlation peak must exceed for an image to be classified. Thus the performance of an optical correlator depends mainly on how the reference images are distributed in this linear vector space. Using this approach, many useful conclusions can be drawn. Issues to be discussed include a simple approach toward calculating SDFs, the limitations of single-filter correlation systems, the relationship between target discrimination and distortion invariance, and the need to implement more sophisticated decision surfaces.

© 1988 Optical Society of America