Abstract

The technique of using correlation filters for optical pattern recognition has received considerable study.¹ Several variations on the matched filter have been suggested. They include phase-only filters (POFs), binary phase-only filters (BPOFs), complex ternary matched filters (CTMFs) and synthetic discriminate functions (SDFs). Generally, in the development of optical correlation filters, little attention has been given to the normalization of the filter output. Goodman suggested that the matched filter be normalized by means of the Cauchy–Schwarz inequality.² The Cauchy–Schwarz inequality can be applied to arbitrary correlation filters. This normalization achieves intensity invariance. It can be seen that the matched filter achieves the maximum normalized value of unity. For all other correlation filters, a value less than unity is obtained. In general, it can be shown that for filters other than the matched filter, there are objects that give normalized correlation outputs greater than the object for which the filter was made. This simple normalization has consequences for the design, bandwidth selection, and discrimination ability for the above mentioned filters. The results of analysis and simple examples will be presented.

© 1990 Optical Society of America