Optical recognition of statistical patterns

Optical implementation of the Fukunaga-Koontz transform (FKT) and the Least-Squares Linear Mapping Technique (LSLMT) is described. The FKT is a linear transformation which performs image feature extraction for a two-class image classification problem. The LSLMT performs a transform from large dimensional feature space to small dimensional decision space for separating multiple image classes by maximizing the interclass differences while minimizing the intraclass variations. The FKT and the LSLMT were optically implemented by utilizing a coded phase optical processor. The transform was used for classifying birds and fish. After the F-K basis functions were calculated, those most useful for classification were incorporated into a computer generated hologram. The output of the optical processor, consisting of the squared magnitude of the F-K coefficients, was detected by a T.V. camera, digitized, and fed into a micro-computer for classification. A simple linear classifier based on only two F-K coefficients was able to separate the images into two classes, indicating that the F-K transform had chosen good features. Two advantages of optically implementing the FKT and LSLMT are parallel and real time processing.