Image classification by an optical implementation of the Fukunaga–Koontz transform

Abstract

The Fukunaga–Koontz (F–K) transform is a linear transformation that performs image-feature extraction for a two-class image classification problem. It has the property that the most important basis functions for representing one class of image data (in a least-squares sense) are also the least important for representing a second image class. We present a new method of calculating the F–K basis functions for large dimensional imagery by using a small digital computer, when the intraclass variation can be approximated by correlation matrices of low rank. Having calculated the F–K basis functions, we use a coherent optical processor to obtain the coefficients of the F–K transform in parallel. Finally, these coefficients are detected electronically, and a classification is performed by the small digital computer.