Abstract

We present a design for the optical implementation of a Bayes classifier using the Parzen window probability density estimation technique. The system can also be configured, with simple hardware modifications, as a k-nearest-neighbor classifier. Both versions are asymptotically optimal in the limit of large training set size, in that the probability of classification error asymptotically approaches the Bayes lower limit. This system is fully optical in both the training and computation phases, with no need for off-line electronic calculations. The classifier is trained by holographically storing all available prototype patterns, which are recorded in sequence via an input spatial light modulator. A second holographic step results in a plane of frequency-multiplexed training images on which the unclassified input pattern is imaged. A resulting set of inner products (between the input and each prototype pattern), followed by optical thresholding and integration, yields an array of estimated class-conditional a posteriori probabilities. Classification is achieved with a maximum detection stage. Theoretical and practical limitations of the system will be assessed in order to determine how closely it can approximate the optimal Bayes classifier.

© 1992 Optical Society of America