Abstract

Optical-pattern-recognition techniques are generally unable to provide an efficient approach to the classification of optical data, because of the linearity of the Fourier transform. A space-variant imaging model is proposed, whose behavior is characterized on the basis of orthonormal polynomials. The optical data are described in an orthonormal space based upon these polynomials. Proper-axis rotation and dimensionality reduction are supplied by the Karhunen–Loève transform. The intrinsic variables then become available, allowing the clustering of the data (considered as belonging to statistical classes). This work is illustrated by examples of handwriting recognition and classification.

© 1975 Optical Society of America

Optical pattern recognition and clustering: Karhunen-Loève analysis

J. Duvernoy
Appl. Opt. 15(6) 1584-1590 (1976)

Hilbert-space Karhunen–Loève transform with application to image analysis

A. Levy and J. Rubinstein
J. Opt. Soc. Am. A 16(1) 28-35 (1999)

Analysis of optical near-field images by Karhunen–Loève transformation

Daniel Charraut, Daniel Courjon, Claudine Bainier, and Laurent Moulinier
Appl. Opt. 35(20) 3853-3861 (1996)

Surface classification by an optoelectronic implementation of the Karhunen–Loève expansion

C. Gorecki
Appl. Opt. 30(31) 4548-4553 (1991)

Restoration of astigmatism and curvature of field*

A. A. Sawchuk and M. J. Peyrovian
J. Opt. Soc. Am. 65(6) 712-715 (1975)