Abstract

A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired.

© 1985 Optical Society of America

Rotationally invariant correlation filtering for multiple images

George F. Schils and Donald W. Sweeney
J. Opt. Soc. Am. A 3(7) 902-908 (1986)

Iterative technique for the synthesis of optical-correlation filters

George F. Schils and Donald W. Sweeney
J. Opt. Soc. Am. A 3(9) 1433-1442 (1986)

Shift- and scale-invariant anamorphic Fourier correlator

Tomasz Szoplik
J. Opt. Soc. Am. A 2(9) 1419-1423 (1985)

Experimental use of iteratively designed rotation invariant correlation filters

Donald W. Sweeney, Ellen Ochoa, and George F. Schils
Appl. Opt. 26(16) 3458-3465 (1987)

Shift and scale-invariant anamorphic Fourier correlator using multiple circular harmonic filters

Tomasz Szoplik and Henri H. Arsenault
Appl. Opt. 24(19) 3179-3183 (1985)