Optics Communications 104 (1994) 285-292 North-Holland OPTICS COMMUNICATIONS Shift- and rotation-invariant interpattern heteroassociation (IHA) model Chii-Maw Uang, Shizhuo Yin, Guowen Lu and Francis T.S. Yu Electrical and Computer Engineering Department, The Pennsylvania State University, University Park, PA 16802, USA Received 29 April 1993; revised manuscript received 26 August 1993 A shift- and rotation-invariant neutral work using an interpattern heteroassociation (IHA) model is illustrated. The shift- and rotation-invariant properties are achieved by using a set of binarized-encoded circular harmonic expansion (CHE) functions in the Fourier domain as the network training set. Becauseof the shift-invariantand symmetric properties of the modulus of Fourier spectrum, the problem of locating the center of the CHE functions can be avoided. Computer simulations and experimental demonstrations that demonstrate the shift- and the rotation-invariant properties of the proposed IHA neural net are provided. 1. Introduction One of the advantages of using associative mem- ory for pattern identification is the tolerance for noise or partial input. Optical implementations of neural nets are generally limited to nonshifted, nonrota- tional and nonscaled input variations. Since the hu- man brain will recognize an object regardless of the location and orientation, the shift- and rotation-in- variant neural networks are critical for practical ap- plications. In recent years, optical pattern recogni- tion systems based upon the rotation-invariant property of circular harmonic expansion techniques have been widely used [ 1-8 ]. Most of these systems use a matched filtering technique which has been shown to be complicated to design and poses severe problems for practical application. In this paper, we shall discuss a simple and straightforward shift- and rotation-invariant hetero- associative memory using the interpattern associa- tion (IPA) model. The technique replaces the ref- erence exemplars training set with a encoded binary data set. The major advantages of this proposed technique are the full range of translation- and ro- tation-invariance and the simplicity of the optical design. In our system we shall use a two-level net- work; the first level encodes the spatial features of the input pattern, and the second level constructs the interpattern hetero-associative (IHA) memory. The first level of the system creates a shift- and the ro- tation-invariant data set. Two methods can be con- sidered; a feature sampling method (i.e., ring detec- tor), which is easy to implement but has low discrimination, and the use of the circular harmonic expansion which requires complex calculation but a higher discrimination is achieved. In this paper, we shall use the circular harmonic expansion method described in the following. 2. Preprocessing To produce a shift- and rotation-invariant net- work, the input exemplars need to be preprocessed in the following manner: the number of data pixels and input neurons are matched, the main features from the input exemplar are preserved, the input ex- emplar is encoded for shift- and rotation-invariance, and the diversity of the sampled data of the training set is optimized such that the discrimination be- tween the stored exemplars is maximized. To achieve these objectives, two methods are considered; one using the feature sampling (ring detector) technique and the other using the circular harmonic expansion method. A commercial hardware Wedge-ring detector (WRD) [11-14] or computer generated ring de- tecting data can be used to sample the modulus of 0030-4018/94/$ 07.00 © 1994 Elsevier Science B.V. All rights reserved. 285