The arbitrary nature of the concept of similarity is discussed, and its consequences on the exploitation of invariants in pattern recognition. After briefly reviewing the main invariants of interest in automated pattern recognition, methods of achieving invariant pattern recognition are reviewed, with emphasis on the use of matched spatial filters made with Circular harmonic components. The progress in using such filters and their derivatives with sidelobe-rejection capability on images of increasing complexity, from simple binary shapes to complex grey-level objects on highly cluttered backgrounds, is described.

A critical review of training-image correlation-based optical pattern recognition algorithms is provided. An assessment of the advantages and limitations of these algorithms is given.

The techniques for the tracking of multiple objects making independent movements are reviewed. Basically, the techniques are based on the creation of multiple channels for the holographic matched filter. Multiple filters instead of one filter are recorded in the Fourier transform plane. Each of these filters, or a combination of them, can be used to track one object. The filter or filters used for each object should have a specific reference beam directed at a specific incident angle so that the output correlation plane associated with each input object can be adequately separated. Two methods of recording and parallel addressing of the multiple filters are described. One is to use a Fourier transform lens in combination with a specifically designed diffraction grating. The other is to use a custom designed multiple-focus holographic lens. The design criterion for both the diffraction grating and hololens is that when these optics are employed, an N x N array of diffraction limited spectra should be produced at the Fourier plane such that an MSF array of equal diffraction efficiency can be obtained. Available techniques will be discussed and their merits assessed.

A method of pattern recognition is presented that can recognize image variations such as different perspective views of a three-dimensional object. The general theory allows many different kinds of image variations, such as rotation, scale, perspective, or combinations of these, to be recognized. The method produces a small bank of about 20 filters to be used in a correlator. We call these filters lock-and-tumbler filters. The theory is illustrated on several different kinds of invariant pattern recognition problems. The correlation filters designed for these invariant recognition problems may be modified to reject certain kinds of clutter in an input scene. An example of modifying these filters to achieve rejection of clutter is given. An implementation of the lock-and-tumbler filter method using a high speed digital correlator is then described.

We investigate the performance of a recently introduced bipolar joint transform image correlator when multiple reference objects and single and multiple targets are present at the input plane. The bipolar joint transform correlator uses nonlinearity at the Fourier plane to threshold the Fourier transform interference intensity to only two values, 1 and -1. The performance of the bipolar correlator is compared to the classical joint transform image correlator when multiple objects are present at the input plane. We show that the performance of the bipolar correlator is substantially superior to that of the classical joint transform image correlator in the areas of autocorrelation peak intensity, autocorrelation peak to sidelobe ratio, autocorrelation bandwidth, and discrimination sensitivity. It is shown that when multiple objects are present at the input plane, the classical joint transform image correlator produces large cross-correlation signals and poorly defined autocorrelation signals with large bandwidth. The large cross-correlation signals are comparable in intensity with the autocorrelation peak and can falsely indicate the presence of many targets. On the other hand, the bipolar joint transform image correlator produces well-defined autocorrelation signals with very low cross-correlation level. Computer simulations are used to test both types of correlators, and 3-D plots of the correlation functions are provided and discussed.

In the past 15 years, a dozen or so designs have been proposed for compact optical correlators. Of these, maybe one-third of them have actually been built and only a few of those tested. This paper will give an overview of some of the systems that have been built as well as mention some promising early and current designs that have not been built. The term compact, as used in the title of this paper, will be applied very loosely; to mean smaller than a laboratory size optical table. To date, only one correlator has been built and tested that actually can be called miniature. This softball size correlator was built by the Perkin-Elmer Corporation for the U. S. Army Missile Command at Redstone Arsenal, Alabama. More will be said about this correlator in following sections.

The spatial coordinates of detected photoevents and the number of detected photoevents in a given area convey information about the classical irradiance of the input scene. In this paper the effectiveness of photon-counting techniques for image recognition is discussed. A correlation signal is obtained by cross correlating a photon-limited input scene with a classical intensity reference function stored in computer memory. Laboratory experiments involving matched filtering, rotation- and scale-invariant image recognition, and image classification are reported. For many images it is found that only a sparse sampling of the input is required to obtain accurate recognition decisions, and the digital processing of the data is extremely efficient. Using available photon-counting detection systems, the total time required to detect, process, and make a recognition decision is typically on the order of tens of milliseconds. This work has obvious applications in night vision, but it is also relevant to areas such as process control, radiological, and nuclear imaging, spectroscopy, robot vision, and vehicle guidance.

The concept and lure of processing data optically has been around nearly three decades, yet it has found application in only a few narrow fields. Its lure is its complete computational parallelsim. With recent advances in algorithms and hardware it may now be possible to make inroads into a few area where digital processing has tailed to solve the problems, namely pattern recognition and machine or robotic vision. We examine the reason for optical processing's past shortcomings, and some of the recent advances that encourage some optimism in this field.

Recent advances, including binary phase-only filters (BPOF) implemented with suitable real-time devices, have enhanced the potential of coherent optical correlation for pattern and object recognition and object location functions which are important in machine vision applications. Hybrid (optical/electronic) systems performing complex vision operations such as recognition, location, and discrimination at attractive rates are portended by these developments. Laboratory systems have demonstrated attractive real-time performance including good agreement with computer models and the application of "smart filter" techniques to improve the distortion invariance of individual filters. Improved smart filter formulations are under development. These combined with high correlation throughput define the high potential of BPOF correlation systems for this type application.

Two basic methods for spreadless nonlinear processing are reviewed--theta coding and the halftone method--and a broad class of threshold-decomposition-based nonlinear image processing operations is then described that relies on combining hard point nonlinearities with linear shift-invariant operations.

Both hybrid optical and digital architectures are being used to perform 2-D Fourier transform based operations. It will be shown in this paper that for rectilinearly formatted data, digital systems are competitive with and in some instances out perform their hybrid-optical counterparts. However, as the input data format deviates significantly from rectilinear, the added reformatting computations which digital systems must undertake in order to utilize the Fast Fourier Transform algorithm degrades system performance and hybrid-optical systems become more attractive. These hybrid-optical processors may be the systems of choice for many potential applications which include tomographic processing, VLA radio telescope image formation, diffraction tomography, seismic cross-borehole tomography, and spotlight SAR image formation. Each of the above applications produce data in a unique non-rectilinear format. Numerous system architectures for both technologies exist today. This paper will enumerate the potential hybrid-optical and digital: architectures and compare their performance characteristics. A common system packaging (size/weight/power) constraint is imposed upon both technolgies to facilitate a fair comparison. A near term performance forecast will also be made for both technologies.

A multiobject shift-invariant pattern recognition system using code division multiplexed binary phase-only correlation is presented. The system computes the binary correlation between an input pattern and a generalized set of pattern functians. This technique uses a filter which consists of a set of binary phase-only code division multiplexed reference pattern functions. There are many advantages in binarizing the filter function. Binary spatial light modulators (SLMs) have been developed that work well in a binary phase-only mode and can be used to synthesize the spatial filters of this type. Binarization also permits the recording of filters of images with larger samples on currently available binary SLMs that have a limited number of pixels. The functions in the reference set may correspond to either different objects or different variations of the object under study. Computer simulations of the correlator are used to study the performance of the pattern recognition system. The correlation signal-to-noise ratio (SNR) and the ratio of the correlation peak intensity to the maximum correlation sidelobe intensity are evaluated as the criteria for the system performance.

The pattern recognition algorithms based on eigenvector analysis (group 2) are theoretically and experimentally compared in this part of the paper. Group 2 consists of Foley-Sammon (F-S) transform, Hotelling trace criterion (HTC), Fukunaga-Koontz (F-K) transform, linear discriminant function (LDF) and generalized matched filter (GMF). It is shown that all eigenvector-based algorithms can be represented in a generalized eigenvector form. However, the calculations of the discriminant vectors are different for different algorithms. Summaries on how to calculate the discriminant functions for the F-S, HTC and F-K transforms are provided. Especially for the more practical, underdetermined case, where the number of training images is less than the number of pixels in each image, the calculations usually require the inversion of a large, singular, pixel correlation (or covariance) matrix. We suggest solving this problem by finding its pseudo-inverse, which requires inverting only the smaller, non-singular image correlation (or covariance) matrix plus multiplying several non-singular matrices. We also compare theoretically the effectiveness for classification with the discriminant functions from F-S, HTC and F-K with LDF and GMF, and between the linear-mapping-based algorithms and the eigenvector-based algorithms. Experimentally, we compare the eigenvector-based algorithms using a set of image data bases each image consisting of 64 x 64 pixels.

A review of spatial light modulator technologies is presented, including the description and performance parameters of the main devices, and their main applications for optical information processing. The various performance trade-offs and their impact on emerging new technologies and future trends of spatial light modulators are discussed.

Neural networks are finding many areas of application. Although they are particularly well-suited for applications related to associative recall such as content-addressable memories, neural nets can perform many other applications ranging from logic operations to the solution of optimization problems. The training of a recently introduced model to perform boolean logical operations such as XOR is described. Such simple systems can be combined to perform any complex boolean operation. Any complex task consisting of parallel and serial operations including fuzzy logic that can be described in terms of input-output relations can be accomplished by combining modules such as the ones described here. The fact that some modules can carry out their functions even when their inputs contain erroneous data, and the fact that each module can carry out its functions in parallel with itself and other modules promises some interesting applications.

We consider a class of neural networks whose performance can be analyzed and geometrically visualized in a signal space environment. Alternating projection neural networks (APNN's) perform by alternately projecting between two or more constraint sets. Criteria for desired and unique convergence are easily established. The network can be taught from a training set by viewing each library vector only once. The network can be configured as either a content addressable memory (homogeneous form) or classifier (layered form). The number of patterns that can be stored in the network is on the order of the number of input and hidden neurons. If the output neurons can take on only one of two states, then the trained layered APNN can be easily configured to converge in one iteration. More generally, convergence is at an exponential rate. Convergence can be improved by the use of sigmoid type nonlinearities, network relaxation and/or increasing the number of neurons in the hidden layer. The manner in which the network generalizes can be directly evaluated.

A programmable optical associative memory for two-dimensional image retrieval is described. Both the stored image and the input image are displayed spatially; therefore, they can be updated in real time more conveniently. The integral product between the input image and the stored images is obtained by nonlinear correlation technique which has a superior performance compared with the conventional optical correlation techniques in the areas of the light efficiency and the correlation signal quality. Thus, better quality images can be reconstructed and the need for optical gain and the optical feedback may be eliminated. There are small losses in the system since no halograms are employed.

Drawing from older fields of optical computing and neural networks, optical neural networks are growing in interest and capability. We show here their unchallenged niches in the whole field of neural networks, their morphology, their difficulties, and their promise. This is an overview not a review.