It has been shown in previous work that the family of filters which includes the minimum average correlation energy (MACE) filter can be formulated as a linear associative memory (LAM) preceded by a linear pre-processor which changes depending on the optimization criterion. We have presented a methodology by which the MACE filter and other synthetic discriminant function (SDF) filters can be extended to nonlinear processing structures (i.e. nonlinear associative memories) resulting in improved performance with respect to generalization and out-of-class target rejection. Our earlier focus was towards developing efficient training algorithms for computing a nonlinear discriminant function without changing the linear pre-processor. In this paper we discuss a nonlinear pre-processing method based on concepts of information theory. We show a simple unsupervised method by which input images can be nonlinearly transformed onto a maximum entropy feature space.

In previous work the author gave a formulation of general spatial filter design as a constrained optimization question. The purpose of this paper is to note that suitable reparameterizations of the optimization problem enable one to eliminate the constraints. This constraint elimination simplifies the optimization and potentially leads to greater computational efficiency. One such reparameterization is examined in detail.

Detection of distorted target images is a common problem in optical pattern recognition. Many distortion-invariant filter designs have been developed. However, while detecting the distorted target, the value of the distortion parameters is lost. We introduce a method of optical morphology that transforms rotated target objects into a single line of bright dots. The location of these lines indicates the location of a target and the angle indicates the rotation of the target. We use a set of complex filter images referred to as super images configured in a correlation filter bank to accomplish this form of morphological transformation. The mathematical characteristics of super images are discussed and examples of their usage are demonstrated numerically.

For optical implementation of correlation filters, we must design filters that can be implemented on available spatial light modulators (SLMs). Previous versions of computer code MEDOF: minimum Euclidean distance optimal filter produced various correlation filters using a single training image. In the newest version of MEDOF, we can use a training set of images to generate composite filters that include system noise and device constraints. In this paper we present implementation issues and results using composite filters generated by MEDOF.

A realizable optimal weighted minimum average correlation energy (MACE) filter with arbitrary spatial light modulator (SLM) constraints is presented. The MACE filter can be considered as the cascade of two separate stages. The first stage is the prewhitener which essentially converts colored noise to white noise. The second stage is the conventional synthetic discriminant function (SDF) which is optimal for white noise, but which uses training vectors subjected to the prewhitening transformation. So the energy spectrum matrix is very important for filter design. New weight function we introduce is used to adjust the correlation energy to improve the performance of MACE filter on current SLMs. The action of the weight function is to emphasize the importance of the signal energy at some frequencies and reduce the importance of signal energy at some other frequencies so as to improve correlation plane structure. The choice of weight function which is used to enhance the noise tolerance and reduce sidelobes is related to a priori pattern recognition knowledge. An algorithm which combines an iterative optimal technique with Juday's minimum Euclidean distance (MED) method is developed for the design of the realizable optimal weighted MACE filter. The performance of the designed filter is evaluated with numerical experiments.

We study the discrimination ability of a recently introduced optimum rotation invariant filter for disjoint noise. The discrimination ability of a sub-optimum filter related to the preceding one but where the non-target images are involved is also studied. The performance of both filters has been tested by computer simulations with a variety of natural and artificial backgrounds. The results obtained show an excellent performance much improved over the classical CHF (the filter that maximizes the SNR ratio while maintaining rotation invariance).

The circular harmonic function (CHF) correlation filter originally proposed by Hsu and Arsenault uses only one harmonic of the reference image and thus ignores much of the discriminatory information contained in the reference image. Various methods have been proposed to make use of multiple harmonics. In this work, we present a method that combines three useful objectives: using multiple circular harmonics, controlling the correlation response to in-plane rotation and minimizing the correlation plane energy in order to achieve sharp correlation peaks. Basic theory underlying this method as well as some simulation results are presented. The implications of dealing with spatially discretized images on the interpretation of CHF coefficients also is discussed.

This paper discusses the combination of the wavelet transform with the scale invariant Mellin transform in an optical joint transform correlator (JTC) architecture. A mathematical and numerical analysis are presented with three optical designs for performing the Mellin-wavelet joint transform.

A new distortion-invariant correlation filter that truly optimizes parameters is described. Shortcomings of other distortion-invariant correlation filters are noted (selecting the number of training images and the control parameter, worse objective function optimization with more training images, lower clutter energy does not correspond to a better (P_FA). A new control parameter (c) definition is used, and new objective functions.

This paper reviews the progress of an ongoing research program at the Institute of Optical Research which addresses optical correlators dedicated to pattern recognition. A two-class discrimination problem with in-plane distortion is considered. For this purpose, we provide here a comparison between the performances of several synthetic discriminant function (SDF) filters implemented on a binary ferroelectric liquid crystal spatial light modulator (FLC SLM). While non-constrained optimal trade-off (OT) SDF filters perform very well, binary filters offer lower efficiencies. The relative merits of direct binarization of the complex transmittance of the filter and the Jared-and-Ennis method (relaxation algorithm) for filter construction are discussed. To overcome the poor modulation capability of available SLMs and take full advantage of the tuning ability of OT SDF filters, we propose to encode composite filters as detour-phase holograms. We illustrate this discussion with computer simulations as well as experimental results obtained with our optical VanderLugt correlator. In-plane rotation tolerance over 90 degrees and two-class target discrimination are experimentally achieved with a single composite filter.

Optical correlation has profited from simultaneous advances in spatial light modulators and algorithms, which have considerably broadened its field of applications. Phase only filters and binary phase only filters present an obvious interest regarding their implementations on existing spatial light modulators. Ferroelectric liquid crystal spatial light modulators are the faster examples. Nevertheless, in many image processing tasks, multiple correlations are required. Optical multichannel correlation architectures have been proposed in the case of conventional Vander Lugt correlators, but few have been realized. We propose and implement a solution for a four channels binary phase only matched filter. We show that this solution is well suited to the use of an electrically addressed Ferroelectric spatial light modulator in the Fourier plane.

This paper describes a case study in which 21 different low-frequency magnitude masks are applied in a set of ternary phase- amplitude filters (TPAFs) to discriminate between 4 different target images. The results of each mask are compared in terms of the height of the in-class correlation peak, the average in-class and out-of-class signal-to-noise ratios, and the discrimination ratio achieved by each filter. From these measurements, a correlator designer can select a preferred TPAF mask based on the relative importance of discrimination ability and optical efficiency. The resulting TPAF can be used as is, or improved further with other optimization techniques.

A voting scheme for the design of composite filter is proposed here. Different types of synthetic discriminant function (SDF) filters, like minimum average correlation energy (MACE), minimum variance SDF (MVSDF), and optimal tradeoff SDF (OTSDF) have been proposed recently for the distortion-invariant recognition. Discretization of these filters is necessary to realize them using the available spatial light modulator (SLM), which limits the efficiency of the continuous domain filters. In this report, we address this SLM-constraint of the composite filter design. Our design starts with a binary SLM. In particular, binary modulation capability of the SLM is incorporated in the composite filter design as a constraint in the form of voting scheme nonlinearity.

Liquid crystal televisions (LCTVs) continue to be used as inexpensive spatial light modulators (SLMs) in coherent optical processing systems. The LCTVs are generally manufactured using twisted-nematic liquid crystal materials. The operating curve of a twisted-nematic liquid crystal television can be varied by adjusting the orientations of the polarizer and analyzer relative to the molecular structure of the liquid crystal cell. The usefulness of the LCTV as a SLM in an optical processing system critically depends on the operating curve selected. This is particularly so when the SLM is used in the filter plane of a coherent optical correlator. We present here several criteria that can be used to evaluate the usefulness of an operating curve for a filter-plane SLM.

Correlators, as any other sophisticated instrument, must be calibrated and adjusted for proper operation. We explore the necessity and feasibility of several techniques to tune its different elements, having in common that they do not require any external setup. This is accomplished by using the correlator to interrogate itself about the convenience of any modification of its nominal characteristics and thus it allows the correction of time-varying as well as correlator- dependent effects.

In order to implement computer generated holograms (CGHs) and correlation plane filters (CPFs) on an LCTV SLM, the pixel-level complex-amplitude properties of the modulator must be accurately known. These properties must then be incorporated into algorithms for achieving the pixel-level control via a frame grabber (FG) and NTSC video signal. Within this investigation we present techniques for measuring the properties of FG-to-video-to-LCTV system, and then develop an algorithm to allow pixel-level control of the LCTV.

Interferometric techniques have been employed by a number of investigators to determine the phase modulating characteristics of popular spatial light modulators. The technique works well but requires the set-up and operation of a sensitive interferometer. A non-interferometric technique is presented for determining the phase modulating characteristics of spatial light modulators. Examining the far field diffraction pattern distribution for specific input functions allows the phase modulation to be calculated. The degree of phase modulation appears in the Fourier transform as an intensity modulation which can be measured. Results are compared with usual interferometric techniques for a liquid crystal based modulator.

We use a liquid crystal spatial light modulator to construct a computed wave that would have emanated from a hypothetical object that we mathematically specify. The method uses optimal filter theory and realistic devices. We show laboratory results. The method applies to video holograms and small head-up displays. The method was inspired by work using binary reflective SLMs, and we adapted it to a continuously variable and highly coupled operating curve.

A miniature optical pattern recognition (OPR) system is proposed in this paper. We use a multiple channel optical correlator to perform real-time image processing, such as dynamic multiple objects recognition, nonlinear operation of fusion of correlation output, and compression and reconstruction of infrared fingerprint images. The preliminary experimental results show that a two-dimensional optical correlator based on binary optics makes the OPR system to tend to practice.

Design of a compact correlator, using a low power He-Ne laser for obtaining optical phase conjugation in BaTiO₃ crystal, is presented in this paper. The angle between the reference and dc beam is optimized to reduce the dimension of the correlator. The overall size of the correlator is reduced further by using separate read beam.

For military and civil use, it is a key to recognize and track a moving target quickly. In the paper, an automatic tracker with optical correlator is presented. It consists of a joint transform correlator (JTC), a computer interface circuit, a power-amplifier and a CCD camera driven by two stepper motors. Experiments demonstrate that it is very effective for tracking targets.

We demonstrate the implementation of an in-line four-wave mixing correlator using a BSO photorefractive crystal as a dynamic holographic medium. The advantage of this correlator is the perfect overlap of the Fourier transforms of the reference and probe images inside the crystal due to its in-line geometry. Therefore the Bragg diffraction is the only limit to the angle between writing beams. An experimental investigation about the Bragg limitation in the shift invariance of the correlator performance is also presented.

We consider detection (locating all objects in a scene) independent of object distortions and contrast differences and in the presence of clutter. We employ several different new detection algorithms; to reduce false alarms. We fuse (combine) the outputs from different detection algorithms. We describe a new peak sorting detection scoring algorithm and 3 different fusion algorithms to combine the results from different algorithms: binary, analog, and hierarchial fusion. Quantitative data on a distortion-invariant six object class is presented; the objects have a wide range of object contrasts including obscured objects and the objects are present in severe clutter.

We report the implementation and performance of a photorefractive joint transform correlator operating as an optical post-processor of an electronic fingerprint database search/identification system. The approach is as follows: in an initial electronic identification step, a list of possible 'candidates' is extracted from a large database, using standard electronic group-classification techniques. This candidate list is processed by optical correlation for final identification. We present the experimental demonstration of database search using a 3500- fingerprint candidate list. More specifically, we have operated on group-1 fingerprints, for which the lack of bifurcation, center and delta prevents efficient electronic classification. Undistorted fingerprints are unambiguously recognized. In this approach, significant fingerprint distortions can be handled. We discuss the system performance in terms of robustness, speed and efficiency.

We propose an optodigital hybrid fingerprint identification system based on the binary phase extraction joint transform correlator (BPEJTC). It is shown that since the BPEJTC provides higher peak-to-sidelobe ratio than that of the conventional JTC and does not cause correlation peaks due to intra-class association, this system is well-adaptive to the multiple object environments. We show that this system allows the simultaneous comparison of an input fingerprint to several reference fingerprints in a single correlation. Experimental results show that this system has a good performance in the presence of multiple images for the fingerprint identification.

Significant problems with a standard shape based approach to object pose estimation are the size of the database needed and the time it takes to search this database. The problems are compounded with highly symmetric objects whose internal detail must be considered for accurate pose determination. Our approach to object pose estimation is based on the reciprocal basis image set. The method is related to the one that uses a suite of gray-scale images of object for analytical object model representation. By representing the object as a Fourier series using a finite sample set of poses, the object model consisting of a reciprocal basis image set can be determined. When an input image is projected onto the reciprocal image basis, an estimate for the object pose can be obtained from the phase of a complex exponential. This allows a suite of images rotated about an axis to be represented by a reciprocal basis image set. Pose estimation about this axis can then be determined by a linear projection of the input object onto this reciprocal basis. The internal detail of the image is thus maintained through a finite reciprocal basis image set, allowing for accurate post estimation of highly symmetric objects. This method can decrease both computation time and disk space from many standard shape based approaches. Examples illustrating the highly accurate performance of object pose estimation using synthetic armor images based on the reciprocal basis approach are given.

This paper addresses some of the performance issues associated with performing the wavelet transform (WT) using the joint transform correlator (JTC), specifically the phase-only JTC (POJTC). The current POJTC architecture, called the POWJTC, utilizes a single liquid crystal television (LCTV) as a spatial light modulator (SLM) operating only on the phase of the incident coherent light. Many JTC-based WT architectures have used hard-clipped bandpass filters as wavelet functions, filtering the joint transform power spectrum (JTPS) to enhance the correlation SNR for two inputs (not including the wavelet). It has been demonstrated that, by encoding the wavelet and the object to be analyzed in the input plane of the POJTC, a true WT, in the sense that the WT is a correlation integral, can be achieved. However, the correlation output contains many more terms than the normal amplitude-only JTC (AOJTC) that may affect the performance, and there are restrictions associated with this encoding process. A mathematical description based on scalar fields, accompanied by simulations and experimental results, is presented.

A portable optical processor, specially designed for optical wavelet transforms for target detection, has been developed at JPL. The system architecture, engineering design and packaging are presented. A new algorithm development in wavelet filter design is discussed. Demonstration for objection detection using this new approach also is provided.

A high-speed, compact optical correlation system is presented utilizing a tapered-fiber bundle, a holographic ring-wedge detector, and simple optical neural networks. This study includes three standard classes of unclassified military smokes and obscurants, standard liquid aerosol smokes, fibrous obscurants, and brass flakes. Digital and optical implementations of the holographic ring-wedge detector directly coupled into an optical neural network are studied as a means of increasing the speed of the decision process for particle characterization. This method has the ability to simultaneously recognize and distinguish the particle classes included in this study and to give a size range for spherical particles. Experimental data are presented utilizing a holographic ring detector and optical neural network combination for characterizing the particulates included in this study. A single holographic optical element fabricated to perform the same function as a ring detector and a simple two-layer, feedforward optical neural network are evaluated. Future work will include expanding the capabilities of the system to include more particulate types and to develop a field competent system.

This paper deals with the recovery of a scene from a pair of images, where each image is acquired from a different viewpoint. The central problem is the identification of corresponding points in all views. Basically two approaches have evolved: area-based methods, which employ local graylevel correlation techniques; and feature-based methods, which use preprocessing steps to extract local feature vectors and match these entities. Previous work has shown that feature-based methods have advantages both in terms of computational complexity, and accuracy. We extend these comparative studies, which had compared both philosophies, to a new type of feature extraction technique. This technique handles the correspondence problem by matching two sets of dense feature vectors, generated by GABOR filters. Gabor filters have been used previously for recognition of blob-type targets and texture classification. We show how the two techniques can be used as two independent sources to derive feature- vectors. Consequently, fusion of the two sources improves the accuracy of correspondence detection.

Optical pre-processing technique was combined with the two-layer neural network (TLNN), designed as multichannel acousto-optic modulator (MAOM) based optical vector-matrix multiplier (OVMM) by means of the PC interface. The system was applied to invariant recognition of planar objects. Pre-processing was presented by invariant moments based holographic feature extraction method. Optical hardware implementation (with the semiconductor laser and liquid crystal spatial light modulator) was investigated. Several other feature extraction methods (besides invariant moments) were applied and the possibility of the real-time implementation was considered.

Experiments investigating the possibility of optical processing through turbulent media were performed. A liquid crystal television (LCTV) operating in a phase-mostly mode was utilized to simulate turbulence. A phase-switching interferometric technique for removing the phase distortion created by the turbulence was also investigated.

An infrared optical modulation using associative memory technique is addressed. The proposed holographic associative memory is used to replace the optical modulator (reticle) by using a Fourier hologram. The target radiant flux is collected by optical system. A hologram is inserted in the optical path between the optical lens of the optical system and the detector in the focal plane of the lens. When the IR fluxes illuminate the hologram, the hologram redirects the flux to the desired direction. After the energy transferred by the detector arrays, we can get the codes, corresponding to the position of target, from the output of detector arrays by particular arrangement of the redirected radiant flux. Thus, generating the electric signal corresponding to target position in the IR tracking system by optical signal processing becomes easy and effective. Besides providing directional information, it can also be used for background suppression. By use of the optical signal processing and neuron network theorem, the background radiation of the IR system can be suppressed effectively.

The forward Radon transform operating on edge enhanced images is identical to the Hough transform in its (rho) -(phi) parametrization. The inverse operation may be used to recover an image from its projection data, acquired using tomography. Both forward and inverse operations may be efficiently computed by exploiting the central slice theorem, the major computational operations then becoming two dimensional and one dimensional Fourier transformation with an intervening coordinate conversion. The paper describes a non-scanning optical arrangement to implement both the forward and inverse Radon transform which may thus be used to compute both the Hough transform of image data and, by exchanging the input and output sections, the reconstruction of projection data. Simulations of the computation of the Hough transform via the central slice theorem are presented which include pixel interpolation in the polar mapping coordinate conversion to more closely approximate the analogue transformation which may be accomplished by the optical processor.

This study was motivated by the infrared search and tracking (IRST) project. The investigation seeks to develop a technique that could detect the presence of a moving target in a cloud cluttered environment. Particularly, the signals, noise and clutters are unknown to the system. Thus, the correlation technique for image processing was developed, demonstrating its ability to detect moving targets of one pixel in size such as missiles and planes. A real-time image processor using this correlation technique was implemented. A Panoramic Imaging System, a 512 by 480 image processor at 30 frames per second was demonstrated. The demonstrated imaging system was operating at 120 mops (million operations per second) using an assembly- line processor architecture. The successful investigation of the correlation technique for image processing led to the developments of a correlation filter and the inspiration to develop the generalized filter. From the investigation, the author found that the Kalman filter, the Weiner filter and the correlation filter are special cases of a generalized filter. These filters can be related through a cost function in the constrained gain matrix of a generalized filter. However, in developing the correlation filter and the real-time imager, the correlation filter was observed to be a very effective noise and clutter rejecter and yet a very powerful detector. The filter was successfully applied to detection of pixel sized targets in noisy and cluttered IR images. Also it has been successfully applied to detection of intruders in cluttered, trees and bushes, video and IR images in security systems. This paper presents the derivation of the correlation filter for detection and estimation of unknown signals in unknown noise. Several noise rejection and cluttered rejection examples are presented.

A distortion-invariant feature is proposed in this paper, which is based on the normalization polar coordinates of closed nohole space targets' boundary. In order to utilize this proposed feature to recognize distortion targets in 2-D, a dynamic compensation matching method for the target's polar coordinates is put forward. Computer simulation shows this approach has the best distortion-invariant recognition ability.

Recent years were marked by persistent attempts to create a hybrid optoelectronic matrix processor realizing matrix-vector multiplication and having greater throughput than its modern and perspective electronic analogues. An experimental breadboard model of such a processor based on the multichannel acousto-optical modulator intended for processing of radar signals is described, results of mathematical simulation and experimental investigations are presented.

This paper demonstrates the use of the single lens joint transform correlator (SLJTC) to precisely determine the target location for on-axis correlation with the targets superimposed. The SLJTC is a two stage processor with an input stage identical to the chirp-encoded joint transform correlator. The first stage computes the chirp-modulated joint power spectrum. The correlation signal in the chirp-encoded joint power spectrum is an amplitude encoded lens function of Fresnel zone plate. The correlation output is in the focal plane of this zone plate. The location of the center of the zone plate is proportional to the correlation location. The magnification of the correlation plane is determined by the chirp displacement. This is used to amplify small shifts in the correlation location. The SLJTC has been experimentally demonstrated with an output plane magnification of 6.3 and a peak-to-noise ratio of 16.7 dB.