Mapping the mesoscale interface structure in polycrystalline materials

A new experimental approach to the quantitative characterization of polycrystalline microstructure by scanning electron microscopy is described. Combining automated electron backscattering diffraction with conventional scanning contrast imaging and with calibrated serial sectioning, the new method (mesoscale interface mapping system) recovers precision estimates of the 3D idealized aggregate function G(x). This function embodies a description of lattice phase and orientation (limiting resolution approximately 1 degree) at each point x (limiting spatial resolution approximately 100 nm), and, therefore, contains a complete mesoscale description of the interfacial network. The principal challenges of the method, achieving precise spatial registry between adjacent images and adequate distortion correction, are described. A description algorithm for control of the various components of the system is also provided.

A closed-form neural network for discriminatory feature extraction from high-dimensional data

We consider a new neural network for data discrimination in pattern recognition applications. We refer to this as a maximum discriminating feature (MDF) neural network. Its weights are obtained in closed-form, thereby overcoming problems associated with other nonlinear neural networks. It uses neuron activation functions that are dynamically chosen based on the application. It is theoretically shown to provide nonlinear transforms of the input data that are more general than those provided by other nonlinear multilayer perceptron neural network and support-vector machine techniques for cases involving high-dimensional (image) inputs where training data are limited and the classes are not linearly separable. We experimentally verify this on synthetic examples.

Modulation transfer function measurement method for electrically addressed spatial light modulators

The modulation transfer function (MTF), when used with amplitude modulation (m(A)) data, is a vital coherent optical performance measure for a spatial light modulator (SLM). A new image plane amplitude MTF (MTF(A)) measurement method is presented for electrically addressed SLMs. It involves digital analysis of the output image of a square-wave pattern written onto the SLM. Modulation-level effects are also addressed. Optical laboratory results are presented for two liquid-crystal SLMs. The need to consider amplitude rather than intensity modulation (when coherent optical processing applications are considered) is noted in terms of SLM biasing.

Detection filters and algorithm fusion for ATR

Detection involves locating all candidate regions of interest (objects) in a scene independent of the object class with object distortions and contrast differences, etc., present. It is one of the most formidable problems in automatic target recognition, since it involves analysis of every local scene region. We consider new detection algorithms and the fusion of their outputs to reduce the probability of false alarm P(FA) while maintaining high probability of detection P(D). Emphasis is given to detecting obscured targets in infrared imagery.

Nonlinear optical hit-miss transform for detection

Morphological processing involves nonlinear low-level image-processing operations that can be realized on optical processors. Amodified version of the hit-miss morphological transform is described for object detection. Simulation results and optical laboratory realizations are presented. Some of the simple filters required can be realized as ternary-phase-amplitude optical filters.

Morphological and wavelet transforms for object detection and image processing

We consider the problem of detecting multiple distorted objects in an input scene with clutter. The input scenes contain different types of background clutter and multiple objects in different classes, with different object aspect views, different object representations, hot/cold/bimodal/partial object variations, and high/low contrast object variations. Several new optical morphological operations for use in the above detection problem and in other general low-level image-processing applications are described, and several examples of their use are provided. For difficult detection problems in which high detection rates and low false-alarm rates are required we combine morphological operations and optical wavelet transforms to reduce clutter and improve object detection. The details of this set of filters and initial testresults are given. The most computationally demanding operations required in all cases are realizable on an optical correlator.

High-capacity neural networks on nonideal hardware

We present a new training-out algorithm for neural networks that permits good performance on nonideal hardware with limited analog neuron and weight accuracy. Optical neural networks are emphasized with the error sources including nonuniform beam illumination and nonlinear device characteristics. We compensate for processor nonidealities during gated learning (off-line training); thus our algorithm does not require real-time neural networks with adaptive weights. This permits use of high-accuracy nonadaptive weights and reduced hardware complexity. The specific neural network we consider is the Ho-Kashyap associative processor because it provides the largest storage capacity. Simulation results and optical laboratory data are provided. The storage measure we use is the ratio M/N of the number of vectors stored (M) to the dimensionality of the vectors stored (N). We show a storage capacity of M/N = 1.5 on our optical laboratory system with excellent recall accuracy, > 95%. The theoretical maximum storage is M/N = 2 (as N approaches infinity), and thus the storage and performance we demonstrate are impressive considering the processor nonidealities we present. Our techniques can be applied to other neural network algorithms and other nonideal processing hardware.

Multitarget-tracking optical processing system

We consider multitarget tracking, estimating the state vector (two-dimensional position and velocity) of each target from physical measurements. We consider a full system for this and the role for analog optical processing within its subsystems. We emphasize the neural network data-association subsystem (which associates measurements in the present input frame with estimates from previous frames of data). Our new optimization neural net results concern associations between measurements and estimates and show that use of a simple fixed-coefficient estimation filter is sufficient. For completeness in our full system approach we briefly describe our optical detection subsystem and its use to reduce frame-to-frame jitter in the measurements. We also briefly note our Hough-transform optical subsystem and discuss its use in detecting and correcting data dropout errors and errors in the data-association and estimator systems. We conclude that analog optical processing has significant use in a full multitarget tracking system.

One-dimensional collimation of laser array outputs

We consider a computer-generated hologram for the one-dimensional collimation in x of the output from a linear laser-diode array in y. Our concern is to produce one-dimensional pencil beams from each laser diode with small cross talk between the output from the separate laser diodes. Such outputs can be used in matrix-vector, neural net, and interconnection applications. The efficiency and the design of the computer-generated hologram are detailed, and initial optical laboratory results with an electron-beam recorded computer-generated hologram are presented.

High-accuracy pipelined iterative-tree optical multiplication

A high-accuracy optical multiplier that uses an optical correlator is described. A symbolic substitution adder that uses the modified signed-digit number representation is used as the basic module. Emphasis is placed on the multiplication of many long words in parallel with minimum latency. The encoding method we employ in the adders permits the use of a new optical algorithm and architecture to generate partial products in symbolic form in parallel. Our multiplication algorithm and architecture are shown to be preferable to other optical techniques and to be competitive with digital technology; they are also shown to be particularly attractive for matrix-vector multiplication applications.

Symbolic substitution modified signed-digit optical adder

A high-accuracy fixed-point optical adder that operates in parallel on many long words and that uses a pipelined correlator architecture is described. A symbolic substitution algorithm with the modified signed-digit number representation is used to perform fixed-point additions with limited carries. A new set of substitution rules and encodings is developed to combine the recognition and substitution steps into one correlation operation. This reduces hardware requirements, improves throughput by reducing the space-bandwidth product needed, and reduces latency (the delay between when data enter the processor and when the final output is available) by a factor of 2. This algorithm and our new modified signed-digit encodings and substitution rules improve the performance of other correlator and noncorrelator optical numeric computing architectures.

High-speed acousto-optic mapping modulator for the generalized Hough transform

We describe a high-speed acousto-optic Hough-transform mapping modulator. This mapping modulator generates any θ slice of the straight line Hough-transform and one-dimensional slices of generalized Hough transforms (e.g., for circles and ellipses). We derive the mapping functions for the acousto-optic modulator for both circle and ellipse Hough transforms and show simulations of generalized Hough transforms using both functions. We also describe how the mapping modulators can compute Hough transforms for nonanalytically describable inputs.

Optical hit-miss morphological transform

We present an optical correlator implementation of the morphological hit-miss transform. This provides improved recognition of objects in clutter compared with standard optical pattern-recognition correlator techniques. The hit-miss transform is modified to use rank-order filtering since this gives better performance in noise and clutter. By varying the correlation plane threshold, we can perform dilations, rank-order filters, and erosions on the same multifunctional coherent optical correlator system. We quantify the thresholds required for generic object part recognition and provide simulated and optical laboratory data.

Minimum noise and correlation energy optical correlation filter

A new distortion-invariant optical correlation filter to produce easily detectable correlation peaks in the presence of noise and clutter and to provide better intraclass recognition is presented. The basic ideas of the minimum variance synthetic discriminant function correlation filter (which minimizes noise variance in the output correlation peak/plane) and the minimum average correlation energy filter (which minimizes the average correlation plane energy over all the training images) are unified in a new filter that produces sharp correlation peaks while maintaining an acceptable signal-to-noise ratio in the correlation plane output. This new minimum noise and correlation energy filter approach introduces the concept of using the spectral envelope of the training images and the noise power spectrum to obtain a tight bound to the energy minimization problem that is associated with distortion-invariant filters in noise while allowing the user a variable parameter to adjust depending on the noise or clutter that is expected. We present the mathematical basis for the minimum noise and correlation energy filter and the initial simulation results.

Advanced distortion-invariant minimum average correlation energy (MACE) filters

The original minimum average correlation energy (MACE) filter is addressed by using a new database (strategic relocatable objects, missile launchers) and including noise performance, depression angle, and resolution effects on the number of training set images that are required. Major attention is given to our new MACE filter algorithms for distortion-invariant pattern recognition: shifted-MACE filters (to suppress large false correlation peaks), minimum variance-MACE filters (for improved noise performance), multiple symbolic encoded filters (to reduce the effect of false correlation peaks), and Gaussian-MACE filters (to improve noise performance and intraclass recognition and reduce the training set size).

Optical correlator production system neural net

A new neural net is described that can easily and cost-effectively accommodate multiple objects in the field of view in parallel. The use of a correlator achieves shift invariance and accommodates multiple objects in parallel. Distortion-invariant filters provide aspect-invariant distortion. Symbolic encoding, the use of generic object parts, and a production system neural net allow large class problems to be addressed. Optical laboratory data on the production system inputs are provided and emphasized. Test data assume binary inputs, although analog (probability) input neurons are possible.

Multitarget data association using an optical neural network

A neural network solution to the data association problem in multitarget tracking is presented. It uses position and velocity measurements of the targets over two consecutive time frames. A quadratic neural energy function, which is suitable for an optical processing implementation, results. Simulation resultsusing realistic target trajectories with target measurement noise including platform movement or jitter are presented. The results show that the network performs well when track data are corrupted by significant noise. Several possible optical neural network architectures to implement this algorithm are discussed, including a new all-optical matrix-vector multiplication approach. The matrix structure is employed to allow binary-ternary spatial light modulators to be used.

Circular-harmonic function, minimum average correlation energy filters

New distortion-invariant correlation filters for in-plane rotation invariance are considered. These use circular-harmonic functions combined with minimum-average correlation-plane filter techniques. Various circular-harmonic function shortcomings are quantified.

Gaussian-minimum average correlation energy filters

Correlation filters with sharp delta-function correlation peaks [such as phase-only filters and minimum average correlation energy (MACE) filters] do not recognize images on which they are not trained. We show that the MACE filter cannot always recognize intermediate images of true class objects (e.g., aspect views or rotations midway between two training images). New Gaussian-MACE filters offer a solution to this problem.

New algorithm for analog optical matrix inversion

A new matrix inversion algorithm is described. It provides a meaningful estimate of the inverse A(-1) of a matrix A on an analog optical processor in a reduced calculation time (compared to other methods). The new nested iterative algorithm has no convergence conditions on the matrix and requires fewer operations than prior iterative neural net and other algorithms.

Optical interpolation and differencing of 2-D image data

We present a new 1-D acoustooptic architecture to subtract two signals that are subpixel shifted. The architecture allows for optical interpolation and electrical control of the shift between frames. We demonstrate the use of 1-D projections of 2-D image frames to achieve subpixel shifts and interpolation between successive image frames for the purpose of detecting and tracking subpixel sized targets.

Optical neural net for matrix inversion

A novel optical neural net for performing matrix inversion is presented. This algorithm does not suffer from accumulative round-off error. Various optical architectures are introduced, and the circumstances in which each of them is advantageous are investigated.

Updating optical pseudoinverse associative memories

Selected algorithms for adding to and deleting from optical pseudoinverse associative memories are presented and compared. New realizations of pseudoinverse updating methods using vector inner product matrix bordering and reduced-dimensionality Karhunen-Loeve approximations (which have been used for updating optical filters) are described in the context of associative memories. Greville's theorem is reviewed and compared with the Widrow-Hoff algorithm. Kohonen's gradient projection method is expressed in a different form suitable for optical implementation. The data matrix memory is also discussed for comparison purposes. Memory size, speed and ease of updating, and key vector requirements are the comparison criteria used.

Key and recollection vector effects on heteroassociative memory performance

Most associative memory work has concentrated on autoassociative memories (AAMs). These associative processors provide reduced noise and error correction in their output data. We will consider heteroassociative memories (HAMs), which are needed to provide decisions on the class of the input data and inferences for subsequent processing. We derive new equations for the storage capacity and noise performance of HAMs, emphasize how they differ from those derived for AAMs, suggest new performance measures to be used, and show how different recollection vector encodings can improve HAM performance.

Optical production systems using neural networks and symbolic substitution

Two optical implementations of production systems are advanced. The production systems operate on a knowledge base where facts and rules are encoded as formulas in propositional calculus. The first implementation is a binary neural network. An analog neural network is used to include reasoning with uncertainties. The second implementation uses a new optical symbolic substitution correlator. This implementation is useful when a set of similar situations has to be handled in parallel on one processor.

Industrial use of a real-time optical inspection system

Real-time optical inspection techniques are discussed and implemented on laboratory systems. Specifically, we show how Fourier transform and Hough transform data can be used in an industrial inspection application. We also discuss how a 1-D synthetic discriminant function is used for label inspection. Real-time optical Hough transform inspection data using a 2-D spatial light modulator is presented and discussed. A color liquid crystal television (LCTV) is used as the input transducer to provide real-time data. New methods to process color image data on color LCTVs are detailed. A new high speed acoustooptic architecture to generate Hough transform slices is also detailed. A specific product inspection case study is discussed.

Optical symbolic substitution for morphological transformations

An optical architecture that uses symbolic substitution to perform morphological transformations is proposed. It is shown how the four basic morphological transformation operations can be posed as symbolic substitution problems. Representative examples of the application of morphological transformations to image processing are given.

Hough transform projections and slices for object discrimination and distortion estimation

A new technique for determining the distortion parameters (location, orientation, and scale) of general 2-D objects is introduced. It uses the straight-line Hough transform as a feature space. The technique is very efficient and robust, since the dimensionality of the feature space is low and since it uses input images directly (with no preprocessing such as segmentation). Because the feature space allows separation of translation and rotation effects, a hierarchical algorithm to discriminate among objects and to detect object rotation and translation using projections and slices of the Hough space is possible.

Real-time optical laboratory solution of parabolic differential equations

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Reduced sensitivity algorithm for optical processors using constraints and ridge regression

Optical linear algebra processors that involve solutions of linear algebraic equations have significant potential in adaptive and inference machines. We present an algorithm that includes constraints on the accuracy of the processor and improves the accuracy of the results obtained from such analog processors. The constraint algorithm matches the problem to the accuracy of the processor. Calculation of the adaptive weights in a phased array radar is used as a case study. Simulation results prove the benefits advertised. The desensitization of the calculated weights to computational errors in the processor is quantified. Ridge regression isused to determine the parameter needed in the algorithm.

Directed graph for adaptive organization and learning of a knowledge base

A directed graph is considered for organization of a knowledge base for neural, associative, model-based, and other advanced processors. Its ability to self-organize itself, delete old information, and add new information and its many interconnections make it most suitable for optical realization and use in advanced neural and adaptive optical processors. An alphanumeric image space example is used as a case study, and an optical processor architecture to achieve this with impressive performance is discussed.

Rule-based symbolic processor for object recognition

The application of symbolic processing and rule-based methods for target recognition using correlation filters is considered. The concept of partitioning images is introduced, and its advantages are described. Techniques for rule development, symbolic substitution, error correction via associative processing, and on-line filter adaptation are advanced. Initial simulation results are also presented and discussed.

Optical associative processor for general linear transformations

A new technique for the realization of general linear transformations using associative memories is described. An optical architecture for its implementation is also presented. A low-level feature space processor using this architecture is proposed. The processor is capable of recognizing and locating objects of various shapes and uses certain linear transformations in the feature space for distortion invariance.

Minimum average correlation energy filters

The synthesis of a new category of spatial filters that produces sharp output correlation peaks with controlled peak values is considered. The sharp nature of the correlation peak is the major feature emphasized, since it facilitates target detection. Since these filters minimize the average correlation plane energy as the first step in filter synthesis, we refer to them as minimum average correlation energy filters. Experimental laboratory results from optical implementation of the filters are also presented and discussed.

Optical iconic filters for large class recognition

Approaches are advanced for pattern recognition when a large number of classes must be identified. Multilevel encoded multiple-iconic filters are considered for this problem. Hierarchical arrangements of iconic filters and/or preprocessing stages are described. A theoretical basis for the sidelobe level and noise effects of filters designed for large class problems is advanced. Experimental data are provided for an optical character recognition case study.

Model-based knowledge-based optical processors

An efficient 3-D object-centered knowledge base is described. The ability to on-line generate a 2-D image projection or range image for any object/viewer orientation from this knowledge base is addressed. Applications of this knowledge base in associative processors and symbolic correlators are then discussed. Initial test results are presented for a multiple degree of freedom object recognition problem. These include new techniques to achieve object orientation information and two new associative memory matrix formulations.

Error-correction coding in an associative processor

A technique for encoding binary outputs from optical filters or matrix memories used in an associative processor for object recognition is discussed. Binary coded output vectors (rather than unit vectors) are used and considerably improve storage capacity. The output codes or matrix memories are chosen from coding theory to enable error correction and detection. The error classification rate for the coded scheme is compared to the noncoded version for different amounts of noise in the input and output planes. Discussion of extensions to more classes, more errors, and multilevel coding are included.

Real-time deformation invariant optical pattern recognition using coordinate transformations

The well-known scale and rotation invariant polar-logarithmic coordinate transformation is used to achieve in-plane distortion invariant pattern recognition. The coordinate transform is produced by a computergenerated hologram on a laser printer. Attention is given to weighting terms in the output and their effect on resolution and the number of input plane pixels removed near the origin. The optically produced coordinate transformed input pattern is interfaced to a correlator by a pocket liquid crystal TV to provide real-time processing. Experimental results are included.

Detection of target trajectories using the Hough transform

Recently developed Hough transform techniques for curved object detection are applied to the detection of target trajectories. Multitarget missile trajectories are considered with noise present and missing data.

Phase correction of light modulators

A new and inexpensive holographic technique for measuring the phase errors of a two-dimensional spatial light modulator (SLM) is described, and experimental verification is provided. A new technique to correct spatial phase errors in any SLM is then detailed and experimentally demonstrated. This technique is employed for the Radio Shack liquid-crystal television SLM, and a shift-invariant correlator is obtained. Additional low-pass filtering techniques (appropriate for any SLM with a fixed pattern of modulating cells) are discussed that provide improved contrast and achieve proper correlations.

Frequency-domain synthesis of modified matched spatial filters

Modified matched spatial filters capable of recognition and discrimination are described. Synthesis of these filters in the frequency rather than the space domain is considered. Synthesis of a deconvolution and a binary frequency filter are discussed, and initial results are presented.

Optical linear algebra processors: noise and error-source modeling

The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.