Unified synthetic discriminant function computational formulation

Design of an optical linear-discriminant filter: optimization for enhancement of filter transmittance and discrimination accuracy

To discriminate fine concave and convex defects on a dielectric substrate, an optical machine learning system is proposed. This system comprises an optical linear-discriminant filter (OLDF) that performs linear discriminant analysis (LDA) of the scattered-wave distribution from target samples. However, the filter output from the OLDF is considerably weak and cannot be measured experimentally. Therefore, an algorithm is also proposed to improve the discrimination accuracy and filter transmittance. The designed filter is validated using a rigorous optical simulator based on vector diffraction theory. We also analyze and discuss a mechanism that provides high transmittance with high discrimination accuracy.

Design of an optical linear discriminant filter for classification of subwavelength concave and convex defects on dielectric substrates

Identification of the defect type on substrate materials is essential for enhancing their yield ratio. We propose a novel optical filter to discriminate between subwavelength-order concave and convex defects on flat surfaces. This filter performs Fisher's linear discriminant analysis using light wave diffraction. The defect type is discriminated by simply comparing the irradiance at an observation point with the threshold value. Neither the defect image nor phase data, nor a large amount of data processing by a computer, is necessary. Numerical discrimination simulations indicate a discrimination error of 0.85%, and the noise tolerance of the proposed system is also discussed.

Trends in correlation-based pattern recognition and tracking in forward-looking infrared imagery

In this paper, we review the recent trends and advancements on correlation-based pattern recognition and tracking in forward-looking infrared (FLIR) imagery. In particular, we discuss matched filter-based correlation techniques for target detection and tracking which are widely used for various real time applications. We analyze and present test results involving recently reported matched filters such as the maximum average correlation height (MACH) filter and its variants, and distance classifier correlation filter (DCCF) and its variants. Test results are presented for both single/multiple target detection and tracking using various real-life FLIR image sequences.

Half a century of optics in computing--a personal perspective [Invited]

Optical signal processing and computing was triggered by the invention of the laser. Starting practically in 1960, it really took off with the introduction of the spatial-matched filter in 1964. Almost half a century later, research and engineering activity in the field continues unabated but in directions that could not have been anticipated in those early days. This paper presents an overview of the developments in the field, discussing the advantages, disadvantages, and limitations of optics in computing paradigms to indicate where and how optics can be exploited in this area. Initially, optical methods were introduced for processing analog signals. Early attempts to extend optical methods toward digital processing failed because the differences between photons and electrons were not properly appreciated. In the last part of the paper we show that some novel concepts and advanced technology may revitalize also optical processes within the digital computing world. This latter development is demonstrated by digital logic functions implemented on simple electro-optic networks. (My personal perspective on the role of optics in computing is deeply rooted in many years of collaboration with my late friend, H. John Caulfield, and I dedicate this paper to his memory.).

Method of synthesized phase objects for pattern recognition: matched filtering

To solve the pattern recognition problem, a method of synthesized phase objects is suggested. The essence of the suggested method is that synthesized phase objects are used instead of real amplitude objects. The former is object-dependent phase distributions calculated using the iterative Fourier-transform (IFT) algorithm. The method is experimentally studied with a Vander Lugt optical-digital 4F-correlator. We present the comparative analysis of recognition results using conventional and proposed methods, estimate the sensitivity of the latter to distortions of the structure of objects, and determine the applicability limits. It is demonstrated that the proposed method allows one: (а) to simplify the procedure of choice of recognition signs (criteria); (b) to obtain one-type δ-like recognition signals irrespective of the type of objects; (с) to improve signal-to-noise ratio (SNR) for correlation signals by 20 - 30 dB on average. The spatial separation of the Fourier-spectra of objects and optical noises of the correlator by means of the superposition of the phase grating on recognition objects at the recording of holographic filters and at the matched filtering has additionally improved SNR (>10 dB) for correlation signals. To introduce recognition objects in the correlator, we use a SLM LC-R 2500 device. Matched filters are recorded on a self-developing photopolymer.

Performance assessment of the modified-hybrid optical neural network filter

We present in detail the recorded results of the modified-hybrid optical neural network (M-HONN) filter during a full series of tests to examine its robustness and overall performance for object recognition tasks. We test the M-HONN filter for its detectability and peak sharpness with within-class distortion of the input object, its discrimination ability between an in-class and out-of-class object, and its performance with cluttered images of the true-class object. The M-HONN filter is found to exhibit good detectability, an ability to maintain its correlation-peak sharpness throughout the recorded tests, good discrimination ability, and an ability to detect the true-class object within cluttered input images. Additionally we observe the M-HONN filter's performance within the tests in comparison with the constrained-hybrid optical neural network filter for the first three series of tests and the synthetic discriminant function-maximum average correlation height filter for the fourth set of tests.

Adaptive phase-input joint transform correlator

An adaptive phase-input joint transform correlator for pattern recognition is presented. The input of the system is two phase-only images: input scene and reference. The reference image is generated with a new iterative algorithm using phase-only synthetic discriminant functions. The algorithm takes into account calibration lookup tables of all optoelectronics elements used in optodigital experiments. The designed adaptive phase-input joint transform correlator is able to reliably detect a target and its distorted versions embedded into a cluttered background. Computer simulations are provided and compared with those of various existing joint transform correlators in terms of discrimination capability, tolerance to input additive noise, and to small geometric image distortions. Experimental optodigital results are also provided and discussed.

Integrated approach for automatic target recognition using a network of collaborative sensors

We introduce what is believed to be a novel concept by which several sensors with automatic target recognition (ATR) capability collaborate to recognize objects. Such an approach would be suitable for netted systems in which the sensors and platforms can coordinate to optimize end-to-end performance. We use correlation filtering techniques to facilitate the development of the concept, although other ATR algorithms may be easily substituted. Essentially, a self-configuring geometry of netted platforms is proposed that positions the sensors optimally with respect to each other, and takes into account the interactions among the sensor, the recognition algorithms, and the classes of the objects to be recognized. We show how such a paradigm optimizes overall performance, and illustrate the collaborative ATR scheme for recognizing targets in synthetic aperture radar imagery by using viewing position as a sensor parameter.

Pattern recognition with an adaptive joint transform correlator

An adaptive joint transform correlator for real-time pattern recognition is presented. A reference image for the correlator is generated with a new iterative algorithm. The training algorithm is based on synthetic discriminant functions. The obtained reference image contains the information needed to reliably discriminate a target against known false objects and a cluttered background. Calibration lookup tables of all optoelectronics elements used are included in the design of the adaptive joint transform correlator. Two methods for the implementation of the proposed joint transform correlator in an optodigital setup are considered. Experimental results are provided and compared with those of computer simulations.

Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition

We present an overview of three-dimensional (3D) object recognition techniques that use active sensing by interferometric imaging (digital holography) and passive sensing by integral imaging. We describe how each technique can be used to retrieve the depth information of a 3D scene and how this information can then be used for 3D object recognition. We explore various algorithms for 3D recognition such as nonlinear correlation and target distortion tolerance. We also provide a comparison of the advantages and disadvantages of the two techniques.

Maximum likelihood localization of 2-D patterns in the Gauss-Laguerre Transform domain: theoretic framework and preliminary results

Usual approaches to localization, i.e., joint estimation of position, orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures, which allow for position estimation independent of scale and orientation. In this paper a Maximum Likelihood method for pattern localization working in the Gauss-Laguerre Transform (GLT) domain is presented. The GLT is based on an orthogonal family of Circular Harmonic Functions with specific radial profiles, which permits optimum joint estimation of position and scale/rotation parameters looking at the maxima of a "Gauss-Laguerre Likelihood Map." The Fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the Cramer Rao Lower Bound. Application of the ML estimation method is discussed and an example is provided.

Pose estimation from a two-dimensional view by use of composite correlation filters and neural networks

We present a technique to estimate the pose of a three-dimensional object from a two-dimensional view. We first compute the correlation between the unknown image and several synthetic-discriminant-function filters constructed with known views of the object. We consider both linear and nonlinear correlations. The filters are constructed in such a way that the obtained correlation values depend on the pose parameters. We show that this dependence is not perfectly linear, in particular for nonlinear correlation. Therefore we use a two-layer neural network to retrieve the pose parameters from the correlation values. We demonstrate the technique by simultaneously estimating the in-plane and out-of-plane orientations of an airplane within an 8-deg portion. We show that a nonlinear correlation is necessary to identify the object and also to estimate its pose. On the other hand, linear correlation is more accurate and more robust. A combination of linear and nonlinear correlations gives the best results.

Pattern recognition with a digital holographic microscope working in partially coherent illumination

We describe the implementation of the automatic spatial-frequency-selection filter for recognition of patterns obtained with a digital holographic microscope working with a partially coherent source. The microscope provides the complex-optical-amplitude field that allows a refocusing plane-by-plane of the sample under investigation by numerical computation of the optical propagation. By inserting a correlation filter in the propagation equation, the correlation between the filter and the propagated optical field is obtained. In this way, the pattern is located in the direction of the optical axis. Owing to the very weak noise level generated by the partially coherent source, the correlation process is shift invariant. Therefore the samples can be located in the three dimensions. To have a robust recognition process, a generalized version of the automatic spatial-frequency-selection filters has been implemented. The method is experimentally demonstrated in a two-class problem for the recognition of protein crystals.

Image recognition in the presence of non-Gaussian noise with unknown statistics

We design receivers to detect a known pattern or a reference signal in the presence of very general and non-Gaussian types of noise. Three sources of input-noise degradation are considered: additive, multiplicative, and disjoint background. The detection process involves two steps: (1) estimation of the relevant noise parameters within the framework of hypothesis testing and (2) maximizing a certain metric that measures the likelihood of the target being at a given location. The parameter estimation portion is carried out by moment-matching techniques. Because of the number of unknown parameters and the fact that various types of input-noise processes are non-Gaussian, the methods that are used to estimate these parameters differ from the standard methods of maximizing the likelihood function. To verify the existence of the target at a certain location, we use l(p)-norm metric for p > or = 0 to measure the likelihood of the target being present at the location of interest. Computer simulations are used to show that for the images tested here, the receivers designed herein perform better than some existing receivers.

Projection-invariant pattern recognition with logarithmic harmonic function and wavelet transform

A logarithmic harmonic filter can detect objects at different projection angles. The Mexican-hat wavelet function can extract edges of equal width for objects, regardless of their sizes. Hence incorporating wavelet filtering in the logarithmic harmonic filter can improve its performance. The theory is presented together with computer simulation. Finally, an experiment using a joint transform correlator is presented to verify the capability of the proposed filter.

Noise robustness of nonlinear filters for image recognition

We analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise ratio (SNR). We obtain a range of nonlinearities for which SNR is robust to the variations in input-noise bandwidth. This is shown both by analytical estimates of the SNR for nonlinear filters and by experimental simulations. Specifically, we analyze the SNR when Fourier plane nonlinearity is applied to the input signal. Using the Karhunen-Loève series expansion of the noise process, we obtain precise analytic expressions of the SNR for Fourier plane nonlinear filters in the presence of various types of additive-noise processes. We find a range of nonlinearities that need to be applied that keep the output SNR of the filter stable relative to changes in the noise bandwidth.

Distortion-tolerant three-dimensional object recognition with digital holography

We present a technique to implement three-dimensional (3-D) object recognition based on phase-shift digital holography. We use a nonlinear composite correlation filter to achieve distortion tolerance. We take advantage of the properties of holograms to make the composite filter by using one single hologram. Experiments are presented to illustrate the recognition of a 3-D object in the presence of out-of-plane rotation and longitudinal shift along the z axis.

Cascaded linear shift-invariant processors in optical pattern recognition

We study a cascade of linear shift-invariant processing modules (correlators), each augmented with a nonlinear threshold as a means to increase the performance of high-speed optical pattern recognition. This configuration is a special class of multilayer, feed-forward neural networks and has been proposed in the literature as a relatively fast best-guess classifier. However, it seems that, although cascaded correlation has been proposed in a number of specific pattern recognition problems, the importance of the configuration has been largely overlooked. We prove that the cascaded architecture is the exact structure that must be adopted if a multilayer feed-forward neural network is trained to produce a shift-invariant output. In contrast with more generalized multilayer networks, the approach is easily implemented in practice with optical techniques and is therefore ideally suited to the high-speed analysis of large images. We have trained a digital model of the system using a modified backpropagation algorithm with optimization using simulated annealing techniques. The resulting cascade has been applied to a defect recognition problem in the canning industry as a benchmark for comparison against a standard linear correlation filter, the minimum average correlation energy (MACE) filter. We show that the nonlinear performance of the cascade is a significant improvement over that of the linear MACE filter in this case.

Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics

We develop algorithms to detect a known pattern or a reference signal in the presence of additive, disjoint background, and multiplicative white Gaussian noise with unknown statistics. The presence of three different types of noise processes with unknown statistics presents difficulties in estimating the unknown parameters. The standard methods such as expected-maximization-type algorithms are iterative, and in the framework of hypothesis testing they are time-consuming, because corresponding to each hypothesis one must estimate a set of parameters. Other standard methods such as setting the gradient of the likelihood function with respect to the unknown parameters will lead to a nonlinear system of equations that do not have a closed-form solution and require iterative methods. We develop an approach to overcome these handicaps and derive algorithms to detect a known object. We present new methods to estimate unknown parameters within the framework of hypothesis testing. The methods that we present are direct and provide closed-form estimates of the unknown parameters. Computer simulations are used to show that for the images tested, the receivers that we have designed perform better than existing receivers.

Review: automatic particle detection in electron microscopy

Advances in cryoEM and single-particle reconstruction have led to results at increasingly high resolutions. However, to sustain continuing improvements in resolution it will be necessary to increase the number of particles included in performing the reconstructions. Manual selection of particles, even when assisted by computer preselection, is a bottleneck that will become significant as single-particle reconstructions are scaled up to achieve near-atomic resolutions. This review describes various approaches that have been developed to address the problem of automatic particle selection. The principal conclusions that have been drawn from the results so far are: (1) cross-correlation with a reference image ("matched filtering") is an effective way to identify candidate particles, but it is inherently unable to avoid also selecting false particles; (2) false positives can be eliminated efficiently on the basis of estimates of particle size, density, and texture; (3) successful application of edge detection (or contouring) to particle identification may require improvements over currently available methods; and (4) neural network techniques, while computationally expensive, must also be investigated as a technology for eliminating false particles.

Statistical performance of cascaded linear shift-invariant processing

The cascaded correlator architecture comprises a series of traditional linear correlators separated by nonlinear threshold functions, trained with neural-network techniques. We investigate the shift-invariant classification performance of cascaded correlators in comparison with optimum Bayes classifiers. Inputs are formulated as randomly generated sample members of known statistical class distributions. It is shown that when the separability of true and false classes is varied in both the first and the second orders, the two-stage cascaded correlator shows performance similar to that of the optimum quadratic Bayes classifier throughout the studied range. It is shown that this is due to the similar decision boundaries implemented by the two nonlinear classifiers.

Gray-level computer-generated hologram filters for multiple-object correlation

Synthesis of gray-level computer-generated holograms allows for an increase of the information storage capability that is usually achieved with conventional binary filters. This is mainly because more degrees of freedom are available. We propose to profit from this feature by synthesizing complex filters formed by many superimposed holograms, each with a different carrier frequency. We apply these gray-level filters to perform multichannel correlation and in this way enhance the capability of optical correlators to process the information in parallel and simultaneously. First, we analyze the behavior of some performance criteria on the impulse response and on the correlation as a function of the number of holograms that are multiplexed. Then we show the results of two experiments: In the first a composed phase-only filter is used in a multiple-object recognition process. In the second a composed synthetic discriminant function filter is used to implement an object classification by means of a binary code.

One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator

We present an architecture in which a multichannel correlator can perform simultaneous optical pattern recognition. Processing in parallel is made possible by use of the different diffraction orders produced by the pixelated structure of the liquid-crystal spatial light modulator employed to display the input scene. We codify additional quadratic phases in the filters to separate the correlation information corresponding to each channel. We demonstrate that the system can recognize different targets simultaneously. Good agreement between experimental and numerically simulated results is obtained.

One-dimensional logarithmic harmonic synthetic discriminant function filters for shift-, scale-, and projection-invariant pattern recognition

We introduce a new approach for shift-, scale-, and projection-invariant pattern recognition that combines the harmonic expansion and the synthetic discriminant function approaches by use of a synthetic discriminant function filter with equal-order one-dimensional logarithmic harmonic components. Because projection invariance in one direction is guaranteed by the harmonics, the required number of training images is much fewer than with classical synthetic discriminant function filters.

Sidelobeless multiple-object discriminant filters recorded as discrete-type computer-generated holograms

The computer generation of sidelobeless multiple-object discriminant correlation filters has been stressed. We propose to synthesize the filter functions by use of the simulated-annealing algorithm. By this method the filters can be obtained as discrete-type computer-generated holograms. The filters can suppress the sidelobes and provide sharp correlation peaks. A computer simulation and an optical experiment were performed, and the expected correlation responses were obtained.

Distortion-invariant fringe-adjusted joint transform correlation

A distortion-invariant joint transform correlator based on the concepts of the fringe-adjusted joint transform correlator and the synthetic discriminant function is presented. Computer-simulation results show that the proposed joint transform correlator is distortion-invariant for the target image from the training set and produces sharper correlation peaks and lower sidelobes compared with the classical joint transform correlator.

Partial rotation-invariant pattern matching and face recognition with a joint transform correlator

We describe the circular-harmonic (CH) image CH(mr), which is based on CH components for rotationally invariant pattern recognition. CH components of the order m, derived from an image in polar coordinates, are used to form a two-dimensional space together with the radial variable r. Filtering the CH(mr) image leads to a reference image with some rotational invariance. For a narrow-pass filter we have a single CH component with full rotation invariance; for an all-pass filter we have the original image with no rotational invariance; for a low-pass filter we form a reference image containing multiple circular harmonics with partial rotation invariance. Results of numerical simulations and optical experiments with a joint transform correlator are given that illustrate partial-rotation-invariant recognition for human face images.

Implementation of arbitrary real-valued correlation filters for the shadow-casting incoherent correlator

We describe an incoherent correlator, based on the shadow-casting principle, that is able to implement any real-valued linear correlation filter. The correlation filter and the input image are displayed on commercial liquid-crystal television (LCTV) panels. Although it cannot handle high-resolution images, the incoherent correlator is lensless, compact, low cost, and uses a white-light source. A bipolar technique is devised to represent any linear filter, computed from a single reference image or composite, in the correlator. We demonstrate experimentally the efficiency of the design in the case of optimal trade-off (OT) filters and optimal trade-off synthetic discriminant function (OT-SDF) filters.

Nonlinear cascaded correlation processes to improve the performances of automatic spatial-frequency-selective filters in pattern recognition

A recognition process consisting of two cascaded correlation stages with a sigmoid nonlinearity applied in the first correlation plane is investigated. The filters are computed to give prespecified central correlation amplitudes in the second correlation plane when inputs are reference images. It is also desired that the second correlation amplitudes with the training images should minimize the cost function of the automatic spatial-frequency selection algorithm to reduce distortion sensitivity and to improve the performance of the filters. Filter computation methods are given, and it is shown why two such correlation processes may improve the correlation performance. Numerical simulations are described and compared with the one-stage correlation system that works with the automatic spatial-frequency selection filter.

Convolution-kernel-based optimal trade-off filters for optical pattern recognition

An architecture for the implementation of optical pattern recognition is proposed that makes use of convolution-kernel-based optimal trade-off filters to allow for an increased speed of operation and filter storage capability. The derivation of these new convolution-kernel-based optimal trade-off filters is presented, and their noise robustness and discrimination capabilities are discussed.

Synthetic circular-harmonic phase-only filter for shift, rotation, and scaling-invariant correlation

A synthetic circular-harmonic phase-only filter is described. With this filter and a Fourier-transform correlator it is possible to obtain shift, rotation, and scaling-invariant correlations.

Filter-feature-based rotation-invariant joint Fourier transform correlator

Rotation-invariant target detection using a trained filter-feature-based joint Fourier transform (JFT) correlator is investigated. First, a composite reference image is obtained from a training set of targets. An optimum filter formulation is then applied on this composite image to come up with a new feature that we refer to as a filter feature. This feature is then used in a JFT correlator, which results in a simple and robust rotation-invariant target recognition system.

Multilevel phase- and amplitude-encoded modified-filter synthetic-discriminant-function filters

The performance of the modified-filter synthetic-discriminant-function (MfSDF) filter with multilevel phase and amplitude (MLAP) constraints is investigated with various in-plane rotated images from an in-class Bradley armored personnel carrier vehicle and an out-of-class Abram MI tank; this is of interest because of the commercial availability of liquid-crystal televisions, which are able to encode the gray-level amplitude and/or the discrete multilevel phase information. The evaluation is performed to explain better the image-distortion range that can be covered effectively by MLAP/MfSDF filters. The results show that the MLAP/MfSDF filter offers much-improved correlator system performance with a greater allowable image-distortion range while maintaining 100% discrimination between in-class and out-ofclass images; furthermore, it shows an improved ability to accommodate the input image noise when compared with the MfSDF filter with a binary phase-only constraint. Thus the MLAP/MfSDF can be implemented effectively by a hybrid optical/digital correlator system to track a vehicle or a tank dynamically as it moves along a random trajectory across the input field.

Performance of an optimum receiver designed for pattern recognition with nonoverlapping target and scene noise

The design of an optimum receiver for pattern recognition is based on multiple-alternative hypothesis testing with unknown parameters for detecting and locating a noisy target or a noise-free target in scene noise that is spatially nonoverlapping with this target. The optimum receiver designed for a noise-free target has the interesting property of detecting, without error, a noise-free target that has unknown illumination by using operations that are independent of the scene-noise statistics. We investigate the performance of the optimum receiver designed for nonoverlapping target and scene noise in terms of rotation and scale sensitivity of the input targets and discrimination against similar objects. Because it is not possible in practical systems to have a completely noise-free target, we examine how the performance of the optimum receiver designed for a noise-free target is affected when there is some overlapping noise on the target. The application of the optimum receiver to binary character recognition is described. Computer simulation results are provided.

Design of a bipolar composite filter by a simulated annealing algorithm

We present the design of a bipolar composite filter (BCF) by a simulated annealing algorithm. By minimizing the energy function of the system, we construct an out-of-plane rotation-invariant bipolar filter. We show that the BCF offers high pattern discrimination capability and can easily be implemented with an electronically addressed spatial light modulator.

Computer-generated multiple-object discriminant correlation filters: design by simulated annealing

The computer generation of multiple-object discriminant correlation filters is studied. The quantization of filter functions influences the correlation response. This may cause misdetection or incorrect classification of patterns and is especially serious in the case of multiple-object discriminant filters. We propose synthesizing the matched-filter functions by the simulated-annealing algorithm. The recording of Lohmann-type computer-generated holograms is considered. By this method the filter functions can be encoded with a reduction in the quantization levels of amplitude and phase. Acomputer simulation is performed, and the expected correlation responses are obtained.

Optical correlation: influence of the coding of the input image

We analyze the influence of different optical coding methods of the input image in optical correlators. The noise robustness and the optical efficiency of the correlator are investigated. We show in particular that the signal-to-noise ratio is greatly dependent on the coding method. It decreases drastically for large phase modulation.

Unconstrained correlation filters

A mathematical analysis of the distortion tolerance in correlation filters is presented. A good measure for distortion performance is shown to be a generalization of the minimum average correlation energy criterion. To optimize the filter's performance, we remove the usual hard constraints on the outputs in the synthetic discriminant function formulation. The resulting filters exhibit superior distortion tolerance while retaining the attractive features of their predecessors such as the minimum average correlation energy filter and the minimum variance synthetic discriminant function filter. The proposed theory also unifies several existing approaches and examines the relationship between different formulations. The proposed filter design algorithm requires only simple statistical parameters and the inversion of diagonal matrices, which makes it attractive from a computational standpoint. Several properties of these filters are discussed with illustrative examples.

Application of correlation filters for texture recognition

We propose a new statistical method to design spatial filters to recognize and to discriminate between various textures. Unlike existing correlation filters, the proposed filters are not meant to recognize specific shapes or objects. Rather, they discriminate between textures such as terrains, background surfaces, and random image fields. The filters do not require any on-line statistical computations for extracting texture information. Therefore optical (or digital) correlators can be used for fast real-time texture recognition without segmentation. The procedure is based on the assumption that textures can be modeled as stationary random processes over limited regions of an image. The optimum filter coefficients are determined by use of eigenvector analysis. Several examples are given to illustrate the proposed scheme.

Random mask encoding of multiplexed phase-only and binary phase-only filters

In the formation of multiplexed filters, the phase-only and binary phase-only operations result in spurious cross terms and a nonlinear scaling. We use complementary random binary patterns having different pattern densities to encode the various functions within the multiplexed function. The orthogonality of these complementary masks permits separability of the phase-only or binary phase-only operations. By changing the pixel density of the random pattern, we can easily change the relative weights of the functions that compose the multiplexed filter. Experimental results are shown that demonstrate the effectiveness of this approach.

Automatic spatial frequency selection algorithm for pattern recognition by correlation

We describe an approach to compute filters that automatically performs a spatial frequency selection to improve interclass discrimination and to reduce intraclass sensitivity. This approach is achieved by using as input to the filter synthesis a set of reference images to compute the filters and a set of distorted images to introduce the distortion or noise model of the reference images. Simulation results of correlation examples are provided for two pattern-recognition problems and are compared with the ones obtained with the standard minimum average correlation energy filters.