This paper details the effect of spatial resolution on target discrimination in Synthetic Aperture Radar (SAR) images.
Multiple SAR image chips, containing targets and non-targets, are used to test a baseline Automatic Target Recognition
(ATR) system with reduced spatial resolution obtained by lowering the pixel count or synthesizing a degraded image.
The pixel count is lowered by averaging groups of adjoining pixels to form a new single value. The degraded image is
synthesized by low-pass-filtering the image frequency space and then lowering the pixel count. To train a linear
classifier, a two-parameter Constant False Alarm Rate (CFAR) detector is tested, and three different types of feature
spaces, are used: size, contrast, and texture. The results are scored using the Area Under the Receiver Operator
Characteristic (AUROC) curve. The CFAR detector is shown to perform better at lower resolution. All three feature sets
together performed well with the degradation of resolution; separately the sets had different performances. The texture
features performed best because they do not rely on the number of pixels on the target, while the size features performed
the worst for the same reason. The contrast features yielded improved performance when the resolution was slightly
reduced.
This research compares alternative performance metrics to those more commonly used in target detection system performance evaluation. The alternative performance metrics examined here include the Fisher ratio, a modification of the Dice similarity coefficient, and the Youden index. These metrics are compared to metrics that have been previously introduced for such target detection system performance evaluation: the receiver operating characteristic (ROC) curve (and the related summary area under the ROC curve (AUC) value), and the confidence error generation (CEG) curve (and the related summary root square deviation (RSD) value). The ROC curve is a discrimination metric that measures the ability of a target detection system to distinguish between target and non-target. The CEG curve quantifies detection system knowledge of its own performance. An approach is presented that combines such metrics; this combination may be dynamically adjusted and updated based on current and future evaluation requirements for particular target detection systems.
The Johnson System for characterizing an empirical distribution is used to model the non-normal behavior of
Mahalanobis distances in material clusters extracted from hyperspectral imagery data. An automated method for
determining Johnson distribution parameters is used to model Mahalanobis distance distributions and is compared to an
existing method which uses mixtures of F distributions. The results lead to a method for determining outliers and
mitigating their effects.
The ability of certain performance metrics to quantify how well a target recognition system under test (SUT) can correctly identify targets and non-targets is investigated. The SUT, which may employ optical, microwave, or other inputs, assigns a score between zero and one that indicates the predicted probability of a target. Sampled target and nontarget SUT score outputs are generated using representative sets of beta probability densities. Two performance metrics, the area under the receiver operating characteristic (AURC) and the confidence error (CE), are analyzed. The AURC quantifies how well the target and nontarget distributions are separated, and the CE quantifies the statistical accuracy of each assigned score. The CE and AURC were generated for many representative sets of beta-distributed scores, and the metrics were calculated and compared using continuous methods as well as discrete (sampling) methods. Close agreement in results with these methods for the AURC is shown. While the continuous and the discrete CE are shown to be similar, differences are shown in various discrete CE approaches, which occur when bins of various sizes are used. A method for an alternative weighted CE calculation using maximum likelihood estimation of density parameters is identified. This method enables sampled data to be processed using continuous methods.
This research investigates the classification of battlespace detonations, specifically the determination of munitions type and size using temporal and spectral features from near-infrared (NIR) and visible wavelength imagers. Key features from the time dependence of fireball size are identified for discriminating various types and sizes of detonation flashes. The five classes include three weights of trinitrotoluene (TNT) and two weights of an enhanced mixture, all of which are uncased and detonated with 10% C-4. Using Fisher linear discriminant techniques, these features are projected onto a line such that the projected points are maximally clustered for the different classes of detonations. Bayesian decision boundaries for classification are then established on class-conditional probability densities and are tested using independent test data. Feature saliency and stability are determined by selecting those features that best discriminate while requiring low variations in class-conditional probability densities and high performance in independent testing. Given similar conditions, the most important and stable feature is the time to the maximum fireball area in the near-infrared wavelength band (0.6 to 1.7 microns). This feature correctly discriminates between TNT and ENE about 90% of the time, whether weight is known or not. The associated class-conditional probability densities separate the two classes with a Fisher ratio of 2.9±0.3 and an area under the receiver operating characteristic, AROC, of 0.992. Also, tmp achieves approximately 54% success rate at discerning both weight and type.
Probability densities for target recognition performance metrics are developed. These densities assist in evaluation of systems under test (SUTs), which are systems that predict the presence of a target after examination of an input. After such examination, a SUT assigns a score that indicates the predicted likelihood that a target is present. From scores for a series of many inputs, the suitability of a SUT can be evaluated through performance metrics such as the receiver operating characteristic (ROC) and the confidence error (CE) generation curve. The ROC is a metric that describes how well the probability densities of target and clutter scores are separated, where clutter refers to the absence of target. The CE generation curve and the corresponding scalar CE is a metric that evaluates the accuracy of the score. Since only a limited number of test scores (scores for which the truth state is known by the evaluator) is typically available to evaluate a SUT, it is critical to quantify uncertainty in the performance metric results. A process for estimating such uncertainty through probability densities for the performance metrics is examined here. Once the probability densities are developed, confidence intervals are also obtained. The process that develops the densities and related confidence intervals is implemented in a fully Bayesian manner. Two approaches are examined, one which makes initial assumptions regarding the form of the underlying target and clutter densities and a second approach which avoids such assumptions. The target and clutter density approach is applicable to additional performance metrics.
The ability of certain performance metrics to quantify how well target recognition systems under test (SUT) can correctly identify targets and non-targets is investigated. The SUT assigns a score between zero and one which indicates the predicted probability of a target. Sampled target and non-target SUT score outputs are generated using representative sets of Beta probability densities. Two performance metrics, Area under the Receiver Operating Characteristic (AURC) and Confidence Error (CE) are analyzed. AURC quantifies how well the target and non-target distributions are separated, and CE quantifies the statistical accuracy of each assigned score. CE and AURC are generated for many representative sets of beta-distributed scores, and the metrics are calculated and compared using continuous methods as well as discrete (sampling) methods. Close agreement in results with these methods for AURC is shown. Also shown are differences between calculating CE using sampled data and calculating CE using continuous distributions. These differences are due to the collection of similar sampled scores in bins, which results in CE weighting proportional to the sum of target and non-target scores in each bin. A method for an alternative weighted CE calculation using maximum likelihood estimation of density parameters is identified. This method enables sampled data to be processed using continuous methods.
The classification of three types of ground vehicle targets from the MSTAR (Moving and Stationary Target Acquisition and Recognition) database is investigated using hidden Markov models (HMMs) and synthetic aperture radar images. The HMMs employ training sets of six power spectrum features extracted from High Range Resolution (HRR) radar signal magnitude versus range profiles of the targets for uniform sequences of aspect angles (7 degree separation). Classification accuracy versus numbers of hidden states (from 3 to 30), sequence length (3, 10, 15, and 30), and discretization level of the features (10 and 30 levels) is explored using test and validation data. Best classification (94% correct) is achieved for 3 hidden states, a sequence length of 30, and 10 feature levels.
This research investigates the classification of battlespace detonations, specifically the determination of munitions type and size using image features from an infrared wavelength camera. Experimental data are collected for the detonation of several types of conventional munitions with different high explosive materials and different weights. Key features are identified for discriminating various types and sizes of detonation flashes. These features include statistical parameters derived from the time dependence of fireball size. Using Fisher linear discriminant techniques, these features are projected onto a line such that the projected points are maximally clustered for different classes of detonations. Bayesian decision boundaries for classification are then determined.
Digital image interpolation using Gaussian radial basis functions has been implemented by several investigators, and promising results have been obtained; however, determining the basis function variance has been problematic. Here, adaptive Gaussian basis functions fit the mean vector and covariance matrix of a non-radial Gaussian function to each pixel and its neighbors, which enables edges and other image characteristics to be more effectively represented. The interpolation is constrained to reproduce the original image mean gray level, and the mean basis function variance is determined using the expected image smoothness for the increased resolution. Test outputs from the resulting Adaptive Gaussian Interpolation algorithm are presented and compared with classical interpolation techniques.
This paper describes and illustrates an optimal nonlinear interpolation method that is appropriate for image line scans. It is particularly suitable for the restoration of digital images corrupted by “salt and pepper” noise in which isolated pixels are driven to their minimum and maximum gray values. It assigns gray values to these pixels so that the original smoothness of each line scan is maintained. The method is significant in that smoothness invariance is not achieved using, for example, ordinary low-pass or standard wavelet filtering methods to remove “salt and pepper” noise.
KEYWORDS: Scattering, 3D modeling, Radar, Optical spheres, 3D acquisition, Data modeling, Detection and tracking algorithms, Fourier transforms, Solid modeling, Sensors
This paper details a model building technique to construct geometric target models from RADAR data collected in a controlled environment. An algorithm to construct three-dimensional target models from a complex RADAR return expressed as discrete sets of scattering center coordinates with associated amplitudes is explained in detail. The model is a three-dimensional extension of proven RADAR scattering models that treat the RADAR return as a sum of complex exponentials. A Fourier Transform converts this to impulses in the frequency domain where the relative phase difference between scattering centers is a wrapped phase term. If the viewing sphere is sampled densely enough, the phase is unambiguously unwrapped. The minimum sampling interval is explicitly determined as a function of the extent of the target in wavelengths. A least squares solution determines the coordinates of each scattering center. Properties of the collection geometry allow the minimum sampling density of the viewing sphere to be increased, but at the cost of testing competing hypotheses to determine which one best fits the phase data. The complex RADAR return of a random object is created sampling a 1 degree(s) slice of the viewing sphere to validate the model-building algorithm All coordinates of the random object are extracted perfectly. Hopefully this algorithm can build three-dimensional scattering center models valid over the entire viewing sphere with each target represented as a discrete set of scattering centers. A rectangular window function associated with each scattering center would model persistence across the viewing sphere.
Equating objects based on shape similarity (for example scaled Euclidean transformations) is often desirable to solve the Automatic Target Recognition (ATR) problem. The Procrustes distance is a metric that captures the shape of an object independent of the following transformations: translation, rotation, and scale. The Procrustes metric assumes that all objects can be represented by a set of landmarks (i.e. points), that they have the same number of points, and that the points are ordered (i.e., the exact correspondence between the points is known from one object to the next). Although this correspondence is not known for many ATR problems, computationally feasible methods for examining all possible combinations are being explored. Additionally, most objects can be mapped to a shape space where translation, rotation, and scaling are removed, and distances between object points in this space can then form another useful metric. To establish a decision boundary in any classification problem, it is essential to know the a prior probabilities in the appropriate space. This paper analyzes basic objects (triangles) in two-dimensional space to assess how a known distribution in Euclidean space maps to the shape space. Any triangles whose three coordinate points are uniformly distributed within a two-dimensional box transforms to a bivariate independent normal distribution with mean (0,0) and standard deviations of 2 in Kendall shape space (two points of the triangle are mapped to {-1/2,0} and {1/2,0}). The Central Limit Theorem proves that the limit of sums of finite variance distributions approaches the normal distribution. This is a reasonable model of the relationship between the three Euclidean coordinates relative to the single Kendall shape space coordinate. This paper establishes the relationship between different objects in the shape space and the Procrustes distance, which is an established shape metric, between these objects. Ignoring reflections (because it is a special case), the Procrustes distance is isometric to the shape space coordinates. This result demonstrates that both Kendall coordinates and Procrustes distance are useful features for ATR.
Desirable features of any digital image resolution- enhancement algorithm include exact interpolation (for 'distortionless' or 'lossless' processing) adjustable resolution, adjustable smoothness, and ease of computation. A given low-order polynomial surface (linear, quadratic, cubic, etc.) optimally fit by least squares to a given local neighborhood of a pixel to be interpolated can enable all of these features. For example, if the surface is cubic, if a pixel and the 5-by-5 pixel array surrounding it are selected, and if interpolation of this pixel must yield a 4- by-4 array of sub-pixels, then the 10 coefficients that define the surface may be determined by the constrained least squares solution of 25 linear equations in 10 unknowns, where each equation sets the surface value at a pixel center equal to the pixel gray value and where the constraint is that the mean of the surface values at the sub-pixel centers equals the gray value of the interpolated pixel. Note that resolution is adjustable because the interpolating surface for each pixel may be subdivided arbitrarily, that smoothness is adjustable (within each pixel) because the polynomial order and number neighboring pixels may be selected, and that the most computationally demanding operation is solving a relatively small number of simultaneous linear equations for each pixel.
Synthetic Aperture Radar (SAR) sensors are being developed with better resolution to improve target identification, but this improvement has a significant cost. Furthermore, higher resolution corresponds to more pixels per image and, consequently, more data to process. Here, the effect of resolution on a many class target identification problem is determined using high resolution SAR data with artificially reduced resolution, a Mean-Squared Error (MSE) criterion, and template matching. It is found each increase in resolution by a factor of two increases the average MSE between a target and possible confusers by five to ten percent. Interpolating SAR images in the spatial domain to obtain artificially higher resolution images results in an average MSE that is actually much worse than the original SAR images. Increasing resolution significantly improves target identification performance while interpolating low- resolution images degrades target identification performance.
Because of the large number of SAR images the Air Force generates and the dwindling number of available human analysts, automated methods must be developed. A key step towards automated SAR image analysis is image segmentation. There are many segmentation algorithms, but they have not been tested on a common set of images, and there are no standard test methods. This paper evaluates four SAR image segmentation algorithms by running them on a common set of data and objectively comparing them to each other and to human segmentations. This objective comparison uses a multi-measure approach with a set of master segmentations as ground truth. The measure results are compared to a Human Threshold, which defines the performance of human segmentors compared to the master segmentations. Also, methods that use the multi-measures to determine the best algorithm are developed. These methods show that of the four algorithms, Statistical Curve Evolution produces the best segmentations; however, none of the algorithms are superior to human segmentations. Thus, with the Human Threshold and Statistical Curve Evolution as benchmarks, this paper establishes a new and practical framework for testing SAR image segmentation algorithms.
Adaptive spline interpolation (which is equivalent to the use of a type of radial basis function neural network) is investigated for digital image interpolation (i.e., for resolution enhancement). Test image results indicate that adaptive spline interpolation of a low-resolution image is superior to non-adaptive interpolation if the adjustable parameters are chosen to yield the best match to a known object in a corresponding high-resolution image.
KEYWORDS: Target recognition, Super resolution, Visualization, Integration, Signal processing, Data processing, Eye, Condition numbers, 3D acquisition, Organisms
Regions of interest that contain small targets often cover a small number of pixels, e.g., 100 or fewer. For such regions vision-based super-resolution techniques are feasible that would be infeasible for regions that cover a large number of pixels. One such technique centers basis functions (such as Gaussians) of the same width on all pixels and adjusts their amplitudes so that the sum of the basis functions integrated over each pixel is its gray value. This technique implements super-resolution in that the sum of basis functions determines the gray values of sub-pixels of any size. The resulting super-resolved visualizations, each characterized by a different basis function width, may enable the recognition of small targets that would otherwise remain unrecognized.
Given data points that sample an unknown function in one independent variable, techniques are described and illustrated that generate additional data points `similar to' the given points. These techniques are optimal in two key respects. First, each technique models the data using a continuous family of functions, where each function is the smoothest possible in that energy is minimized. Here energy is a linear combination of lack-of-smoothness (defined as integrated squared second derivative of the function) and lack-of-fit (defined as sum squared deviation of the function from either the given points or the given points displaced to intersect their least squares line). Second, many members of the family compete in a robust evolutionary process to acquire energy, and the result of this competition determines the relative contribution of each member function. The techniques model the given points in that they yield probability density functions of the dependent variable for any value of the independent variable. Thus they enable the implementation of many pattern recognition and data visualization procedures.
The 'Elton John' problem envisions candles blowing in the wind to motivate reasoning about prediction methods. The 'maximize smoothness but maintain trend' method has desirable parsimony when both data quantity and understanding are limited.
Two categories of optical beam steering micro-electro- mechanical systems (MEMS) were investigated: variable blaze gratings (VBGs) and linear optical phased arrays. All devices were surface micromachined using the multi-user MEMS processes (MUMPs). VBGs use an adjustable blaze angle to direct the majority of reflected light into a selectable diffraction order. Diffraction efficiencies greater than 50% were demonstrated. Linear optical phased arrays use a single row of piston micromirrors to create a far-field pattern with a steerable main lobe along one axis. All devices were constructed of polysilicon and gold and were actuated with electrostatic force. Electrostatic actuation provides high speed operation at a very low drive power. These optical beam steering devices discussed in this work are less optically efficient than a single pivoting mirror, but they require no post-fabrication assembly and can handle large beam diameters. Also, the low individual mass of the elements in surface micromachined VBGs and optical phased arrays yield faster system response times than a single macroscale pivoting mirror.
The design, fabrication, and potential performance of micro- actuated mirrors for beam steering are considered. Micro- actuators are by definition small devices that implement small displacements; they typically function using either electrostatic attraction or thermal expansion and are much smaller and less expensive than voice coil, piezoelectric stack, and related macro-actuators. Mirrors for use with micro-actuators may consist of rigid optically flat plates, continuous deformable membranes of facesheets, or arrays of elements with many possible element shapes, spacings, and displacement patterns. In general, the number of potentially practical micro-actuated mirror designs for beam steering increases as angular range, aperture size, steering speed, optical quality, and optical power requirements decrease.
Radial basis function neural network models of a time series may be developed or trained using samples from the series. Each model is a continuous curve that can be used to represent the series or predict future vales. Model development requires a tradeoff between a measure of roughness of the curve and a measure of its error relative to the samples. For roughness defined as the root integrated squared second derivative and for error defined as the root sum squared deviation (which are among the most common definitions), an optimal tradeoff conjecture is proposed and illustrated. The conjecture states that the curve that minimizes roughness subject to given error is a weighted mean of the least squares line and the natural cubic spline through the samples.
Micromirror arrays have been designed, fabricated, and tested that can steer coherent beams and that can simultaneously implement continuous phase control for beam shaping or aberration correction. A typical micromirror consists of a polysilicon plate (metalized for reflection) that is less than 100 microns in maximum dimension. Each micromirror is suspended a few microns above a polysilicon electrode by flexure hinges, and potentials of less than 50 volts applied to the electrodes displace the micromirrors over continuous ranges. Applications for arrays of these micromirrors include adaptive optics, active optical interconnections, and laser radar and communications.
KEYWORDS: Convolution, Image processing, Visual process modeling, Visualization, Digital imaging, Digital image processing, Spatial resolution, Systems modeling, Image segmentation, Imaging systems
A digital image smoothing procedure is described that meets two requirements inferred from a recent model of biological vision. First, the smoothed image is a linear combination of basis functions formed by convolving a Gaussian function with each pixel. Second, the linear coefficients are evaluated by requiring that the integral of the smoothed image over each pixel equal the product of the gray value and area of that pixel. These requirement are in accordance with a model of visual hyperacuity that explains the ability of biological vision systems to resolve some image details that are much smaller than system photoreceptors. The procedure is demonstrated and compared with standard Gaussian convolution smoothing for both a simple one- dimensional example and a practical corner-of-an-eye test image.
Micromirror arrays are being developed that can have up to tens of thousands of micromirror elements, each as small as 20 microns on a side, each spaced relative to neighbors so that optical efficiency exceeds 90 percent, and each individually controlled with response times as small as 10 microseconds for piston-like phase-mostly displacements that cover more than one- half optical wavelength. These arrays may be well suited for active aberration control of the focused coherent beams used in many applications, including optical disk storage, optical scanning, and laser radar systems. Active aberration control requires determination of the voltage supplied to the micromirror array elements so that constructive and destructive interference in light reflected from many elements yields the desired result. This paper discussed an approach in which the voltages are determined off-line by simulated annealing optimization and stored for real-time use.
The growing availability of commercial foundry processes allows easy implementation of micro-opto-electro-mechanical systems (MOEMS) for a variety of applications. Such applications go beyond single devices to include whole optical systems on a chip, comprising mirrors, gratings, Fresnel lenses, shutters, and actuators. Hinged and rotating structures, combined with powerful and compact thermal actuators, provide the means for positioning and operating these components. This paper presents examples of such systems built in a commercial polycrystalline silicon surface-micromachining process, the ARPA-sponsored multi-user MEMS process. Examples range from optical subcomponents to large mirror arrays and micro-interferometers. Also presented are linear arrays for combining the output of laser diode sources and for holographic data storage systems. Using the examples discussed in this paper, a designer can take advantage of commercially available surface-micromachining processes to design and develop MOEMS without the need for extensive in-house micromachining capabilities.
Hexagonal micromirror arrays and associated test structures have been fabricated using a commercial surface-micromachining process. The hexagonal micromirrors are 50 micrometers across and are arranged in a hexagonal array of 127 mirrors with 75 micrometers center-to-center spacing between nearest micromirrors. Each micromirror is supported by three flexure hinges, each of which surrounds one third of the micromirror perimeter. Each micromirror in the array can be displaced independently through a vertical distance of over 1 micrometers by a voltage applied to an underlying address electrode. The flexures and other highly diffracting or poorly reflecting areas can be covered by a statinary reflecting plate with holes that expose the moving micromirrors. These micromirror arrays function as efficient phase-mostly spatial light modulators. Applications for these micro-opto-electro-mechanical systems include optical processing, coherent beam shaping, and adaptive optics. This design has several important advantages. First, the hexagonal micromirror and array geometries maximize the active surface area of the array. Second, the use of three flexures instead of four, as is typical for square phase-mostly micromirrors, lowers the required drive voltage. Third, the reflecting cover plate ensures that light efficiency is maximized and that a substantial stationary coherent reference plane is provided. Design considerations for fabricating the arrays in commercial surface mciromachining processes are discussed. The deflection versus voltage behavior of the hexagonal micromirror is determined analytically and experimentally. Test results are used to design the next generation array.
An innovative method that enhances detail in digital images by smoothing image pixels while introducing minimal distortion is described and tested. In particular, a 14 by 14 pixel region of a diital image is smoothed using a constrained Gaussian radial basis function method. This method centers on each pixel a Gaussian distribution of amplitude such that the sum of all distributions correctly reproduces the gray level of each pixel. To assess the method, the distortion of the smoothed image is measured by the deviation of its power spectrum, from that of the unsmoothed image, determined as a function of the Gaussian distribution width, and comparisons are made with bilinear interpolation, a conventional convolution smoothing technique. The new method is capable of removing more 'pixel noise' while introducing less image distortion, thus permitting the detection and examination of otherwise hidden detail in digital images. Examples include the detection and assessment of enemy weapons in military images and cancerous tumor medical images.
The flexure-beam micromirror device (FBMD) developed by Texas Instruments, Inc., is presently being considered for use in communication and imaging systems. This device consists of thousands of individually addressable micromirror elements with phase-mostly responses, greater than 70% active area, and response times of 10 microseconds. Accurate determination of individual mirror element amplitude and phase responses versus address voltage is important for understanding the effect this device will have in the various applications. an experimental setup based on a laser microscopic interferometric technique was used to precisely map the surface displacement of individual mirror elements as a function of address voltage. The test structure consisted of an 8 X 8 array of 25 X 25 micrometers square flexure-beam elements. A phase response of greater than 2(pi) radians at a wavelength of 632.8 nm was observed for address voltages ranging from 0 to 5.8 V. The phase versus voltage relationship is shown to be nonlinear.
A technique for handwritten signature verification is proposed which combines the pattern recognition abilities of neural networks with the feature extraction capabilities of optics. This two-part technique enables real time signature verification based upon power spectrum features and stored linear least squares and Gaussian radial basis function neural network weights.
The new flexure-beam micromirror (FBM) spatial light modulator devices developed by Texas Instruments Inc. have characteristics that enable superior acquisition, tracking, and pointing in communications and other applications. FBM devices can have tens of thousands of square micromirror elements, each as small as 20 microns on a side, each spaced relative to neighbors so that optical efficiency exceeds 90 percent, and each individually controlled with response times as small as 10 microseconds for piston-like motions that cover more than one-half optical wavelength. These devices may enable order-of-magnitude improvements in space-bandwidth product, efficiency, and speed relative to other spatial light modulator devices that could be used to generate arbitrary coherent light patterns in real time. However, the amplitude and phase of each mirror element cannot be specified separately because there is only one control voltage for each element. This issue can be addressed by adjusting the control voltages so that constructive and destructive interference in the coherent light reflected from many elements produces the desired far field coherent light pattern. Appropriate control voltages are best determined using a robust software optimization procedure such as simulated annealing. Simulated annealing yields excellent results, but it is not real time (it may require hours of execution time on workstation-class computers). An approach that permits real-time applications stores control voltages determined off-line by simulated annealing that produce key desired far field coherent light beam shapes. These stored results are then used as training data for radial basis function neural networks that interpolate in real time between the training cases.
This study developed texture extraction techniques for classifying natural background scenes using singular values features. Singular values (obtained using singular value decomposition) were used to produce a reduced one-dimensional feature space of texture attributes of natural scene regions. Scenes with tree, grass, and water regions were taken from FLIR imagery. Classification error was determined using a Bayes error estimate and Bhattacharyya distance was used to quantify separation of features between regions. Although there were variations within regional texture samples, good classification results were obtained using the singular value features.
We present a design for a 3D display system that is simultaneously autostereoscopic (no viewer eyewear is required), multiperspective or look-around (horizontal parallax is achieved without head tracking), raster-filled (all pixels have gray scale), and dynamic (live or real-time scenes may be displayed). This system will enable the demonstration of improved pilot performance and situation awareness due to multiperspective (i.e., look-around) viewing capability. The system uses twenty separate small liquid crystal televisions (LCTVs) with corresponding perspective views projected onto a pupil-forming screen consisting of a Fresnel lens and a pair of crossed lenticular arrays. The system will provide design data necessary for the development of a more compact and optically efficient system that uses digital micromirror devices instead of LCTVs.
Smart zooming refers to certain digital image processing algorithms that enable the examination of detail ordinarily obscured by pixelation effects. These algorithms use radial basis function interpolation to smooth image blockiness due, for example, to magnification by pixel replication. They may permit more smoothing flexibility while retaining more image detail than conventional convolution smoothing methods.
It is shown that images with missing pixels can be approximately and usefully reconstructed using an interpolation function derived from as few as 10% of the original pixels in the image. The interpolation procedure uses Gaussian radial basis functions to `hammer' a plane to the given data points, where the basis function widths are calculated according to diagonal dominance criteria. In this paper the effectiveness of the reconstruction technique is investigated as a function of the degree of diagonal dominance.
The design of a 3D display system that is simultaneously autostereoscopic, look-around, raster-filled, and dynamic and that is enabled by new digital micromirror device technology is discussed.
Stretch and hammer neural networks use radial basis function methods to achieve advantages in generalizing training examples. These advantages include (1) exact learning, (2) maximally smooth modeling of Gaussian deviations from linear relationships, (3) identical outputs for arbitrary linear combination of inputs, and (4) training without adjustable parameters in a predeterminable number of steps. Stretch and hammer neural networks are feedforward architectures that have separate hidden neuron layers for stretching and hammering in accordance with an easily visualized physical model. Training consists of (1) transforming the inputs to principal component coordinates, (2) finding the least squares hyperplane through the training points, (3) finding the Gaussian radial basis function variances at the column diagonal dominance limit, and (4) finding the Gaussian radial basis function coefficients. The Gaussian radial basis function variances are chosen to be as large as possible consistent with maintaining diagonal dominance for the simultaneous linear equations that must be solved to obtain the basis function coefficients. This choice insures that training example generalization is maximally smooth consistent with unique training in a predeterminable number of steps. Stretch and hammer neural networks have been used successfully in several practical applications.
This paper reviews work on binary phase-only (BPOF) and ternary phase-amplitude (TPAF) correlation and highlights recent investigations of neural network approaches for augmenting correlation-based hybrid (optical/electronic) automatic target recognition systems. The theory and implementation of BPOF and TPAF correlation using available spatial light modulators is reviewed, including recent advances in smart TPAF formulations. Results showing the promise of neural networks for enhancing correlation system operation in the areas of estimating distortion parameters, adapting filters, and improving discrimination are presented and discussed.
Backpropagation-trained neural networks with optical correlation inputs are used to predict target rotation and to synthesize simplified optical correlation filters for rotated targets.
A locally linear neural network for interpolation and extrapolation is described. Desirable characteristics of this network include exact recall of training data optimal linear generalization of testing data and training in a known number of computational steps.
The convergence of a neural network model based on optical
resonator designs is examined for Boolean logic operations.
Computer simulations are performed to investigate convergence
performance and to assess possible optical implementations.
The model is a simple and general mathematical formulation
obtained using standard methods in which plane wave
amplitudes and phases are specified at discrete times
separated by the resonator period. The model is trained and
tested as an associative memory neural network using an input
state vector and a hologram matrix that evolves in time
according to a set of coupled nonlinear difference equations.
In general, these equations represent a high-order threshold
logic, and the hologram matrix is a function of the outer
product matrix of the evolving complex-element state vector.
Model parameters are explored to provide insight on
convergence mechanisms, robustness to input perturbations,
and optimization of convergence times for both training and
testing. The model is of interest for optical resonator
designs that incorporate (1) dynamic holograms for massively
parallel interconnection and storage functions and (2)
nonlinear components such as phase conjugate mirrors (with
thresholding and gain) for decision operations.2 These
components are often incorporated into resonator loops to
provide feedback and adaptation interactions. The neural
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