Distortion-invariant pattern recognition with Fourier-plane nonlinear filters

The use of nonlinear techniques in the Fourier plane of pattern-recognition correlators can improve the correlators' performance in terms of discrimination against objects similar to the target object, correlation-peak sharpness, and correlation noise robustness. Additionally, filter designs have been proposed that provide the linear correlator with invariance properties with respect to input-signal distortions and rotations. We propose simple modifications to presently known distortion-invariant correlator filters that enable these filter designs to be used in a nonlinear correlator architecture. These Fourier-plane nonlinear filters can be implemented electronically, or they may be implemented optically with a nonlinear joint transform correlator. Extensive simulation results are presented that illustrate the performance enhancements that are gained by the unification of nonlinear techniques with these filter designs.     

Comparison of analog continuum correlators for remote sensing andradio astronomy

Two different designs of analog correlators for radiometry are compared in this paper. A continuum correlator based on a microwave nonlinear device is a simple and inexpensive way to detect wide-band polarized signals. Analysis and extensive measurements including linearity, dynamic range, amplitude response, phase balance, and stability are presented, and the suitability of the designs for microwave radiometry is discussed. Both correlators showed nearly ideal performance. A novel method for determining the correlator degradation factor is applied     

A comparison of two correlation schemes

Processes involving the cross-correlation of two noisy data streams are frequently encountered in signal processing. The performances of two commonly used correlators, the simple and complex correlators, are examined. The conventional view is that the complex correlator is superior to the simple correlator by a factor of the square root of two in output signal-to-noise ratio (SNR). However, by modifying the simple correlator to utilize all the available information, its performance is improved. The development of the modified correlator is explained, and a computer simulation shows that this modified correlator is approximately equivalent to the complex correlator in noise performance     

Nonlinearity optimization in nonlinear joint transform correlators

Three types of nonlinear transformations of the joint spectrum in nonlinear joint transform correlators (NLJTC's) are investigated with the purpose of achieving the highest discrimination capability in target location in a cluttered background: logarithmic transformation and the (1/k)th law transformation in combination with the limitation of the signal dynamic range and binarization by thresholding. By computer simulation carried out on a set of test images, it is shown that application of these transformations in NLJTC's may considerably improve the correlator's capacity to locate and recognize properly small objects on a cluttered background, provided there is proper selection of nonlinearity parameters. It is also shown that a moderate blur of the joint spectrum in such NLJTC's before nonlinear transformation is permissible, which simplifies the requirements of correlator optical alignment, the resolution power of correlator electronic components, or both.     

Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination conditions

The correlation performance of binary joint transform correlators with unknown input-image light illumination is investigated for different thresholding methods used in the Fourier plane. It is shown that a binary joint transform correlator that uses a spatial frequency dependent threshold function for binarization of the joint power spectrum is invariant to uniform input-image illumination. Computer simulations and optical experimental results are provided.     

Application of serial- and parallel-projection methods to correlation-filter design

We describe generalized projection procedures for the design of arbitrary filter functions for correlators. More specifically, serial and parallel implementations of projection-based algorithms are employed. The novelty of this procedure lies in its generality and its ability to handle wide varieties of constraints by the same procedure. The procedure is demonstrated by the design of filters for the 4-? linear correlator, the phase-extraction correlator, and variants thereof. The filters are subject to a variety of constraints, including rotation-invariant pattern recognition and class discrimination. Examples are given to show the versatility, flexibility, and applicability of the design process to a variety of pattern-recognition tasks. Satisfactory results are also obtained because of the combination with the special nonlinear correlators proposed for pattern recognition.     

Multiresolution correlator analysis and filter design

The concept of multiresolution optical correlators is formally introduced. A mathematical analysis is performed for a generalized multiresolution correlator that emphasizes the roles of both input and filter spatial light modulator resolutions. Conditions are derived for overlapping and nonoverlapping correlation orders. A simulation is performed in which it is shown that the predicted performance of composite binary-phase-only filters designed by the conventional design procedure is different from the actual performance when they are implemented in a real optical correlator. The training of filters on multiresolution approximations of high-resolution discrete Fourier transforms generated by multiresolution wavelet analysis (MWA) techniques is proposed. An analysis is performed that shows that training on MWA approximations results in filters whose performance is the same in a real correlator as that predicted by the design procedure. This analysis is confirmed by simulation. Further simulations show that the performance of reduced-resolution filters designed by MWA techniques is markedly superior to the performance of those designed by conventional means. Finally, an analysis is performed that explains why the ratio of zero- to higher-order correlation peak intensities is much greater for the former than the latter.     

Comparison of automatic target recognition system performance with full- and reduced-resolution correlators

The performance of an automatic target recognition (ATR) system with full- and reduced-resolution correlators was compared. In addition, the ATR system performance with reduced-resolution filter sets designed by use of multiresolution analyasis (MA) and downsampling (DS) techniques was also compared. It was discovered that results obtained at the optical correlator subsystem level, pertaining to the relative merits of the MA and the DS techniques, could not be extrapolated to the system level. This was because target signature differences between the test and the training imagery were discovered to have a greater influence on system performance than the choice of filter design technique. In addition, it was found that, for the case in which the target signature and the reduced-resolution filter were of the same size, there was some degradation in the receiver-operating-characteristic curve for reduced resolution compared with full. Nevertheless, this was deemed to have no practical significance, and thus the use of reduced-resolution optical correlators for ATR merits serious consideration.     

All-optical pattern recognition for digital real-time information processing

To recognize digital streams of digital data, all-optical and passive techniques able to discriminate optical bit words in real time are presented. Discrimination capability of different correlators, both in free space architectures and in delay lines structures, is theoretically and experimentally analyzed. Experimental performances in word recognition are shown in the case of a volume holographic correlator, in the case of a lithographic phase-only-filter correlator, and in the case of a novel coherent delay lines correlator operating at the wavelength 1550 nm and at the bit rate of 2.5 Gbit/s.     

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.     

Characterization of an Optimized Nonlinear Joint Transform Correlator

Abstract

The performance of a nonlinear joint transform correlator which employs a GEC-Marconi optically addressed spatial light modulator in the Fourier plane is investigated in terms of the device operating conditions and other system parameters. We discuss the optimum performance characteristics of the correlator and the sensitivity to changes in the rotation, scale and separation of the objects in the input plane.     

Spatial-domain implementation of optimal multicriteria correlation filters

We show that optimal regions of support for correlation filters in the frequency domain can be approximated by relatively small convolution kernels in the spatial domain. We present an optimal approach for generating regions of support, as well as a fast nonoptimal approach for conventional optical correlators. Because the convolution kernels are similar to low-pass filters, the resulting input image to a correlator is always positive valued. We show that the performance of the convolution-based approach is comparable with the optimal frequency-domain approach. An important advantage of our method is that it can be implemented on low-cost arithmetic frame grabbers that can perform convolution with small kernels in real time. In addition, our method can be used in conjunction with a filter spatial light modulator that cannot produce a zero state.     

Anamorphic Multiple Matched Filter for Character Recognition,Performance with Signals of Equal Size

Abstract

The construction and performance of an anamorphic multiple matched filter for character recognition is presented, in the usual situation of characters of equal input size and having the same size in the target. So a simple anamorphic correlator can be employed to obtain the recognition of a given character. In order to avoid false alarms the characters in the target are rotated by different angles depending on the angular tolerance of the correlator, which is rotationally variant and smaller than in symmetrical systems within a certain angular region. Thus the number of signals to which the filter can be matched can be greater than with spherical optics correlators.     

小波域的频率扩展信道的信号检测

由于海洋动力学和目标起伏引起发射信号包络的时变衰减，相应于频域就是频率扩展，这种信道称为频率扩展信道，又名快速衰落信道(FFD)。在FFD信道中，理想信道的最佳检测器——匹配滤波器的性能将有所下降，Baggenstoss已经证明FFD信道的最佳检测器是分段副本相关器(SRC)。近年来出现的小波变换具有和宽带相关处理相似的计算结构，所以文章拟从连续小波变换的理论和性质出发，推导FFD信道小波变换域最佳检测器的形式，并针对一个仿真算例，进一步用Monte-Carlo实验计算出该检测器的性能曲线，结果表明该检测器的性能优于小波域的副本相关器。     

Neural-network classifiers for automatic real-world aerial image recognition

We describe the application of the multilayer perceptron (MLP) network and a version of the adaptive resonance theory version 2-A (ART 2-A) network to the problem of automatic aerial image recognition (AAIR). The classification of aerial images, independent of their positions and orientations, is required for automatic tracking and target recognition. Invariance is achieved by the use of different invariant feature spaces in combination with supervised and unsupervised neural networks. The performance of neural-network-based classifiers in conjunction with several types of invariant AAIR global features, such as the Fourier-transform space, Zernike moments, central moments, and polar transforms, are examined. The advantages of this approach are discussed. The performance of the MLP network is compared with that of a classical correlator. The MLP neural-network correlator outperformed the binary phase-only filter (BPOF) correlator. It was found that the ART 2-A distinguished itself with its speed and its low number of required training vectors. However, only the MLP classifier was able to deal with a combination of shift and rotation geometric distortions.     

Basic properties of nonlinear global filtering techniques and optimal discriminant solutions

The basic properties of nonlinear global filtering techniques are analyzed. A nonlinear processor for pattern recognition that is optimum in terms of discrimination and that is tolerant of variations of the object to be recognized is presented. We compare this processor with power-law and nonlinear joint transform correlators.     

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.     

Quadratic correlation filter design methodology for target detection and surveillance applications

A novel method is presented for optimization of quadratic correlation filters (QCFs) for shift-invariant target detection in imagery. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. For example, multiple correlators work in parallel to optimize jointly the QCF performance metric and produce a single combined output, which leads to considerable simplification of the postprocessing scheme. In addition, QCFs also yield better performance than their linear counterparts for comparable throughput requirements. The primary application considered is target detection in infrared imagery for surveillance applications. In the current approach, the class-separation metric is formulated as a Rayleigh quotient that is maximized by the QCF solution. It is shown that the proposed method results in considerable improvement in performance compared with a previously reported QCF design approach and many other detection techniques. The results of independent tests and evaluations at the U.S. Army's Night Vision Laboratory are also presented.     

Joint wavelet representation correlator for pattern recognition

A joint wavelet representation correlator is proposed as a newarchitecture to combine wavelets and the joint transformcorrelator. It performs wavelet representation preprocessing andthe correlation operation simultaneously. An intensity filter usedfor wavelet representation is the power spectrum of the waveletfunction and can easily be synthesized and displayed. Computersimulation shows that, as compared with previous joint wavelettransform correlators, its discrimination capability is better and itsperformance is more stable under input noise.     

Fatigue life prediction of composite materials using polynomial classifiers and recurrent neural networks

Due to their massively parallel structure and ability to learn by example, artificial neural networks can deal with nonlinear problems for which an accurate analytical solution is difficult to obtain. These networks have been used in modeling the mechanical behavior of fiber-reinforced composite materials. Although promising results were obtained using such networks, more investigation on the appropriate choice of their structure and their performance in the presence of limited and noisy data is needed. On the other hand, polynomials networks have been known to have excellent properties as classifiers and are universal approximators to the optimal Bayes classifier. Not being dependant on various user defined parameters, having less computational requirements makes their use over other methods, such as neural networks, an advantage.

In this work, the fatigue behavior of unidirectional glass fiber/epoxy composite laminae under tension–tension and tension–compression loading is predicted using feedforward and recurrent neural networks. These predictions are compared to those obtained using polynomial classifiers. Experimental data obtained for fiber orientation angles of 0°, 19°, 45°, 71° and 90° under stress ratios of 0.5, 0 and –1 is used.

It is shown that, even when a small number of experimental data points is used to train both polynomial classifiers and neural networks, the predictions obtained are comparable to other current fatigue life-prediction methods. Also, polynomial classifiers are shown to provide accurate modeling between the input parameters (maximum stress, R-ratio, fiber orientation angle) and the number of cycles to failure when compared to neural networks.