Filter design for optical pattern recognition: multicriteria optimization approach

Optimal trade-off filters for compressed Raman classification and spectrum reconstruction

Compressed Raman spectroscopy is a promising technique for fast chemical analysis. In particular, classification between species with known spectra can be performed with measures acquired through a few binary filters. Moreover, it is possible to reconstruct spectra by using enough filters. As classification and reconstruction are competing, designing filters allowing one to perform both tasks is challenging. To tackle this problem, we propose to build optimal trade-off filters, i.e., filters so that there exist no filters achieving better performance in both classification and reconstruction. With this approach, users get an overview of reachable performance and can choose the trade-off most fitting their application.

Cancelable face verification using optical encryption and authentication

In a cancelable biometric system, each instance of enrollment is distorted by a transform function, and the output should not be retransformed to the original data. This paper presents a new cancelable face verification system in the encrypted domain. Encrypted facial images are generated by a double random phase encoding (DRPE) algorithm using two keys (RPM1 and RPM2). To make the system noninvertible, a photon counting (PC) method is utilized, which requires a photon distribution mask for information reduction. Verification of sparse images that are not recognizable by direct visual inspection is performed by unconstrained minimum average correlation energy filter. In the proposed method, encryption keys (RPM1, RPM2, and PDM) are used in the sender side, and the receiver needs only encrypted images and correlation filters. In this manner, the system preserves privacy if correlation filters are obtained by an adversary. Performance of PC-DRPE verification system is evaluated under illumination variation, pose changes, and facial expression. Experimental results show that utilizing encrypted images not only increases security concerns but also enhances verification performance. This improvement can be attributed to the fact that, in the proposed system, the face verification problem is converted to key verification tasks.

Zero-Aliasing Correlation Filters for Object Recognition

Correlation filters (CFs) are a class of classifiers that are attractive for object localization and tracking applications. Traditionally, CFs have been designed in the frequency domain using the discrete Fourier transform (DFT), where correlation is efficiently implemented. However, existing CF designs do not account for the fact that the multiplication of two DFTs in the frequency domain corresponds to a circular correlation in the time/spatial domain. Because this was previously unaccounted for, prior CF designs are not truly optimal, as their optimization criteria do not accurately quantify their optimization intention. In this paper, we introduce new zero-aliasing constraints that completely eliminate this aliasing problem by ensuring that the optimization criterion for a given CF corresponds to a linear correlation rather than a circular correlation. This means that previous CF designs can be significantly improved by this reformulation. We demonstrate the benefits of this new CF design approach with several important CFs. We present experimental results on diverse data sets and present solutions to the computational challenges associated with computing these CFs. Code for the CFs described in this paper and their respective zero-aliasing versions is available at http://vishnu.boddeti.net/projects/correlation-filters.html.

Maximum Margin Correlation Filter: a new approach for localization and classification

Support vector machine (SVM) classifiers are popular in many computer vision tasks. In most of them, the SVM classifier assumes that the object to be classified is centered in the query image, which might not always be valid, e.g., when locating and classifying a particular class of vehicles in a large scene. In this paper, we introduce a new classifier called Maximum Margin Correlation Filter (MMCF), which, while exhibiting the good generalization capabilities of SVM classifiers, is also capable of localizing objects of interest, thereby avoiding the need for image centering as is usually required in SVM classifiers. In other words, MMCF can simultaneously localize and classify objects of interest. We test the efficacy of the proposed classifier on three different tasks: vehicle recognition, eye localization, and face classification. We demonstrate that MMCF outperforms SVM classifiers as well as well known correlation filters.

Image correlation method for DNA sequence alignment

The complexity of searches and the volume of genomic data make sequence alignment one of bioinformatics most active research areas. New alignment approaches have incorporated digital signal processing techniques. Among these, correlation methods are highly sensitive. This paper proposes a novel sequence alignment method based on 2-dimensional images, where each nucleic acid base is represented as a fixed gray intensity pixel. Query and known database sequences are coded to their pixel representation and sequence alignment is handled as object recognition in a scene problem. Query and database become object and scene, respectively. An image correlation process is carried out in order to search for the best match between them. Given that this procedure can be implemented in an optical correlator, the correlation could eventually be accomplished at light speed. This paper shows an initial research stage where results were “digitally” obtained by simulating an optical correlation of DNA sequences represented as images. A total of 303 queries (variable lengths from 50 to 4500 base pairs) and 100 scenes represented by 100 x 100 images each (in total, one million base pair database) were considered for the image correlation analysis. The results showed that correlations reached very high sensitivity (99.01%), specificity (98.99%) and outperformed BLAST when mutation numbers increased. However, digital correlation processes were hundred times slower than BLAST. We are currently starting an initiative to evaluate the correlation speed process of a real experimental optical correlator. By doing this, we expect to fully exploit optical correlation light properties. As the optical correlator works jointly with the computer, digital algorithms should also be optimized. The results presented in this paper are encouraging and support the study of image correlation methods on sequence alignment.

Robust classification method of tumor subtype by using correlation filters

Tumor classification based on gene expression profiles, which is of great benefit to the accurate diagnosis and personalized treatment for different types of tumor, has drawn a great attention in recent years. This paper proposes a novel tumor classification method based on correlation filters to identify the overall pattern of tumor subtype hidden in differentially expressed genes. Concretely, two correlation filters, i.e., Minimum Average Correlation Energy (MACE) and Optimal Tradeoff Synthetic Discriminant Function (OTSDF), are introduced to determine whether a test sample matches the templates synthesized for each subclass. The experiments on six publicly available datasets indicate that the proposed method is robust to noise, and can more effectively avoid the effects of dimensionality curse. Compared with many model-based methods, the correlation filter based method can achieve better performance when balanced training sets are exploited to synthesize the templates. Particularly, the proposed method can detect the similarity of overall pattern while ignoring small mismatches between test sample and the synthesized template. And it performs well even if only few training samples are available. More importantly, the experimental results can be visually represented, which is helpful for the further analysis of results.

3D passive photon counting automatic target recognition using advanced correlation filters

In this Letter, we present results for detecting and recognizing 3D objects in photon counting images using integral imaging with maximum average correlation height filters. We show that even under photon starved conditions objects may be automatically recognized in passively sensed 3D images using advanced correlation filters. We show that the proposed filter synthesized with ideal training images can detect and recognize a 3D object in photon counting images, even in the presence of occlusions and obscuration.

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.

Wavelet packet correlation methods in biometrics

We introduce wavelet packet correlation filter classifiers. Correlation filters are traditionally designed in the image domain by minimization of some criterion function of the image training set. Instead, we perform classification in wavelet spaces that have training set representations that provide better solutions to the optimization problem in the filter design. We propose a pruning algorithm to find these wavelet spaces by using a correlation energy cost function, and we describe a match score fusion algorithm for applying the filters trained across the packet tree. The proposed classification algorithm is suitable for any object-recognition task. We present results by implementing a biometric recognition system that uses the NIST 24 fingerprint database, and show that applying correlation filters in the wavelet domain results in considerable improvement of the standard correlation filter algorithm.

Markovian and autoregressive clutter-noise models for a pattern-recognition Wiener filter

Most modem pattern recognition filters used in target detection require a clutter-noise estimate to perform efficiently in realistic situations. Markovian and autoregressive models are proposed as an alternative to the white-noise model that has so far been the most widely used. Simulations by use of the Wiener filter and involving real clutter scenes show that both the Markovian and the autoregressive models perform considerably better than the white-noise model. The results also show that both models are general enough to yield similar results with different types of real scenes.

Digital three-dimensional image correlation by use of computer-reconstructed integral imaging

We use integral images of a three-dimensional (3D) scene to estimate the longitudinal depth of multiple objects present in the scene. With this information, we digitally reconstruct the objects in three dimensions and compute 3D correlations of input objects. We investigate the use of nonlinear techniques for 3D correlations. We present experimental results for 3D reconstruction and correlation of 3D objects. We demonstrate that it is possible to perform 3D segmentation of 3D objects in a scene. We finally present experiments to demonstrate that the 3D correlation is more discriminant than the two-dimensional correlation.

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.

Distortion tolerant image recognition receiver by use of a multiple-hypothesis method

A multiple-hypothesis method is used to detect a target or a reference signal in the presence of additive noise with unknown statistics. The receiver is designed to detect the target and to be tolerant of the variations in rotation and illumination of the target. A multiple-hypothesis test with unknown-noise parameters is used to locate the target position. The proposed method does not use any specific distortion-invariant-filtering technique, but it relies on a multiple-hypothesis approach. Maximum-likelihood estimates of the illumination constant and the unknown noise parameters are obtained. Computer simulations are presented to evaluate the performance of the receiver for various distorted noisy true-class targets with varying illumination and false-class objects.

Implementation of high-resolution diffractive optical elements on coupled phase and amplitude spatial light modulators

We propose the optical implementation of diffractive optical elements onto electrically addressed liquid-crystal spatial light modulators. We compare the classic implementations onto amplitude-only or phase-only domains with the implementations onto coupled phase and amplitude (spiral) domains. We demonstrate that the coupling between amplitude and phase provides a trade-off between diffraction efficiency and the signal-to-noise ratio in the reconstruction. Furthermore, when investigating the influence of the maximum dephasing on phase domains and spiral domains through the use of optimal trade-off design, we show that phase-only domains with limited maximum dephasing can provide satisfactory performance. Finally, optical implementations are provided.

Optimal multicriteria approach to the iterative fourier transform algorithm

We propose a unified approach to the multicriteria design of diffractive optics. A multicriteria version of the direct binary search that allows the user to adjust the compromise between the diffraction efficiency and the signal-to-noise ratio already exists. This technique has proved to be extremely powerful but also very time consuming. We extend this multicriteria approach to the iterative Fourier transform algorithm, which helps to reduce the computation time dramatically, especially for multilevel domains. Simulations as well as experimental validations are provided.

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.

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.

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.

Three-dimensional object recognition by use of a photorefractive volume holographic processor

We present a photorefractive volume holographic processor for recognition of three-dimensional (3D) objects. The templates are recorded by use of a volume hologram in a photorefractive LiNbO(3):Fe crystal located at the Fresnel diffraction region and correlated in real time with a 3D object illuminated by coherent light. Experimental results for recognition of 3D objects are presented and discussed. To the best of our knowledge, this is the first time a photorefractive volume holographic technique for 3D object recognition has been reported.

Real-time three-dimensional object recognition with multiple perspectives imaging

A novel system for recognizing three-dimensional (3D) objects by use of multiple perspectives imaging is proposed. A 3D object under incoherent illumination is projected into an array of two-dimensional (2D) elemental images by use of a microlens array. Each elemental 2D image corresponds to a different perspective of the 3D object. Multiple perspectives imaging based on integral photography has been used for 3D display. In this way, the whole set of 2D elemental images records 3D information about the input object. After an optical incoherent-to-coherent conversion, an optical processor is employed to perform the correlation between the input and the reference 3D objects. Use of micro-optics allows us to process the 3D information in real time and with a compact optical system. To the best of our knowledge this 3D processor is the first to apply the principle of integral photography to 3D image recognition. We present experimental results obtained with both a digital and an optical implementation of the system. We also show that the system can recognize a slightly out-of-plane rotated 3D object.

Fully complex synthetic discriminant functions written onto phase-only modulators

Synthetic discriminant functions (SDF's) are an effective tool for pattern-recognition applications. However, their experimental implementation is difficult because of the difficulty in writing full complex modulation functions onto spatial light modulators (SLM's) with restricted coding domains. Iterative methods are required for the implementation of SDF filters in real SLM's. A great deal of experimental research has been done with phase-only filters because they can be successfully implemented with liquid-crystal SLM's. We have recently introduced a technique for encoding arbitrary amplitude information onto the phase-only filter, thus allowing us to encode an arbitrary complex function onto a phase-only SLM. We apply this technique to the generation of arbitrary complex SDF filters, thus avoiding the necessity of iterative algorithms. We examine the discrimination capabilities of fully complex SDF filters designed with different parameters and constraints. Experimental results obtained with liquid-crystal SLM's are included.

Optimal processors for images with an arbitrary number of gray levels

We present a new group of processors, optimal in a maximum-likelihood sense, for target location in images with a discrete number of gray levels. The discrete gray-level distribution can be of any arbitrary form. We compare the performance of the processor derived for five discrete levels with the performance of a processor derived for a continuous Gaussian distribution and show that there are cases when only the processor derived for discrete levels will exhibit satisfactory performance. We give an explanation of this difference based on moment analysis and show how the correlation orders are related to statistical moments of the input scene.

Generalizations of the maximum average correlation height filter

Recently several approaches have been presented in which the shape of the correlation peak is used to distinguish between target and clutter. The well-known maximum average correlation height (MACH) filter was specifically designed to produce similar correlation planes for target variations present in the training set. Results are presented of a study of certain generalizations of the MACH filter intended to enhance the performance in clutter. It is shown that by taking into account the nonoverlapping character of the background noise and focusing the MACH correlation plane similarity requirement to the peak neighborhood, it is possible to simultaneously achieve a small variation in correlation peak shape and high peak-to-sidelobe ratios for cluttered images.

Intraclass and between-class training-image registration for correlation-filter synthesis

Correlation filters have traditionally been designed without much attention given to the issue of the training images within a class or the relative spatial position between classes. We examine the impact of training-set registration on correlation-filter performance and develop techniques for centering the training images from a class that result in improved performance. We also show that it is beneficial to adjust the spatial position of the classes relative to one another. Although the proposed techniques are relevant for many types of correlation filter, we limit our discussion to algorithms for the maximum average correlation height filter and the distance classifier correlation filter.

Three-dimensional object recognition by use of digital holography

We present a technique for performing three-dimensional (3D) pattern recognition by use of in-line digital holography. The complex amplitude distribution generated by a 3D object at an arbitrary plane located in the Fresnel diffraction region is recorded by phase-shifting interferometry. The digital hologram contains information about the 3D object's shape, location, and orientation. This information allows us to perform 3D pattern-recognition techniques with high discrimination and to measure 3D orientation changes. Experimental results are presented.

Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response

Correlation methods are becoming increasingly attractive tools for image recognition and location. This renewed interest in correlation methods is spurred by the availability of high-speed image processors and the emergence of correlation filter designs that can optimize relevant figures of merit. In this paper, a new correlation filter design method is presented that allows one to optimally tradeoff among potentially conflicting correlation output performance criteria while achieving desired correlation peak value behavior in response to in-plane rotation of input images. Such controlled in-plane rotation response is useful in image analysis and pattern recognition applications where the sensor follows a pre-arranged trajectory while imaging an object. Since this new correlation filter design is based on circular harmonic function (CHF) theory, we refer to the resulting filters as optimal tradeoff circular harmonic function (OTCHF) filters. Underlying theory, OTCHF filter design method, and illustrative numerical results are presented.

Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator

An improved method for implementing correlation filters in the joint transform correlator architecture is proposed. We derived the method from computer-generated holography techniques. It allows us to use any correlation filters, especially ones that provide an optimal trade-off between noise robustness, peak sharpness, and optical efficiency, with any spatial light modulator (SLM). This method also allows for an objective comparison of the performance of the coding domains of various SLM's.

Distortion-invariant filter for nonoverlapping noise

A new heuristic filter based on the optimum filter for disjoint noise developed by Javidi and Wang [J. Opt. Soc. Am. A 11, 2604 (1995)] is presented. In this new filter a number of optimum filters built from single training images are combined linearly by use of the synthetic discriminant function (SDF) approach into a distortion-invariant filter for disjoint noise. Like the traditional SDF approach, this summation technique makes it possible to control the height of the correlation peak easily, for example, if a uniform filter response is needed. The filter is compared with the distortion-invariant version of the optimum filter on images with low contrast and high levels of nonoverlapping clutter. The new filter shows good results, demonstrating that it is, with very simple heuristic methods, possible to improve the performance of distortion-invariant filters for nonoverlapping noise.

Synthetic discriminant function filter employing nonlinear space-domain preprocessing on bandpass-filtered images

Previously [Appl. Opt. 36, p. 9212 (1997)] we examined the performance of the linear and nonlinear preprocessed difference-of-Gaussians filter, and it was shown that this operation results in greater tolerance to in-class variations while maintaining excellent discrimination ability. The introduction of nonlinearity was shown to provide greater robustness to the filter's response to noise and background clutter in the input scene. We incorporate this new operation into the synthesis of a modified synthetic discriminant function filter. The filter is shown to produce sharp peaks, excellent discrimination without the need to include out-of-class objects, and good invariance to out-of-plane rotation over a distortion range of up to 90 degrees . Additionally, the introduction of nonlinearity is shown to provide greater robustness of the filter response to background clutter in the input scene.

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.

Application of nonlinearity to wavelet-transformed images to improve correlation filter performance

A useful filter for pattern recognition must strike a compromise between the conflicting requirements of in-class distortion tolerance and out-of-class discrimination. Such a filter will be bandpass in nature, the high-frequency response being attenuated to provide less sensitivity to in-class variations, while the low frequencies must be removed, since they compromise the discrimination ability of the filter. A convenient bandpass is the difference of Gaussian (DOG) function, which provides a close approximation to the Laplacian of Gaussian. We describe the effect of a preprocessing operation applied to a DOG filtered image. This operation is shown to result in greater tolerance to in-class variation while maintaining an excellent discrimination ability. Additionally, the introduction of nonlinearity is shown to provide greater robustness in the filter response to noise and background clutter in the input scene.

Minimum-mean-square-error filters for detecting a noisy target in background noise

A minimum-mean-square-error filter is proposed to detect a noisy target in spatially nonoverlapping background noise. In this model, both the background noise that is spatially nonoverlapping with the target and the noise that is additive to the target and the input image are considered. The criterion used to design the filter is to minimize the mean-square-error between the filter output and a delta function located at the target position in the presence of the noise. Computer-simulation results for a number of noisy input images are presented, and the performance of the filter is determined. We also test the filter discrimination against undesired objects and tolerance to target distortions, such as rotation and scaling.

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.

Reduction in correlation-filter sensitivity to background clutter by the automatic spatial frequency selection algorithm

We propose an automatic spatial frequency selection correlation filter that reduces the sensitivity to nonoverlapping noise or background clutter. This is achieved by inclusion of distorted versions of the reference images surrounded by nonoverlapping background clutter. Furthermore, we impose that the window functions of the reference images give response zero-correlation amplitudes. Simulation results are provided in the case of a two-class pattern-recognition problem and show that the results are appreciably increased. The results are compared with a normal automatic spatial frequency selection.

Optimal detection of a target with random gray levels on a spatially disjoint background noise

We describe a pattern-recognition processor that is optimal for detection and location of a target with white Gaussian random gray levels on a white random spatially disjoint background. We show that this algorithm consists of correlations of the silhouette of the reference object with preprocessed versions of the scene image. This result can provide a theoretical basis for pattern-recognition techniques that use nonlinear preprocessing of images before correlation.

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.

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.

Performance of minimum-mean-square-error filters for spatially nonoverlapping target and input-scene noise

Using computer simulations, we investigate the performance of a minimum-mean-square-error filter for input-scene noise that is spatially nonoverlapping (disjoint) with a target for a limited set of images. Different input-scene-noise statistics are used to test the filter performance. We show that in the presence of spatially nonoverlapping target and input-scene noise, the output of the minimummean- square-error filter has a well-defined correlation peak, small sidelobes, and a high peak-to-correlationenergy ratio compared with other widely used filters such as the classical matched filter, the phase-only filter, and the inverse filter. We also test the robustness of the minimum-mean-square-error filter to errors in noise statistics used in the filter design. We show that, for the images tested here, the performance of the minimum-mean-square-error filter is not sensitive to errors in noise statistics and the filter can detect the target even if a considerable error exists. The discrimination capability and the illumination sensitivity of the minimum-mean-square-error filter are also tested.

Optimum filter for detection of a target in nonoverlapping scene noise

A filter function is derived for input signals containing a target that is spatially disjoint (that is, nonoverlapping) with the input scene noise. The optimization metric is the ratio of the square of the expected value of the correlation peak to the expected value of the output signal energy. In this model the effects of the nonwhiteness of the scene noise, the nonstationarity of the scene noise that is due to the limited size of the input scene, the nonoverlapping of the target and the scene noise, and the unknown variations of the target illumination are considered. We show that, for the nonoverlapping target and the scene noise, the target window and the scene-noise window strongly influence the optimum filter function.