Minimum noise and correlation energy optical correlation filter

Sparse representation based SAR vehicle recognition along with aspect angle

As a method of representing the test sample with few training samples from an overcomplete dictionary, sparse representation classification (SRC) has attracted much attention in synthetic aperture radar (SAR) automatic target recognition (ATR) recently. In this paper, we develop a novel SAR vehicle recognition method based on sparse representation classification along with aspect information (SRCA), in which the correlation between the vehicle's aspect angle and the sparse representation vector is exploited. The detailed procedure presented in this paper can be summarized as follows. Initially, the sparse representation vector of a test sample is solved by sparse representation algorithm with a principle component analysis (PCA) feature-based dictionary. Then, the coefficient vector is projected onto a sparser one within a certain range of the vehicle's aspect angle. Finally, the vehicle is classified into a certain category that minimizes the reconstruction error with the novel sparse representation vector. Extensive experiments are conducted on the moving and stationary target acquisition and recognition (MSTAR) dataset and the results demonstrate that the proposed method performs robustly under the variations of depression angle and target configurations, as well as incomplete observation.

Multifeature distortion-insensitive constellation detection

Many applications require detection of multiple features that locally remain consistent in shape and intensity characteristics, but may globally change position with respect to one another over time or under different circumstances. We refer to these feature sets, defined by their characteristic relative positioning, as multifeature constellations. We introduce a method of processing in which multiple levels of correlation, using specially designed composite feature detection filters, are used to first detect local features, and then to detect constellations of these local features. We include experimental procedures and results indicating how the use of multifeature constellation detection may be utilized in applications such as sign language recognition and fingerprint matching.

Pose and position tracking with super image vector inner products

We introduce a new and efficient distortion-invariant super image tracker and pose estimator based on a linear phase coefficient composite filter. The super image consists of a weighted sum of training images chosen to span the distortion range under analysis. Unlike correlation-based composite filter design, the super image is implemented by means of a complex vector inner product operation. A super image vector inner product is implemented by elementwise multiplication of a super image template by a window of interest in the input scene and summation of the elementwise operations. The resulting amplitude indicates target detection, and the resulting phase indicates the value of scale, orientation, or movement of the target object. The mathematical characteristics of the super image vector inner product are presented, and its application is demonstrated.

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.

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.

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.

Reduced-resolution synthetic-discriminant-function design by multiresolution wavelet analysis

Several approaches to the design of reduced-resolution synthetic discriminant functions (SDF's) using multiresolution wavelet analysis (MWA) techniques are investigated. In the first approach, reducedresolution approximations of a full-resolution SDF are obtained by MWA. In the second approach, reduced-resolution approximations of the training-image Fourier transforms are obtained by MWA, and a reduced-resolution SDF is obtained directly by training on these. For both approaches, reducedresolution MICE-SDF filters were designed with MWA and conventional down-sampling techniques. Simulations showed that filters designed by the second approach with MWA techniques permitted reductions in the number of filter pixels from 128 × 128 to 32 × 32, while still satisfying the design constraints. In comparison, the performances of 32 × 32 filters designed by conventional downsampling techniques were significantly degraded.

Unconstrained correlation filters

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

Sidelobe elimination for generalized synthetic discriminant functions by a two-filter correlation and subsequent postprocessing of the intensity distributions

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

Locally nonlinear matched filtering

A new matched filter for pattern recognition is introduced. Previous researchers have introduced matched filters that are nonlinear functions of the spectrum, for which the classical matched filter is divided by some power m of the spectrum of interest. We further generalize this filter by making the power m a function of the spatial frequency; this permits the design of filters that combine the advantageous properties of matched filters, phase-only filters, and inverse filters without the corresponding disadvantages. The first computer experiments indicate that the new filter yields sharper correlation peaks and better discrimination than the matched filter and the phase-only filter and yields more robustness against noise.

Optimality of trade-off filters

We compare the optimal trade-off approach for synthetic discriminant function filters and an approach introduced recently, the minimum noise and correlation energy filter, using an objective quantitative figure of merit. A new general definition of multicriteria optimal trade-off correlation filters is introduced based on this comparison.

Tutorial survey of composite filter designs for optical correlators

A tutorial survey is presented of the many composite filter designs proposed for distortion-invariant optical pattern recognition. Remarks are made throughout regarding areas for further investigation.