Advanced distortion-invariant minimum average correlation energy (MACE) filters

Spectral optimized asymmetric segmented phase-only correlation filter

We suggest a new type of optimized composite filter, i.e., the asymmetric segmented phase-only filter (ASPOF), for improving the effectiveness of a VanderLugt correlator (VLC) when used for face identification. Basically, it consists in merging several reference images after application of a specific spectral optimization method. After segmentation of the spectral filter plane to several areas, each area is assigned to a single winner reference according to a new optimized criterion. The point of the paper is to show that this method offers a significant performance improvement on standard composite filters for face identification. We first briefly revisit composite filters [adapted, phase-only, inverse, compromise optimal, segmented, minimum average correlation energy, optimal trade-off maximum average correlation, and amplitude-modulated phase-only (AMPOF)], which are tools of choice for face recognition based on correlation techniques, and compare their performances with those of the ASPOF. We illustrate some of the drawbacks of current filters for several binary and grayscale image identifications. Next, we describe the optimization steps and introduce the ASPOF that can overcome these technical issues to improve the quality and the reliability of the correlation-based decision. We derive performance measures, i.e., PCE values and receiver operating characteristic curves, to confirm consistency of the results. We numerically find that this filter increases the recognition rate and decreases the false alarm rate. The results show that the discrimination of the ASPOF is comparable to that of the AMPOF, but the ASPOF is more robust than the trade-off maximum average correlation height against rotation and various types of noise sources. Our method has several features that make it amenable to experimental implementation using a VLC.

An associative memory readout for ESNs with applications to dynamical pattern recognition

The use of echo state networks (ESN) to find patterns in time (dynamical pattern recognition) has been limited. This paper argues that ESNs are particularly well suited for dynamical pattern recognition and proposes a linear associative memory (LAM) as a novel readout for ESNs. From the class of LAMs, the minimum average correlation energy (MACE) filter is adopted because of its high rejection characteristics that allow its use as a detector in the automatic pattern recognition literature. In the ESN application, the MACE interprets the states of the ESN as a two-dimensional "image", one dimension being time and the other the processing element index (space). An optimal template image for each class, which associates ESN states with the class label, can be analytically computed using training data. During testing, ESN states are correlated with each template image and the class label of the template with the highest correlation is assigned to the input pattern. The ESN-MACE combination leads to a nonlinear template matcher with robust noise performance as needed in non-Gaussian, nonlinear digital communication channels. A real-world data experiment for chemical sensing with an electronic nose is included to demonstrate the validity of this approach. Moreover, the proposed readout can also be used with liquid state machines eliminating the need to convert spike trains into continuous signals by binning or low-pass filtering.

Affine-permutation invariance of 2-D shapes

Shapes provide a rich set of clues on the identity and topological properties of an object. In many imaging environments, however, the same object appears to have different shapes due to distortions such as translation, rotation, reflection, scaling, or skewing. Further, the order by which the object's feature points are scanned changes, i.e., the order of the pixels may be permuted. Relating two-dimensional shapes of the same object distorted by different affine and permutation transformations is a challenge. We introduce a shape invariant that we refer to as the intrinsic shape of an object and describe an algorithm, BLAISER, to recover it. The intrinsic shape is invariant to affine-permutation distortions. It is a uniquely defined representative of the equivalence class of all affine-permutation distortions of the same object. BLAISER computes the intrinsic shape from any arbitrarily affine-permutation distorted image of the object, without prior knowledge regarding the distortions or the undistorted shape of the object. The critical step of BLAISER is the determination of the shape orientation and we provide a detailed discussion on this topic. The operations of BLAISER are based on low-order moments of the input shape and, thus, robust to error and noise. Examples illustrate the performance of the algorithm.

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.

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.

Theory and optical implementation of the geometrical approach of multiple circular harmonic filters

The circular harmonic filter contains only one component of the image. Its discrimination capability has been questionable. The geometrical approach of multiple circular harmonic filters uses relative locations of the correlation peaks as the rotation-, shift-, and intensity-invariant features for pattern recognition. Each feature depends on the entire image. This approach has a good discrimination capability. Optical real-time implementation of the on-axis continuous phase-only circular harmonic filters by the use of a commercial liquid-crystal television is shown. A harmonic analysis shows that the phase-mostly filter can tolerate coupled amplitude modulation at the acceptable expense of the output signal-to-noise ratio. An optical experiment of the geometrical approach of multiple circular harmonic filters for a multiple-image input is described. The cross-correlation peaks between the individual filters and the clutter are eliminated, because they are not in good locations.

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.

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.

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.