Maximum likelihood for target location in the presence of substitutive noise.

We consider the optimal likelihood algorithm for the estimation of a target location when the images are corrupted by substitutive noise. We show the relationship between the optimal algorithm and the sliced orthogonal nonlinear generalized (SONG) correlation. The SONG correlation is based on the application of a linear correlation to corresponding binary slices of both the input scene and the reference object with appropriate weight factors. For a particular case, we show that the optimal strategy is a function of only the number of pixels for which the gray values in the noisy image match the ones of the reference image when the substitutive noise is uniformly distributed. This is exactly what a particular definition of the SONG correlation does.

Homomorphic cameo filter for pattern recognition that is invariant with changes in illumination.

We introduce a new matched filter method that yields correlation peaks that are invariant with changes in the illumination of any targets. A scene containing objects at unknown locations is first subjected to a logarithmic transformation that changes the multiplicative constant to an additive background, which is then discriminated against by means of a composite filter containing a cameo of the true target and a term with which to discriminate against other false targets. Experimental results are shown.

Nonlinear rotation-invariant pattern recognition by use of the optical morphological correlation.

We introduce a modification of the nonlinear morphological correlation for optical rotation-invariant pattern recognition. The high selectivity of the morphological correlation is conserved compared with standard linear correlation. The operation performs the common morphological correlation by extraction of the information by means of a circular-harmonic component of a reference. In spite of some loss of information good discrimination is obtained, especially for detecting images with a high degree of resemblance. Computer simulations are presented, as well as optical experiments implemented with a joint transform correlator.

Invariant pattern recognition based on centroids.

A new method for pattern recognition that is invariant under changes of position, orientation, intensity, and scale is presented. The centroids of objects provide unique points that are related to the energy distribution. For obtaining more such unique points a conformal transform can be used to rearrange the energy distribution of the object. By means of the conformal transform many different centroids can be produced from the same object. A useful pattern-recognition and object-registration method that yields a position-, rotation-, intensity-, and scale-invariant feature vector based on these centroids can be created.

Fresnel transform-based correlator.

We present a new technique for information processing using Fresnel transform-based correlation. The main emphasis is on the design of a correlator involving the reference object and its near-field diffraction pattern at an optimized distance. The input-scene image and its diffraction pattern constitute the input pattern of the new correlator. The new technique shows a significant increase in discrimination ability and optical efficiency. Moreover, different encoding methods, such as the phase-only filter or the matched filter, can be used in conjunction with this method. A theoretical analysis as well as examples are given.

Scale-adapted wavelet transform.

A modified wavelet transform, the scale-adapted wavelet transform (SAWT), is proposed. The scale factor is adaptively changed according to the local structure of the input signal. The transformed image keeps the same dimensions as the input signal without losing the meaningful multiresolution representation. Some simple applications of the SAWT are discussed.

Optimum rotation-invariant filter for disjoint-noise scenes.

We introduce an optimum matched filter for rotation-invariant pattern recognition in scenes with disjoint noise. The optimum filter maximizes the ratio between the correlation-peak intensity and the correlation-output energy; in order to ensure rotation invariance, we assume the filter to take the form of a circular-harmonic function. The performance of this new filter is tested by computer simulations with a variety of natural and artificial backgrounds. The results obtained from these tests show an excellent performance much better than the classical circular-harmonic function (the filter that maximizes the signal-to-noise ratio while maintaining rotation invariance).

Dammann-grating-based optodigital position converter.

An optodigital position converter based on a Dammann grating is proposed. The converter is based on a diffraction grating with a high diffraction efficiency coupled with a binary encoding mask. The module permits parallel processing of a scene so that one can extract the position of a correlation peak. Compression of the information is also performed. The binary output is compatible with digital systems.

Single-rail translation-invariant optical associative memory.

A single-rail optical memory is proposed. The associated memory is based on a double-correlator architecture coupled with an optoelectronic thresholding feedback module. The latter permits complete translation invariance of the neural network. The system requires only a single 35-mW He-Ne laser. The associative memory is recorded with the help of computer-generated holograms. The global iterative coding [Opt. Eng. 32, 2216 (1993)] technique provides good performance with high diffraction efficiency.

Phase calibration and applications of a liquid-crystal spatial light modulator.

A simple phase-characterization method for spatial light modulators is proposed. The low-cost method permits high-precision measurement and provides data for the setting of the spatial-light-modulator operating point in the phase-modulation mode. The dynamic phase response is used to perform efficient kinoform recording. In order to record the kinoform, we modify the global iterative coding to compute phase holograms. Finally, modified phase-phase correlation is introduced. The phase-phase correlator permits sharper correlation peaks, better energy transmission, and higher discrimination than an amplitude-phase correlation. Optical experimental results are presented.

Optoelectronic thresholding module for winner-take-all operations in optical neural networks.

A simple optoelectronic architecture for carrying out optical thresholding operations is proposed. The architecture is suitable for optical neural network implementations and for image processing. The module is based on liquid-crystal television, on a CCD camera, and on beam-sampling optical components. The module does not need an additional light source, shows translation invariance, and does not break the beam propagation path. Experimental results involving images and correlations are presented. Finally, an architecture for an automatic winner-take-all extractor for neural network architectures is proposed.

Invariant optical-pattern recognition based on a contour bank.

We propose a new optical pattern-recognition method that is invariant to shift, rotation, and scale changes. By means of a zero-order circular-harmonic filter the input object can be transformed into a correlation peak whose outline retains a shape similar to the outline of the input object. After multilevel thresholding and binarization, a bank composed of many contours with different sizes is formed. The invariant recognition can be obtained by a small contour line being taking as a reference and its second-order circular-harmonic component being taken as a filter. In addition to the scale invariance the correlation peak is superior to the classical circular-harmonic filter and the phase-only circular-harmonic filter in terms of peak intensity, half-maximum width, and peak-to-sidelobe ratio.

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.

Optical binary phase-only filters for circular harmonic correlations.

In our previous paper we proposed using successively binary cosine and sine filters and combining the correlation intensities for rotation-invariant phase-only circular harmonic correlation. This paper presents an alternative method that uses a single filter. We present theory and optical and computer experimental results to show that, with a spatial frequency carrier, the binary phase-only filter [1, -1] and the binary filter [1, 0] yield the impulse response of a continuous phase-only filter. Compared with conventional computer-generated holographic filters, the binary phase-only filter and the binary filter have no representation-related error, require a minimum space-bandwidth product, and may be implemented in a spatial light modulator.

Deconvolution of two-dimensional images with zeros in the transfer function.

Although it is generally believed that the information at the zeros of the transfer function is lost and cannot be recovered, this is not true: the information can be recovered, even in the presence of noise, because the lost information is coded into intermediate points where the transfer function is not zero. We extend our previous one-dimensional treatment [Can. J. Phys. 49: 1865 (1971)] to two dimensions and apply the results to the restoration of images degraded by noise and by linear filtering, such as movement blurring. The filter used is an honest filter in the sense that in the absence of noise, it yields a perfect restoration, including frequencies at the zeros of the transfer function. It is shown that the method considerably improves the restoration of linearly degraded real images.

Recording holograms with diagonal coding on binary spatial light modulators for pattern recognition.

The performance of computer-generated holographic matched filters recorded on 128 x 128 pixel supports was studied experimentally, with the objective of recording holograms on spatial light modulators such as the Semetex SIGHT-MOD for rotation-invariant pattern recognition. A new method of diagonal coding is introduced. This method yields good results, as it allows a more accurate phase quantization. Experimental results from computer simulations show that high speed rotation-invariant recognition of simple shapes is possible with such holograms.

Object detection from a real scene using the correlation peak coordinates of multiple circular harmonic filters.

Most proposed methods for rotation invariant multiple circular harmonic filters combine the intensities or amplitudes of the center correlations. We propose combining the coordinates of the correlation peaks of multiple circular harmonic filters. The new method is used to detect objects from a cluttered noisy input scene. High cross-correlation peaks coming from clutter do not cause false alarms. Experimental results are shown.

Rotation invariant phase-only and binary phase-only correlation.

Phase-only circular harmonic filters and binary phase-only circular harmonic filters are proposed. Both filters have full rotation invariance and excellent performance for discrimination between objects and against background noise. Their properties have been studied and implemented for computer applications. The binary filters are appropriate for real-time applications using spatial light modulators.

Rotation-invariant digital pattern recognition using circular harmonic expansion: author's reply to comments.

As Danielsson says in his comment on the paper by Arsenault, the phase information is not used and the same signature vectors can have different shapes. However, in practice the method works well.