Richard D. Juday

Optimal realizable filters and the minimum Euclidean distance principle

Minimizing a Euclidean distance in the complex plane optimizes a wide class of correlation metrics for filters implemented on realistic devices. The algorithm searches over no more than two real scalars (gain and phase). It unifies a variety of previous solutions for special cases (e.g., a maximum signal-to-noise ratio with colored noise and a real filter and a maximum correlation intensity with no noise and a coupled filter). It extends optimal partial information filter theory to arbitrary spatial light modulators (fully complex, coupled, discrete, finite contrast ratio, and so forth), additive input noise (white or colored), spatially nonuniform filter modulators, and additive correlation detection noise (including signaldependent noise). An appendix summarizes the algorithm as it is implemented in available computer code.

Correlation with a spatial light modulator having phase and amplitude cross coupling

In correlation filtering a spatial light modulator is traditionally modeled as affecting only the phase or only the amplitude of light. Usually, however, a single operating parameter affects both phase and amplitude. An integral constraint is developed that is a necessary condition for optimizing a correlation filter having single parameter coupling between phase and amplitude. The phase-only filter is shown to be a special case.

Autonomous real-time object tracking with an adaptive joint transform correlator

A hybrid optical/digital system for tracking an object in a sequence of images is described. Since a joint transform correlator does not require a matched spatial filter in the correlation process, object tracking can be carried out by continuously updating the reference image with the object image in the previous frame. This adaptive property of a joint transform correlator, together with the parallelism and high processing speed of an optical system, ensure high correlation between objects in two sequential frames. The relative position of the object can then be determined based on the location of the correlation peak. System performance is evaluated and experimental demonstrations are presented.

A programmable video image remapper

NASAs Johnson Space Center (JSC) has created the specifications for a new kind of image processing machine, a video-rate coordinate remapper. JSC has contracted with Texas Instruments for its detailed design and construction. Previous image processing machines for machine vision typically have done point operations without changing the geometry of the image. The JSC/TI Programmable Remapper offers complete flexibility in changing the coordinates of an input image at video rates. Presented here are the main capabilities and some of the applications of such a device.

Optimal real correlation filters

Expressions are derived for real filters that have a maximum correlation signal to noise ratio. Both continuous and discrete cases are treated and shown to have similar forms. The signal can be complex, and the case of a real signal is considered and related to previous results.

Data association multiple target tracking using a phase-mostly liquid crystal television

This paper presents a technique of using data association target tracking in a motion sequence via an adaptive joint transform correlator. The massive data in the field of view can be reduced to a few correlation peaks. The average velocity of a target during the tracking cycle is then determined from the location of the correlation peak. We have used a data association algorithm for the analysis of these correlation signals, with which multiple targets can be tracked. A phase-mostly LCTV is used in the hybrid joint transform correlation system, and simultaneous tracking of three targets is demonstrated.

Automated self-alignment procedure for optical correlators

We propose a general and fully automated procedure that enables the self-correction of the errors and performance losses produced by the misalignment of the components of an optical correlator. This method is simple, is carried out entirely by software, and has minimal operating constraints. There are no moving parts and no extra hardware is required.

Relaxation Method Of Compensation In An Optical Correlator

An iterative method is proposed for the sharpening of programmable filters in a 4-f optical correlator. Continuously variable spatial light modulators (SLMs) permit the fine adjustment of optical processing filters so as to compensate for the departures from ideal behavior of a real optical system. Although motivated by the development of continuously variable phase-only SLMs, the proposed sharpening method is also applicable to amplitude modulators and, with appropriate adjustments, to binary modulators as well. A computer simulation is presented that illustrates the potential effectiveness of the method: an image is placed on the input to the correlator, and its corresponding phase-only filter is adjusted (allowed to relax) so as to produce a progressively brighter and more centralized peak in the correlation plane. The technique is highly robust against the form of the systems departure from ideal behavior.

Generalized Rayleigh quotient approach to filter optimization

Through the Rayleigh quotient (the ratio of intensity responses of a filter to different objects) we may generalize a great number of metrics used in optical pattern recognition. The Rayleigh quotient has been optimized in linear digital systems under the constraint of unit-energy filters. In optical pattern recognition at least two considerations violate the conditions under which the quotient has been digitally optimized: the noise background of the measurement invokes nonlinearity, and filters are constrained other than to unit energy. I show a solution that optimizes the ratio of biased measurements, subject to constraining filter values to arbitrary subsets of the complex plane. Previous solutions are discussed as special cases. A metric’s numerator and denominator may now both include the objects’ phase.

Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition.

Matched filtering followed by a minimum Euclidean distance projection onto realizable filter values was previously shown to optimize the signal-to-noise ratio for single training images in optical correlation pattern recognition. The algorithm is now shown to solve the combination of (1) standard statistical pattern-recognition metrics with multiple training images, (2) additive input noise of known power spectral density and also additive detection noise that is irreducible by the filter, (3) the building of the filter on arbitrary subsets of the complex unit disk, and (4) the use of observable correlator outputs only. The criteria include the Fisher ratio, the Bayes error and Bayes cost, the Chernoff and Bhattacharyya bounds, the population entropy and expected information, versions of signal-to-noise ratio that use other than second power in their norm, and the area under the receiver operating characteristic curve. Different criteria are optimized by different complex scalar weights.