Synthetic Discriminant Function Research Articles

Optical pattern recognition using a synthetic discriminant amplitude-compensated matched filter

A technique for optical pattern recognition using an amplitude-compensated matched filter is presented. With the synthetic discriminant function in a matched spatial filtering application an iterative technique is employed to first obtain the synthetic discriminant functions for the phase-only matched filter and then is extended to the amplitude-compensated matched filter. Computer simulation shows that the suggested spatial filter has a high signal-to-noise ratio and good Horner efficiency, and it is more sensitive to changes in the input image.

Case study of binary and ternary synthetic discriminant function filters with similar in-class and out-of-class images

We compare computer simulation results of optical correlator performance using synthetic discriminantfunction filters encoded in binary phase versus ternary phase and amplitude for distortion-tolerant pattern recognition. We examine two different ternary filter formulations designed to enhance discrimination and SNR. The simulated situation is for very similar in-class and out-of-class images, which makes discrimination between the two sets difficult. The ultimate performance criterion of interest is the probability of correct identification in the presence of image noise, which we address as a function ofthe range of distortion tolerance offered by the filters. We find that the ternary filters offer improved system performance and greater possible distortion range in comparison to the binary filters, and in particular that the ternary filters with a region of support designed to enhance SNR have the best performance for the image sets studied here. Knowledge of the out-of-class images allows the filter designer to create filters that maximize the probability of correct identification. We present numerical examples of this performance figure for two sets of training images.

Theoretical framework for the design of purely real synthetic-discriminant-function-type correlation filters

A general algorithm for synthesizing purely real correlation filters in the frequency domain is developed by using the method of Lagrange multipliers. This method can be applied to filters that are derived by using linearly constrained quadratic minimization. The synthesis of purely real versions of minimum average correlation energy filters, minimum-variance synthetic discriminant functions, and other synthetic-discriminant-function-type filters is discussed to illustrate this approach. Their performance is found to be somewhat less than that of the original complex filters but still adequate for practical applications. The main advantage of this approach is that optimum purely real filters can be generated that are easy to implement in spatial light modulators without holograms and that yield the correlation output on the zero-order beam.

Multiple-Object Discriminant Filter Generated by Simulated Annealing

A method of generating a new type of multiple-object discriminant filter, of which the filter function has discrete values, is presented. In order to reduce the error in peak-correlation response of a quantized synthetic discriminant function filter, the simulated annealing technique is used for filter design. As a result, the error is greatly reduced. Results of computer simulations are demonstrated.

Incoherent optical associative memory by using synthetic discriminant function filters

A new associative memory system applying incoherent correlators is presented. With this system, which is composed of a nonlinear processor and optical-electronic feedback loop, memorized patterns can be recalled without cross talk. To realize a high association ability and stable operation, a synthetic discriminant function filter is applied. Results of the computer simulation and actual experiments by using the system that is constructed here are demonstrated.

Minimum noise and correlation energy optical correlation filter

A new distortion-invariant optical correlation filter to produce easily detectable correlation peaks in the presence of noise and clutter and to provide better intraclass recognition is presented. The basic ideas of the minimum variance synthetic discriminant function correlation filter (which minimizes noise variance in the output correlation peak/plane) and the minimum average correlation energy filter (which minimizes the average correlation plane energy over all the training images) are unified in a new filter that produces sharp correlation peaks while maintaining an acceptable signal-to-noise ratio in the correlation plane output. This new minimum noise and correlation energy filter approach introduces the concept of using the spectral envelope of the training images and the noise power spectrum to obtain a tight bound to the energy minimization problem that is associated with distortion-invariant filters in noise while allowing the user a variable parameter to adjust depending on the noise or clutter that is expected. We present the mathematical basis for the minimum noise and correlation energy filter and the initial simulation results.

Hybrid composite filter banks for distortion-invariant optical pattern recognition

In the past, several different approaches to synthetic discriminant function (SDF) filter design have been proposed, including conventional SDFs, which control the correlation values at the origin; minimum variance SDFs (MVSDFs), which minimize the noise sensitivity of the filters; minimum average correlation energy (MACE) filters, which maximize the peak sharpness; and linear phase coefficient composite (LPCC) filters, which are obtained as the sum of training images weighted by linear phase coefficients. We introduce a new family of SDF filters of which all the above are special cases. Each filter in this family is characterized by two parameters α₁ and α₂. Various choices of (α₁ , α₂) lead to the above special filters. For example, α₁ = 1 and α₂ = 0 leads to MACE LPCC filters, which are hybrid versions of MACE and LPCC filters. This family of filters is evaluated using the minimum probability of error (MPE) criterion and a database of aircraft images. These simulation experiments confirm the superior performance of this filter family. Also, we observe the interesting result that the MPE is at its lowest not for one of the four special filters listed above, but for a combination of them.

Performance of synthetic discriminant functions for binary phase-only filtering of thresholded imagery

Imagery from infrared sensors was used for automatic object recognition using a digital simulation of an optical correlator with binary phase-only filters (BPOFs). The method was tested primarily for applications that involve objects with a nonrepeatable signature. In imagery from actual sensors, object boundaries can be poorly defined, and the same object can vary in shape significantly, depending on a host of variables. Digital image processing techniques were used to threshold gray-level images before correlation so that variations due to environmental conditions and other variables can be limited. A synthetic discriminant function made from a training set of thresholded imagery was used to create BPOFs. The potential of the recognition method was evaluated with imagery that varied in an unknown or nonrepeatable manner. The method presented here reduced the sensitivity of a BPOF to changes in an object's appearance when the object varied in an unknown way.

Minimum squared error synthetic discriminant functions

A new synthetic discriminant function (SDF) design approach is presented that yields the best approximation of arbitrary output correlation shapes in the minimum squared error (MSE) sense. We term such filters as MSE-SDFs. Simulation results are presented to illustrate the advantages of MSE-SDFs. Also, we show that MSE-SDFs generalize minimum average correlation energy filters.

Use of synthetic discriminant functions for handwritten-signature verification

Handwritten-signature verification is treated as a two-class synthetic discriminant function (SDF) problem. Images of valid and casually forged signatures are collected and binarized, using an electronic digitizing camera. Performance of this approach with a small number of valid signatures in the training set is examined, and substantial improvement is demonstrated when forgeries are included in the set. In particular, the equal-error rate for the SDF classifier with forgeries included is shown to average approximately 4% across nine different subjects. The effects of image preprocessing on false acceptance and true rejection rates are examined. The use of alternatives to forged signatures in the training matrix is explored. Finally, SDF performance is shown to deteriorate when the tested forgeries are produced with some a priori knowledge of the target signature.

Synthetic discriminants and eigenvector decompositions

The relationships between the synthetic discriminant function and the filters constructed from two eigenvector decompositions are developed and examined.

Normalized correlation for pattern recognition

The normalization of the correlation filter response effects intensity invariance. We discuss the implications of a normalization based on the Cauchy-Schwarz inequality for the discrimination problem. It is shown that normalized phase-only and synthetic discriminant functions do not provide the discrimination/recognition obtained with the classical matched filter.

Optical pattern recognition based on convex functions

Spatial filters based on the properties of convex functions can be generated directly on a hybrid electro-optical system. As an example, simulated annealing was used to design highly selective spatial filters. Laboratory experiments demonstrated efficient pattern recognition and class discrimination. Several procedures for designing synthetic discriminant functions discussed in the literature are shown to be special cases of the present procedure.

Application of the projection-onto-constraint-sets algorithm for optical pattern recognition

Projection-onto-constraint sets is an efficient algorithm for constructing synthetic discriminant functions to be employed in pattern-recognition systems. The algorithm is implemented by a digital procedure based on a simulated joint-transform correlator.

Phase selection of synthetic discriminant function filters

In this paper, we address the problem of correlation peak phase selection for synthetic discriminant function filters. We show that the minimization of the output variance and the optimization of the correlation peak form are problems of the same complexity (analogous to the determination of the ground state of a magnetic disordered system). We propose a general framework and, with examples, we show that, although the variance reduction by a proper selection of the correlation peak phases can be interesting in some situations, the optimization of the sharpness of the correlation peak is often more fruitful.

Filter design for optical pattern recognition: multicriteria optimization approach

A method of constructing optimal multicriteria filters for optical pattern recognition is presented. In the particular case of synthetic discriminant function filters, this method is illustrated for double-optimization criteria, and filters that are not overspecialized are obtained, in contrast with traditional techniques. Furthermore, a rigorous comparison between different filters, with respect to the considered criteria, is provided with this approach.

Improved synthetic discriminant function performance using Fresnel lens-encoded binary phase-only filters

Synthetic discriminant functions (SDFs) made using Fresnel lens-encoded binary phase-only filters are shown to yield increased performance relative to SDFs constructed using conventional binary phase-only filters. We present both computer simulations and experimental results in which these SDFs are written onto the magnetooptic spatial light modulator.

Selection of optimum output correlation values in synthetic discriminant function design

In the use of synthetic discriminant functions for the classification of scenes, the specification of output correlation values by the user is of utmost importance, since the filter performance significantly depends on these values. A systematic procedure for determining these values is developed in this paper. The proposed technique provides an optimal selection of the output correlation values in the sense that they result in a minimization of the probability of error in detection. Specific algorithms are developed for various situations of practical importance, which include the general multiple-class, multiple-training image problems. Several numerical examples are included to illustrate the performance improvements that result from employment of the proposed scheme.

Experimental verification of modified synthetic discriminant function filters for rotation invariance

A modified binary synthetic discriminant function filter designed to recognize objects over a range of rotated views has been verified on a laboratory optical correlator. A binary synthetic discriminant function filter has been previously described that will produce a specified correlation response for a set of training images. [See D. A. Jared and D. J. Ennis, "Inclusion of Filter Modulation in Synthetic-Discriminant-Function Construction," Appl. Opt. 28, 232-239 (1989).] In the filter design, the modulation characteristics of the device onto which the filter is mapped are included in the synthesis equations. The system of nonlinear equations is then solved using an iteration procedure based on the Newton-Raphson algorithm. The development of the filter-SDF (fSDF) method was driven by the practical concern to make currently available spatial light modulators with limited modulation capabilities functional for distortion invariant pattern recognition. This technique is used to synthesize filters for a binary magnetooptic spatial light modulator (MOSLM), the Sight-MOD produced by Semetex. Two MOSLMs are used in the laboratory correlator, one in the filter plane and one in the input plane. We demonstrate that a single filter produces equal correlation peaks for a sample object (a Shuttle Orbiter in these tests) over in-plane and out-of-plane rotation ranges up to 75 degrees . The correlator is able to track dynamically the shuttle as it moves along a curved path across the input field. Views of the object in between those in the training set are also recognized when training images are sufficiently close in angle (~5 degrees apart).

Unified framework for the synthesis of synthetic discriminant functions with reduced noise variance and sharp correlation structure

An inherent implementational limitation of the recently developed minimum average correlation energy (MACE) filters arises from the circular correlation implicit in the discrete frequency domain approach followed. An alternative methodology that uses space domain computations to overcome these limitations is presented. An improved synthetic discriminant function (SDF) that satisfies the conflicting requirements of reduced noise variance and sharp correlation peaks to facilitate ease of detection is developed by employing a unified framework for design. A quantitative evaluation of the performance characteristics of the new filter is conducted and is shown to compare favorably with the well known minimum variance SDF and the space domain MACE filter, which are special cases of the present design.