Synthetic Discriminant Function Research Articles

Distortion range of filter synthetic discriminant function binary phase-only filters

This paper considers the performance of filter synthetic-discriminant-function binary-phase-only filters (fSDF-BPOFs) with images in the distortion range that were not members of the training set. This evaluation was performed to understand better the distortion range that can be effectively covered by fSDF-BPOFs. The peak correlation and peak clutter responses were measured over various distortion ranges for in-plane and out-of-plane rotations. The peak correlation initially decreased rapidly as the distortion range increased but decreased gradually as the distortion range became larger for the images used in this study. The distortion ranges that can be effectively covered by fSDF-BPOFs appear to be modest: 0-30 degrees for inplane rotation and 0-10 degrees for out-of-plane rotation. The results indicate that a temporal multiplexing scheme will be required to cover a large distortion range when BPOFs are used.

Properties of computer-generated, phase-only synthetic discriminant filters

The paper presents the experimental properties of the phase-only synthetic discriminant functions (SDF) filter when trained for invariance to in-plane rotation. Digital simulations and optical implementations by computer-generated holography are presented with results showing rejection of objects with a mean intensity six times that of the training class.

Optical pattern recognition and associative memory: an introduction by the feature editor

The feature in the 15 Jan. 1989 issue of Applied Optics includes papers dealing with the problem of pattern recognition including triple correlation, preprocessing, differentiating spatial light modulators, synthetic discriminant functions, circular harmonics for space-invariant pattern recognition, and adaptive associative memory techniques. The feature issue concludes with a paper comparing conventional digital-optical image processing to artificial neural networks.

Industrial use of a real-time optical inspection system

Real-time optical inspection techniques are discussed and implemented on laboratory systems. Specifically, we show how Fourier transform and Hough transform data can be used in an industrial inspection application. We also discuss how a 1-D synthetic discriminant function is used for label inspection. Real-time optical Hough transform inspection data using a 2-D spatial light modulator is presented and discussed. A color liquid crystal television (LCTV) is used as the input transducer to provide real-time data. New methods to process color image data on color LCTVs are detailed. A new high speed acoustooptic architecture to generate Hough transform slices is also detailed. A specific product inspection case study is discussed.

Comparison of statistical pattern-recognition algorithms for hybrid processing I Linear-mapping algorithms

Two groups of pattern-recognition algorithms for hybrid optical–digital computer processing are theoretically and experimentally compared. The first group is based on linear mapping, while the second group is based on feature extraction and eigenvector analysis. We study the relations among various linear-mapping-based algorithms by formulating a more general unified pseudoinverse algorithm. We show that the least-squares linear-mapping technique, the simplified least-squares linear-mapping technique, the synthetic discriminant function, the equal-correlation-peak method, and the Caulfield–Maloney filter are in fact all special cases of the unified pseudoinverse algorithm. When the total number of the training images (KM, where K is the number of classes and M is the number of training images in each class) is larger than the dimension of the images (N), the overdetermined case of the unified pseudoinverse algorithm is the same as the least-squares linear-mapping technique, because both algorithms are based on optimization processes of minimization of the mean-square error. When KM < N, the underdetermined case of the unified pseudoinverse algorithm is the same as the least-squares linear-mapping technique and the synthetic discriminant function. Furthermore, when KM < N, the synthetic discriminant function method can be considered a degenerate case of the least-squares linear-mapping technique. Among the algorithms studied, the simplified least-squares linear-mapping technique requires the least computation time for filter synthesis. Experimental results on classification with linear-mapping-based algorithms are provided and show good agreement with the theoretical analysis.

Multiple degree of freedom object recognition using optical relational graph decision nets

Multiple degree of freedom object recognition concerns objects with no stable rest position with all scale, rotation, and aspect distortions possible. We assume that the objects are in a fairly benign background, so that feature extractors are usable. In-plane distortion invariance is provided by use of a polar-log coordinate transform feature space, and out-of-plane distortion invariance is provided by linear discriminant function design. Relational graph decision nets are considered for multiple degree of freedom pattern recognition. The design of Fisher linear discriminant functions and synthetic discriminant functions for use at the nodes of binary and multidecision nets is discussed. Case studies are detailed for two-class and multiclass problems. Simulation results demonstrate the robustness of the processors to quantization of the filter coefficients and to noise.

Generalized synthetic discriminant functions

A generalization of the conventional synthetic discriminant function (SDF) solution in both spatial and frequency domains is provided. It is based on the concept of the generalized inverse. The results of this generalization are shown to specialize to previous work (namely, the minimum-output-variance SDF). A link is established between the quantities characterizing the spatial-domain SDF solutions and the frequency-domain ones through the pseudo-discrete Fourier-transform operation. Several properties of the various relevant matrices are presented to provide a general framework for characterizing SDF solutions. To help to illustrate the advantages of the generalized SDF solution method, two examples of SDF’s (a phase-only and a two-level SDF) are investigated.

Constraint phase optimization in minimum variance synthetic discriminant functions

It is shown that proper selection of constraint phases in minimum variance synthetic discriminant functions can further reduce the output variance due to input noise. It is demonstrated with the help of examples that this reduction in variance can range from being negligible to being significant. The exact amount of reduction depends on the constraint magnitudes, training images, and the noise covariance matrix.

Conventional and composite matched filters with error correction: a comparison

A common pattern recognition problem is finding a library object which most closely matches a received image. For additive white Gaussian input noise, optimal detection performance is obtained using a matched filter for each of the N possible library objects. The use of composite matched filters (CMFs) (also called synthetic discriminant functions or linear combination filters) is one technique of reducing the number of filters required for the recognition problem. For two-level composite matched filter outputs, the reduction is from N to Q = log(2) (N) filters. The CMF's performance, however, can be suboptimum. Using CMFs with bipolar (+1,-1) outputs, this paper examines the detection performance improvement obtained by using error correcting codes. Use of varying levels of error correction is shown to allow trade-off between detection probability and the number of bank filters. Also, we show that in the case of inexact processing, the CMF can perform better than the conventional matched filter.

Composite matched filter output partitioning

A common pattern recognition problem is finding a library element closest, in some sense, to a given reception. In many scenarios, optimal detection requires N matched filters for N library elements. Since N can often be quite large, there is a need for suboptimal techniques that base their decisions on a reduced number of filters. The use of composite matched filters (CMFs) (also called synthetic discriminant functions or linear combination filters) is one technique to achieve this reduction. For two level CMF outputs, the reduction is from N to log(2)N matched filters. Previously, the coefficients of the CMF output were restricted to positive values-often 0 and 1. We refer to such filters as binary CMFs. An alternative approach is to use -1 and +1 for filter coefficients. This alternative filter will be called a bipolar CMF. This paper demonstrates how the extension from a binary to a bipolar CMF greatly improves the detection performance while still maintaining the reduced computational requirements of the binary CMF. Furthermore, the bipolar CMF is invariant to scale: multiplying the input by a positive constant gives the same processor output. This desirable behavior does not exist for the binary CMF.

Computer-generated and phase-only synthetic discriminant function filters

The laboratory realization of smart matched spatial filters (specifically snythetic discriminant functions) is considered and studied via computer simulation. The realization of these distortion-invariant correlator functions by computer-generated hologram and other methods is considered. Multiclass filters are addressed in this work. Phase-only filters and filters with a quantized number of amplitude and phase levels are considered. Phase-only filters are found to perform well for some imagery, but filters with some amplitude response are preferable. We also considered the number of phase and magnitude levels required and found four levels of each to be adequate.

Minimum-variance synthetic discriminant functions

The conventional synthetic discriminant functions (SDF’s) determine a filter matched to a linear combination of the available training images such that the resulting cross-correlation output is constant for all training images. We remove the constraint that the filter must be matched to a linear combination of training images and consider a general solution. This general solution is, however, still a linear combination of modified training images. We investigate the effects of noise in input training images and prove that the conventional SDF’s provide minimum output variance when the input noise is white. We provide the design equations for minimum-variance synthetic discriminant functions (MVSDF’s) when the input noise is colored. General expressions are also provided to characterize the loss of optimality when conventional SDF’s are used instead of optimal MVSDF’s.

Correlation synthetic discriminant functions

Advanced filters are described for distortion-invariant space-invariant object identification and location in clutter using correlators. These correlation synthetic discriminant functions (SDFs) are extensions of earlier projection SDFs. They provide control of the sidelobe levels and the shape of the output correlation function as well as its peak intensity. The theory for synthesis of three such SDFs and a discussion of correlation plane detection criteria for use with these filters are presented.

Optical Processing And Space Station Automation

Optical information processing research aimed at Space Station automation applications is reviewed. The emphasis of the NASA Ames Research Center program is on intelligent optical pattern recognition and optical control processing. Attention is given to the primary functions of an overall scene understanding system: distortion-invariant optical feature generation, dimensionality reduction, object classification, and contextual information processing. A method of using synthetic discriminant functions to facilitate learning in a high-speed optical correlator is described. A discussion is presented of candidate analog and digital architectures for the optical implementation of state-estimation algorithms needed for the control of high-dimension dynamic systems. The multivariate system chosen for the optical control technology demonstration - a segmented, adaptive mirror and interferometrically based wavefront sensor - is also described.

Applying the phase-only filter concept to the synthetic discriminant function correlation filter

A modified form of a composite or multiplexed matched filter has been computer simulated and tested. The modification consists of using only the phase function and setting the amplitude function equal to unity—a so-called phase-only filter (POF). The original filter was D. Casasent's synthetic discriminant function (SDF) filter. The filter and test images were made from actual IR imagery. The results are compared in terms of efficiency, correlation peak height and width, and signal/noise ratio. A binary phase version of the SDF/POF was also tested. Its performance is between the SDF and the SDF/POF.

Coherent Optical Pattern Recognition: A Review

Recent progress in coherent optical pattern recognition is reviewed. Emphasis is given to techniques for multiclass distortion-invariant pattern recognition. Real-time and practical architectures and algorithms are described, and recent results on extensive data bases are noted. Feature-extraction and correlation architectures are chosen as the two major approaches. The feature-extraction techniques considered include Fourier coefficients, chord distributions, and moments. The correlator approaches emphasize the use of synthetic discriminant functions to achieve multiclass distortion-invariant pattern recognition.

Projection Synthetic Discriminant Function Performance

Synthetic discriminant functions (SDFs) allow distortion invariance to be achieved in optical correlators, thus making such systems more practical. The synthesis of four different types of SDFs is reviewed. Their performance in extensive projection tests on 144 images is presented, together with initial performance tests in the presence of noise. This distortion-invariant and shift-invariant pattern recognition algorithm can also be implemented digitally.

Simulation Of Synthetic Discriminant Function Optical Implementation

The optical implementation of geometrical shape and synthetic discriminant function matched filters is computer modeled. The filter implementation utilizes the Allebach-Keegan computer-generated hologram algorithm. Signal-to-noise and efficiency measurements were made on the resultant correlation planes.

Unified synthetic discriminant function computational formulation

A most attractive approach to distortion-invariant pattern recognition uses a synthetic discriminant function (SDF) as the matched spatial filter in a correlator. In this paper, we (1) provide a general basis function and hyperspace description of SDFs, (2) advance a derivation showing the generality of the correlation matrix observation space that we use in our filter synthesis, and (3) detail a unified SDF filter synthesis technique for five different types of pattern recognition problem.