James D. Brasher

Fractional-power synthetic discriminant functions

Abstract The standard synthetic discriminant function (SDF) generalizes well. That is, it recognizes objects represented by, but not included in, the training set from which it is synthesized. However, it also correlates with objects not represented by the training set. That is, it does not discriminate well. Conversely, the minimum average correlation energy (MACE) SDF discriminates, but does not generalize, well. By using a power spectrum normalization procedure, a parametric SDF which generalizes better than the MACE SDF and discriminates better than the standard SDF is obtained.

Relationship between maximizing the signal-to-noise ratio and minimizing the classification error probability for correlation filters

For some correlation filters, maximizing the signal-to-noise ratio is equivalent to minimizing the probability of classification error (P(e)) when the underlying probability distribution functions are Gaussian. For other filters, maximizing the signal-to-noise ratio does not automatically minimize P(e), so both should be considered separately when optimizing filter performance.

Synthetic discriminant functions for recognition of images on the boundary of the convex hull of the training set

Abstract In designing synthetic discriminant function (SDF) filters, the usual choice for the correlation constraint is a real-valued constant for all training images of a given class. However, this choice of constraints results in a filter that recognizes all images in the convex hull of the training set, which is generally undesirable. The use of appropriate complex-valued constraints, though, produces an SDF filter which recognizes only images near the boundary of this convex hull and thus provides improved discrimination performance. This improvement in discrimination can be accomplished without degrading the generalization performance of the filter.

Nonlinear decision boundaries from the use of complex constraints in synthetic discriminant function filters

Conventional Synthetic Discriminant Function (SDF) filter formulations employ the same real correlation output (at origin) for all input training images from the same class, but this leads to poor discrimination. However, this can be overcome by using complex correlation constraints in the SDF filter design. In this paper, we characterize the recognition sets for such SDF filters.

Role of the constraint values in synthetic discriminant function filter design

Several methods of designing Synthetic Discriminant Function (SDF) filters exist. All of these require that the correlation output take on specified values at origin. In this paper, we examine the role of these correlation plane constraints. We show that the conventional practice (of forcing the correlation outputs to a constant for all training images from a single class) leads to poor discrimination. We introduce a new method to improve the discrimination capabilities of SDF filters.

Correlation filters assessed in terms of probability of detection and probability of false alarm

Many correlation filters (e.g., matched spatial filters, phase-only filters, binary phase-only filters, etc.) are usually evaluated in terms of metrics such as signal-to-noise ratio, peak-to- correlation energy and Horner light efficiency. In this paper, we compare the MSF and POF using more direct performance measures, the probability of detection (PD) and the probability of false alarm (PFA).

Landscaping the correlation surface

A very common operation in optical processing is cross correlation of an input scene with a filter to extract information from the input scene. For instance, in the identification mode a correlation surface should contain a high value at the location corresponding to the position of the object in the input space and significantly lower values at all other locations. The performance of this operation is unfortunately degraded when the input contains noise, or the object is distorted, rotated, shifted, occluded, or changes in aspect. A corrupted input requires that the filter have some generalization capability. This capability is usually gained at the expense of the peak sharpness and height. Thus, filter architectures that mold the correlation surface to effectively trade peak sharpness and generalization need to the considered. This paper considers several filters of the SDF family with regard to their ability to shape the output correlation surface.

SDFs for sensor/data fusion

We describe how the synthetic discriminant function (SDF) can be employed in sensor/data fusion. This is accomplished by exploiting the isomorphism between the SDF formalism and the parallel distributed processing (PDP) architecture of neural networks.

Layered optical processing architectures

The function of any processor is to map input data to output data. Multi-layer processing systems can implement mappings not feasible in single-layer systems. A layered architecture not only facilitates the implementation of non-linear operations, but also provides successive stages for linear processing. We describe the use of layered architectures in optical processing.

Optical processing architectures for machine vision functions

Manufacturers must increase production rates and simultaneously tighten quality/process controls in order to meet ever-increasing competition and consumer demands for high quality products. This requires that products be manufactured more efficiently, at reducing cost, and with minimum scrap/waste. This in turn demands higher-speed inspection, with higher accuracy and consistency as well as intelligence. Achieving these goals will require highly parallel systems that perform image processing and pattern recognition in real time in various manufacturing environments. This paper presents a hybrid architecture combining state-of-the- art optical processing with conventional digital processing. A Solid Optical Correlator (SOC) system has been built and validated. The SOC incorporates rigidity, stability, and manufacturability--attributes which facilitate the use of the optical correlator in real-world industrial machine vision applications.