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A method of measuring surface roughness is provided in which a video image of a surface area is formed and partitioned into a set of regions that cover the video image. Each region is of equal size. A fractal dimension value is calculated for each region.

This paper discusses statistical, data analytic and related software that is useful in the realm of astronomy and spaces sciences. The paper does not seek to be comprehensive, but rather to present a cross section of software used by practicing statisticians. The general layout is first to discuss commercially available software, then academic research software and finally some possible future directions in the evolution of data-oriented software. We specifically exclude commercial database software from the discussion, although it is relevant. The paper focuses on providing internet (world wide web) pointers for a variety of the software discussed.

We are developing a synthetic environment to be used in combination with real environments for the purpose of mine counter measures. Two examples of our work involve applications to land-based minefields and an application to submarine defense. In the former application, imaging is done with six spectral bands. It has been shown empirically that a sequence of images taken in six spectral bands when viewed sequentially will allow one to distinguish between real mines, partially buried real mines, decoys, other metallic objects, and other manner of debris. The image can be viewed as a 2-dimensional image with an 6-dimensional vector attached to each pixel location. We use the grand-tour technique (Wegman and Shen, 1993) to find an optimal discrimant between real mines and other objects. We then use a head-mounted display (HMD) which is semitransparent so that the real-world objects can be seen through it. After processing the scene, the suspected sites of real mines are superimposed on the visual field so that the soldier wearing the HMD is alerted to the presence of mines. The submarine application is similar. We use Crystal Eyes technology and Silicon Graphics Onyx systems in our laboratory.

A self-organizing neural network and method for classifying a pattern signature having N-features is provided. The network provides a posteriori conditional class probability that the pattern signature belongs to a selected class from a plurality of classes with which the neural network was trained. In its training mode, a plurality of training vectors is processed to generate an N-feature, N-dimensional space defined by a set of non-overlapping trained clusters. Each training vector has N-feature coordinates and a class coordinate. Each trained cluster has a center and a radius defined by a vigilance parameter. The center of each trained cluster is a reference vector that represents a recursive mean of the N-feature coordinates from training vectors bounded by a corresponding trained cluster. Each reference vector defines a fractional probability associated with the selected class based upon a ratio of (1) a count of training vectors from the selected class that are bounded by the corresponding trained cluster to (2) a total count of training vectors bounded by the corresponding trained cluster. In the exercise mode, an input vector defines the pattern signature to he classified. The input vector has N-feature coordinates associated with an unknown class. One of the reference vectors is selected so as to minimize differences with the N-feature coordinates of the input vector. The fractional probability of the selected one of the reference vectors is the a posteriori conditional class probability that the input vector belongs to the selected class. (KAR) p. 1, Supersedes PAT-APPL-936 369-92, AD-D016 455.

A discrete non-linear estimator is provided to establish a probability density function useful in classification of a feature as belonging to one of two classes. A first and second known feature space associated with respective first and second classes are each converted to a plurality of voltages reflecting corresponding first and second feature space bins. A first and second one-dimensional, non-linear resistive grid has input nodes that continuously receive the voltages reflecting the respective first and second known feature space. Each resistive grid produces an output voltage at each of a corresponding plurality of first and second output nodes. Each of a plurality of voltage comparators are used to compare voltages at corresponding first and second output nodes to output a discrete probability density function that considers corresponding ones of the first and second feature space bins. A display may be used to visually or otherwise provide each probability density function from each voltage comparator. (AN), Supersedes PAT-APPL-157 553-93.

A network is provided for the detection and correction of local boundary misalignments in a two-dimensional pixel space between a reference and transformed image. An input layer has input layer sections, each of which contains a plurality of input nodes associated with a cell. The cell is centered on a pixel and divided along a straightline orientation into first and second cell sections. Each of the input nodes outputs a digital signal indicative of the presence or absence of a contrast gradient as measured by the two cell sections. A second layer has a plurality of second layer sections, each of which is associated with one of the input layer sections and contains a plurality of second layer nodes. Each second layer node is responsive to a combination of input nodes to indicate the presence or absence of a boundary misalignment between the reference and transformed images. Presence of a contrast gradient at the combination of nodes defines a local boundary misalignment., Supersedes PAT-APPL-920 700.

This paper focuses on recent work which analyzes the expectation maximization (EM) evolution of mixtures based estimators. The goal of this research is the development of effective visualization techniques to portray the mixture model parameters as they change in time. This is an inherently high dimensional process. Techniques are presented which portray the time evolution of univariate, bivariate, and trivariate finite and adaptive mixtures estimators. Adaptive mixtures is a recently developed variable bandwidth kernel estimator where each of the kernels is not constrained to reside at a sample location. The future role of these techniques in developing new versions of the adaptive mixtures procedure are also discussed.

The existence of outliers in a data set and how to deal with them is an important problem in statistics. The Minimum Volume Ellipsoid (MVE) estimator is a robust estimator of location and shape; however its use has been limited because few computationally attractive methods exist to calculate it. Determining the MVE consists of two parts: finding the subset of points to be used in the estimate and finding the ellipse that covers this set. This paper will address the first problem. The proposed method of subset selection is called the Effective Independence Distribution (ElD) method which chooses the subset by mnimizing determinants of matrices containing the data. This method is deterministic yielding reproducible estimates of location and scatter for a given data set. The ElD method of finding the MVE is applied to several regression data sets where the true estimate is known. Results show that the EID method produces the subset of data in less than a second and that there is less than 6% relative error in the estimates. (AN)

Given i.i.d. observations x1,x2,x3,,,,xn drawn from a mixture of normal terms one is often interested in determining the number of terms in the mixture and their defining parameters. Although the problem of determining the number of terms is intractable under the most general assumptions there is hope of elucidating the mixture structure given appropriate caveats on the underlying mixture. This paper examines a new approach to this problem based on the use of Akaike Information Criterion (AIC) based pruning of data driven mixture models which are obtained from resampled data sets. Results of the application of this procedure to artificially generated and real world data sets are provided., Sponsored in part by Grants N00014-92-J-1303, N00014-93-1-0527.

A multi-layer neural network is provided for the detection and correction of local boundary misalignments in a two-dimensional pixel space between a reference and transformed image.