Abstract: A method of measuring surface roughness is provided in which a video image f 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. The fractal dimension values for the regions are averaged to form an average fractal dimension value associated with the particular region size. The steps of partitioning, calculating and averaging are repeated for additional set(s) of regions with each region from an additional set being of an equal and unique size. When all average fractal dimension values are plotted as a function of region size, a best-fit straight line is defined. A combination of the slope and y-intercept of the straight line is indicative of surface roughness of the surface area.

Abstract: 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.

Abstract: A discrete non-linear estimator is provided to establish a probability dety 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.

Abstract: 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.