Abstract: Individual objects are located according to a coordinate system in time-successive patterns and correlated between patterns. The objects are correlated by assigning identifiers to each in both patterns. The locations are transformed by reorientation to their centroid. The average of the transformed coordinate differences is used to adjust the centroid of the objects in a subsequent pattern and the transformed coordinate differences adjusted for the centroid displacement. A figure of merit is taken as the root-mean-square of the adjusted differences and used to determine which possible combination of correlated objects between two patterns is most likely.

Abstract: Individual objects are located according to a coordinate system in time-successive patterns and correlated between patterns. The objects are correlated by assigning identifiers to each in both patterns. The locations are transformed by reorientation to their centroid. The average of the transformed coordinate differences is used to adjust the centroid of the objects in a subsequent pattern and the transformed coordinate differences adjusted for the centroid displacement. A figure of merit is taken as the root-mean-square of the adjusted differences and used to determine which possible combination of correlated objects between two patterns is most likely.

Abstract: Consistent and unambiguous pattern sorting and assignment of indices to clustered K objects in a multidimensional space. The dispersion along each dimension is calculated and the order of dimensions by which the sort sequence is arranged corresponds to the inverse order of the dispersion values. For each dimension, unsorted objects are grouped and arranged according to coordinate values. The sort sequence, i.e., assignment of indices, is performed by comparing the coordinate value in successive dimensions of each object with its successor or its predecessor. If the magnitudes of the differences are less than one or more predetermined thresholds, the points are transferred to another array which is sorted along the next dimension. The groupings and index assignments continue until all objects have been assigned an index.