ENUMERATION OF ANOMALY/PEAK BASES AND EDGE DETECTION IN TWO-DIMENSIONAL INTENSITY HISTOGRAMS. APPLICATION OF GRAPH THEORY TO CRYSTALLOGRAPHIC DATA IMAGING. Joseph H. Reibenspies, Department of Chemistry, Texas A & M University, College Station, Texas 77843 USA

Bragg peaks, spikes, intensity streaks and other anomalies generate unique domains in two-dimensional intensity histograms. Examination of the shape and edges of these domains can contribute to the identification of the type of phenomenon that generated them. The points which define the anomaly bases, when connected, with imaginary lines, will form unique base graphs. Individual base graphs, in turn, can be enumerated by employing Graph Theoretical notation and the base graph shapes classified. In edge detection, the shortest spanning tree (SST), where the tree is defined as a nonbranching, noncyclic, binary graph, can be employed. Individual domains can thus be isolated by defining their edges. Since the SST method is domain sensitive it is possible, in theory, to identify anomalies whose intensities are below the detection limit. The application of Graph Theoretical techniques to anomaly bases and edges can thus provide insight into the nature of the intensities distributed through out the two-dimensional crystallographic data image.