Two-dimensional shape decomposition using fuzzy subset theory applied to automated chromosome analysis

This paper describes a technique to transform a two-dimensional shape into a generalized fuzzy binary relation whose clusters represent the meaningful simple parts of the shape. The fuzzy binary relation is defined on the set of convex and concave boundary points, implying a piecewise linear approximation of the boundary, and describes the dissemblance of two vertices to a common cluster. Next some fuzzy subsets are defined over the points which determine the connection between the clusters.The decomposition method first determines nearly convex regions, which are subgraphs of the total graph, and then selects the greatest nearly convex region which satisfies best the defined fuzzy subsets and relations. Using this procedure on touching chromosomes defining the simple parts to be the separated chromosomes, the decomposition often corresponds well to the decomposition that a human might make.