Clustering analysis of multidimensional fuzzy sets using mathematical morphology

The tools of mathematical morphology originally developed for image analysis can be generalized for structural analysis of the general class of multidimensional fuzzy data sets. In this chapter we discuss morphological tools useful for clustering analysis of fuzzy sets. Morphological techniques can perform cluster segmentations that are stable with respect to relative scale changes of the axes of the multidimensional space. We briefly explain a few simple approaches to convert data sets from continuous spaces to discrete spaces where the morphological algorithms can be applied. Morphological filters can be designed to eliminate noise which can cause large clusters to split into smaller clusters. Connectivity preserving filters can play an important role in removing noise while preserving important features of the data set which may be vulnerable to filtering processes. Morphological tools can segment complex data sets such as those consisting of shell type of clusters. We have reviewed several morphological algorithms useful for clustering of binary and fuzzy data sets.