Convexity dependent morphological transformations for mode detection in cluster analysis

摘要

An approach to unsupervised pattern classification is discussed, based on both the mathematical morphology and convexity analysis of the underlying probability density function. The density function, which is estimated from the input data, is dilated when it is concave and eroded when it is convex. Iterations of these convexity dependent morphological transformations tend to enhance the modes and to enlarge the valleys of the underlying p.d.f., so that mode detection becomes trivial. Examples of the performance of the clustering scheme based on the so-detected modes are given using artificially generated data sets.