Two-dimensional shape representation using morphological correlation functions

A new descriptor for representing two-dimensional continuous or discrete signals is introduced. The proposed shape descriptor, which is called the geometrical correlation function (GCF), is based on the principle of mathematical morphology. The properties of this shape descriptor are examined. It is shown that the family of GCFs associated with different orientations of a particular shape is translation, scale, and rotation invariant. Geometrical properties such as the area and perimeter of the shape can be derived from the GCF family. The utilization of the GCFs for shape recognition is considered. The GCF family can be computed using the associated morphological correlator which is composed of m parallel computation units and a feature-function selection unit where a small subset of the GCF family is selected for classification. It is shown that with a suitable criterion for selecting the feature function, promising results for successful classification are obtained