Morphological shape description using geometric spectrum on multidimensional binary images

A useful morphological shape description tool is presented called geometric spectrum or G-spectrum, for quantifying the geometric features on multidimensional binary images. The basis of this tool relies upon the cardinality of a set of non-overlapping segments in an image using morphological operations. The G-spectrum preserves the translation invariance property. With a chosen set of isotropic structuring elements the G-spectrum also preserves the rotation invariance. After the procedure of normalization, the G-spectrum can also preserve the scaling invariance. The properties and proofs of the G-spectrum are discussed.