Parametrical and morphological spectra

A generic formalism of parametric spectra is proposed for describing all spectra of this type from a common viewpoint. The parametric spectrum represents the density of distribution of some pattern/image measure (numerical characteristic) over the parameter under analysis. The measure depends monotonically on the analyzed parameter. The classification of parametric spectra is made. The most general case of parametric spectra are the spectra of the measurement accuracy as a function of the resolution parameter. They include as special cases: spectra based on descriptors, spectra based on filtering, partial order spectra, spectra based on monotone filtering operators, spectra based on enclosed projectors and distance, spectra based on normalized linear spaces. A subclass of morphological spectra that represent reconstruction accuracy spectra by the description complexity parameter is considered. The connection between the parametrical spectra and relevant parametrical decompositions is shown.