OPTIMAL AND ADAPTIVE RECONSTRUCTIVE GRANULOMETRIC BANDPASS-FILTERS

Granulometric spectral decomposition results from partitioning an imag e according to the manner in which a granulometry diminishes the image , An optimal granulometric bandpass filter is one that passes spectral components in a way to minimize the expected area of the symmetric di fference between the filtered and ideal images. The present paper trea ts bandpass optimization for reconstructive granulometries. For these, each connected grain in the input image is either fully passed or eli minated, Such filters are well-suited for elimination of clutter or; e quivalently, locating grains in size-shape bands. The observed image i s typically modeled as a disjoint union of signal and clutter grains a nd the filter is designed to best eliminate clutter while maintaining the signal. The method is very general: grains are considered to be re alizations of random sets; there are no shape constraints on signal an d noise grains; there are no similarity constraints between granulomet ric and image generators; and the method applies to overlapping grains by filtering the image model resulting from segmentation preprocessin g. Three filter design paradigms are considered, one for optimal and t wo for adaptive filters. (C) 1997 Elsevier Science B.V.