Generalized multiscale connected operators with applications to granulometric image analysis

In this paper, generalized granulometric size distributions and size histograms (a.k.a ´pattern spectra´) are developed using generalized multiscale lattice operators of the opening and closing type. The generalized size histograms are applied to granulometric analysis of soil-section images. An interesting structure is obtained when the histogram is based on area openings. Furthermore, a fast implementation of the generalized size histograms is presented using threshold analysis-synthesis. Comparisons with size distributions based on conventional morphological operators indicate that the generalized histograms provide a more direct and informative description of the image content in objects with scale-dependent geometric attributes. Applications are also developed for studying the structure of soilsection images