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.