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Mathematical morphology tools for 3D image analysis of porous media

This paper presents mathematical morphology tools for 3D image analysis, namely, the geodesic granulometries and the neck histogram. The family of openings which constitutes the geodesic granulometries is parameterized by the radius of the digital disks utilized as structuring elements. We demonstrate the validity of the granulometry thus obtained. The resulting granulometric distributions are determined by the underlying metric associated with the digital disks. Next we propose an algorithm to compute the neck histogram, which is an analysis tool that gives statistical information concerning the occurrence of constrictions in the object studied. Finally, we demonstrate the applicaiton of the proposed analysis tools in the characterization of a 3D experimental sample designed as a model for a porous medium.