Shape connectivity: multiscale analysis and application to generalized granulometries

Abstract. This paper develops a multiscale connectivity theory for shapes based on the axiomatic definition of new generalized connectivity measures, which are obtained using morphology-based nonlinear scale-space operators. The concept of connectivity-tree for hierarchical image representation is introduced and used to define generalized connected morphological operators. This theoretical framework is then applied to establish a class of generalized granulometries, implemented at a particular problem concerning soilsection image analysis and evaluation of morphological properties such as size distributions. Comparative results demonstrate the power and versatility of the proposed methodology with respect to the application of typical connected operators (such as reconstruction openings). This multiscale connectivity analysis framework aims at a more reliable evaluation of shape/size information within complex images, with particular applications to generalized granulometries, connected operators, and segmentation