Tutorial on Connective Morphology

Morphological operators may be taken up from the two entries of dilation and of connection. This tutorial focuses on the second entry, and leads to optimum partitionings of the images under study. Five notions, which derive from each other, are successively explored. The “set connection,” which generalizes the usual connectivities, opens the series, and yields the “connective segmentation,” which associates connection with maximum partition. Then the “connected operators” allow to construct “hierarchies of partitions” whose the laws of “optimal cuts” are given.