Connective segmentation

These last five years, mathematical morphology evolved in a few directions, an important one being a theory and practice of segmentation. This theory is based on the search for maximal partitioning of the space. The central theorem of the paper (Theorem 7) identifies segmentation with some classes of connections. Just as connections, the segmentations can then be regrouped by suprema and infima, which permits serial and parallel combinations. The segmentation classes turn out to be independent of their location in the measuring field, assuming that a convenient neighborhood is experimentally accessible.