LOCALITY AND ADJACENCY STABILITY CONSTRAINTS FOR MORPHOLOGICAL CONNECTED OPERATORS

This paper investigates two constraints for the connected operator cla ss. For binary images, connected operators are those that treat grains and pores of the input in an all or nothing way, and therefore they d o not introduce discontinuities. The first constraint, called connecte d-component (c.c.) locality, constrains the part of the input that can be used for computing the output of each grain and pore. The second, called adjacency stability, establishes an adjacency constraint betwee n connected components of the input set and those of the output set. A mong increasing operators, usual morphological filters can satisfy bot h requirements. On the other hand, some (non-idempotent) morphological operators such as the median cannot have the adjacency stability prop erty. When these two requirements are applied to connected and idempot ent morphological operators, we are lead to a new approach to the clas s of filters by reconstruction. The important case of translation inva riant operators and the relationships between translation invariance a nd connectivity are studied in detail. Concepts are developed within t he binary (or set) framework; however, conclusions apply as well to fl at non-binary (gray-level) operators.