The construction of morphological filters by iteration of an arbitrary increasing operator is described. The role of continuity is emphasized. It is shown that the finite window operators are suitable for this. All translation-invariant operators that use finite structuring elements belong to this family.

Centre operator, Continuity conditions, Convergence, Filter construction, Finite window operators, Idempotence, Iteration, Middle filter, Self-duality
Advances in Imaging and Electron Physics
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Heijmans, H.J.A.M. (2020). Filtering and iteration. Advances in Imaging and Electron Physics, 216, 431–471. doi:10.1016/bs.aiep.2020.07.013