An increasing operator is known as a filter if it is idempotent. Such filters are important for such tasks as the suppression of noise, where it is essential to know whether repeated application of some operator has converged. The lattices of filters and of strong filters are discussed, the structure of the invariance domain is examined. The middle filter and alternating sequential filters are described.

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Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Heijmans, H.J.A.M. (2020). Morphological filters. In Advances in Imaging and Electron Physics (pp. 403–430). doi:10.1016/bs.aiep.2020.07.012