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Article | REF: AF1515 V1

Mathematical morphology and image processing

Author: Isabelle BLOCH

Publication date: October 10, 2012, Review date: July 30, 2021

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3. Mathematical formalisms

Set and function theory, used directly in the previous section, provides a first formal framework for mathematical morphology. The most general framework, for increasing deterministic operations, is the algebraic framework of complete lattices. A lattice is a set T with a partial order relation ≤ , such that any pair of elements (or any finite family) has an upper bound (denoted x∨y ) and a lower bound (denoted

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