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- W1530208864 abstract "Abstract The basic morphological operations of erosion, dilation, opening, and closing are a part of every image processing toolbox. So too are many basic algorithms such as the watershed and top‐hat transforms. This article reviews the fundamental algebraic theory of mathematical morphology as applied to Euclidean set theory, the context in which it was originally conceived by Matheron and Serra from mathematical operations dating back to Minkowski and Hadwiger. Thorough knowledge of basic algebraic theory is required for anyone engaged in serious research in morphological image processing and is very beneficial for anyone interested in advanced applications. Since its original set‐theoretic formulation, mathematical morphology has been extended to real‐valued functions and to lattice‐valued functions. These extensions take note of the fact that the operations and propositions of the algebraic theory depend on order relations. This can be seen in the direct generalization of many binary definitions and properties to lattices based on the partial order relation among sets. In many cases, the definitions in this article are extended to lattices (including real‐valued and integral‐valued functions) by changing the subset relation ⊂ to the order relationship ≤. This article restricts attention to binary morphology." @default.
- W1530208864 created "2016-06-24" @default.
- W1530208864 creator A5010097254 @default.
- W1530208864 date "2002-01-15" @default.
- W1530208864 modified "2023-10-13" @default.
- W1530208864 title "Foundations of Morphological Image Processing" @default.
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- W1530208864 doi "https://doi.org/10.1002/0471443395.img069" @default.
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