The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Why mathematical morphology needs complete lattices
Signal Processing
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
Mathematical theory of domains
Mathematical theory of domains
Lattice calculus of the morphological slope transform
Signal Processing
Morphology on Convolution Lattices with Applications to the Slope Transform and Random Set Theory
Journal of Mathematical Imaging and Vision
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Mathematical Models in Engineering and Management Science
Fuzzy Mathematical Models in Engineering and Management Science
Grey-scale morphology based on fuzzy logic
Grey-scale morphology based on fuzzy logic
Fuzzy logic and mathematical morphology
Fuzzy logic and mathematical morphology
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
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In this paper, we study inverses and quotients of mappings between ordered sets, in particular between complete lattices, which are analogous to inverses and quotients of positive numbers. We investigate to what extent a generalized inverse can serve as a left inverse and as a right inverse, and how an inverse of an inverse relates to the identity mapping. The generalized inverses and quotients are then used to create a convenient formalism for dilations and erosions as well as for cleistomorphisms (closure operators) and anoiktomorphisms (kernel operators).