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In discrete signal and image processing, many dilations and erosions can bewritten as the max-plus and min-plus product of a matrix on a vector. Previousstudies considered operators on symmetrical, unbounded complete lattices, suchas Cartesian powers of the completed real line. This paper focuses onadjunctions on closed hypercubes, which are the complete lattices used inpractice to represent digital signals and images. We show that this constrainsthe representing matrices to be doubly-0-astic and we characterise theadjunctions that can be represented by them. A graph interpretation of thedefined operators naturally arises from the adjacency relationship encoded bythe matrices, as well as a max-plus spectral interpretation.

Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing