This paper develops an abstract theory for mathematical morphology on complete lattices. The approach is based upon the idea that objects are only known through information provided by a given collection of measurements (called evaluations in this paper). This abstract approach leads in a natural way to the concept of convolution lattice (where `convolution' has to be understood in the sense of an abstract Minkowski addition), the morphological slope transform, and the notion of `random lattice element'.

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CWI
Department of Operations Research, Statistics, and System Theory [BS]

Heijmans, H.J.A.M, & Molchanov, I.S. (1996). Morphology on convolution lattices with applications to the slope transformand random set theory. Department of Operations Research, Statistics, and System Theory [BS]. CWI.