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'.

Ordered sets (msc 06Axx), None of the above, but in MSC2010 section 06Fxx (msc 06F99), Geometric probability and stochastic geometry (msc 60D05), Image processing (msc 68U10)
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.