Morphology on convolution lattices with applications to the slope transformand random set theory

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'.