First steps towards a self-dual morphology

Classical morphology is built up in such a way that all operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon, which is a straightforward consequence of the duality principle, often prohibits the construction of tools that treat the foreground and background of signals in exactly the same way. We discuss an alternative framework for morphological image processing that gives rise to image operators which are intrinsically self-dual.