  Sampling is a basic operation in image processing. In classic literature, a
morphological sampling theorem has been established, which shows how sampling
interacts by morphological operations with image reconstruction. Many aspects
of morphological sampling have been investigated for binary images, but only
some of them have been explored for grey-value imagery. With this paper, we
make a step towards completion of this open matter. By relying on the umbra
notion, we show how to transfer classic theorems in binary morphology about the
interaction of sampling with the fundamental morphological operations dilation,
erosion, opening and closing, to the grey-value setting. In doing this we also
extend the theory relating the morphological operations and corresponding
reconstructions to use of non-flat structuring elements. We illustrate the
theoretical developments at hand of examples.
