There are papers describing measures of correspondence or similarity between two binary images or their parts, but only two papers suggest a measure for a comparison of objects of two grey-scale images. However, there are numerous applications of a measure for grey-scale images as whole entities. A useful application is the comparison of different algorithms devoted to the same task (edge detection, thresholding, image enhancement, segmentation and image reconstruction). This paper proposes some results to define such a measure. They are based on two different representations of grey-scale images: as `surfaces' and as `stacks' or umbra. We study an adaptation of some known formulas used for binary images to grey-scale images, and present a geometrical variant of such a measurement. We study different measures of diversity, based on different digital metrics, direct calculations of distances, and digital functions adapted to grey-scale images. We show that the `stack' representation needs more calculation time and that measures based on the representation are not sensitive to small image shifts, but very sensitive to noise.