The chicken-and-egg problem of machine vision is that (a) abstracting objects requires images to be segmented, (b) segmentation requires greyscale statistics, (c) greyscale statistics are defined by segmented regions, and this leads back to (a). New image structures called gradient runs and gradient polygons are presented. These lead to new types of three-dimensional histograms.The histogram of a whole image mixes histograms from different regions within the image. These regions and their histrograms may need separating. Global histrograms can be used for preliminary segmentations. These then generate new historagms of the statistics for more coherent locally structured regions. These ideas have used to binarise documents for automated document reading systems, and they may be developed in the desingn of machine vision systems for other areas of application.