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Error measures can be used to numerically assess the differences between two images. Much work has been done on binary error measures, but little on objective metrics for grey-scale images. In our discussion here we introduce a new grey-scale measure, Δ^sup g^, aiming to improve upon the most common grey-scale error measure, the root-mean-square error. Our new measure is an extension of the authors' recently developed binary error measure, Δ^sup b^, not only in structure, but also having both a theoretical and intuitive basis. We consider the similarities between Δ^sup b^ and Δ^sup g^ when tested in practice on binary images, and present results comparing Δ^sup g^ to the root-mean-squared error and the Sobolev norm for various binary and grey-scale images. There are no previous examples where the last of these measures, the Sobolev norm, has been implemented for this purpose.[PUBLICATION ABSTRACT]