Quantitative comparison of images and transforms

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Many different measures are currently used for quantifying the difference between pairs of images. Those in common use are surveyed, their interrelationships are made clear and their dependence on transform band-width pointed out. Adaptations to image transforms, with complex data, are given. For comparing simulated with experimental images, the χ2 difference is recommended as allowing a simple prediction of the likelihood of obtaining at random a difference as great as that actually obtained. In particular, theχ2 difference in Fourier space is shown to be the only interpretable difference measure available in cases when the image noise is not normally distributed or when - as is normally the case - the noise in neighbouring image pixels is not independent.

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