Statistics of natural and urban images
We investigated ensembles of artificial and real-world grey-scale images to find different invariance properties: translation invariance, scale invariance and a new hierarchical invariance recently proposed by Ruderman . We found that the assumption of translational invariance can be taken for granted. Our results concerning the scale invariance are qualitatively the same as those found by Ruderman  and others. The deviations of the distributions of the logarithmically transformed images from a Gaussian distribution cannot be seen as clearly as stated by Ruderman . Depending on the preprocessing of the images the results concerning the hierarchical invariance differed widely. It seems that this new invariance can be confirmed only for logarithmically transformed images.
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