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 [1]. 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 [1] 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 [1]. 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.