The article by Daniel L. Ruderman reviews the statistical properties of natural images, emphasizing their importance in both image compression and biological vision. Natural images are characterized by scale invariance, meaning that their statistical properties do not change with the angular scale of the image. This property is supported by evidence from power spectrum scaling and histogram analysis. The study also reveals a hierarchical invariance in natural scenes, suggesting that objects can appear at any scale. These symmetries significantly restrict the form of the image distribution, making it highly non-Gaussian. The article discusses the implications of these properties for image processing and biological vision, including the design of efficient neural encodings and the optimization of visual systems. The authors present new findings on the scaling of power spectra and the predictability of natural images, as well as a novel invariance related to the hierarchical structure of natural scenes. They also explore the use of local nonlinear transformations to modify the histogram tails, which can make the distribution more Gaussian-like.The article by Daniel L. Ruderman reviews the statistical properties of natural images, emphasizing their importance in both image compression and biological vision. Natural images are characterized by scale invariance, meaning that their statistical properties do not change with the angular scale of the image. This property is supported by evidence from power spectrum scaling and histogram analysis. The study also reveals a hierarchical invariance in natural scenes, suggesting that objects can appear at any scale. These symmetries significantly restrict the form of the image distribution, making it highly non-Gaussian. The article discusses the implications of these properties for image processing and biological vision, including the design of efficient neural encodings and the optimization of visual systems. The authors present new findings on the scaling of power spectra and the predictability of natural images, as well as a novel invariance related to the hierarchical structure of natural scenes. They also explore the use of local nonlinear transformations to modify the histogram tails, which can make the distribution more Gaussian-like.