Hierarchical model of natural images and the origin of scale invariance

The study of natural images and how our brain processes them has been an area of intense research in neuroscience, psychology, and computer science. We introduced a unique approach to studying natural images by decomposing images into a hierarchy of layers at different logarithmic intensity scales and mapping them to a quasi-2D magnet. The layers were in different phases: cold and ordered at large-intensity scales, hot and disordered at small-intensity scales, and going through a second-order phase transition at intermediate scales. There was a single critical layer in the hierarchy that exhibited long-range correlation similar to that found in the 2D Ising model of ferromagnetism at the critical temperature. We also determined the interactions between layers mapped from natural images and found mutual inhibition that generated locally frustrated antiferromagnetic states. Almost all information in natural images was concentrated in a few layers near the phase transition, which has biological implications and also points to the hierarchical origin of scale invariance in natural images.