Origins of scaling in natural images.

One of the most robust qualities of our visual world is the scale invariance of natural images. Not only has scaling been found in different visual environments, but the phenomenon also appears to be calibration-independent. This paper proposes a simple property of natural images which explains this robustness: they are collages of regions corresponding to statistically independent "objects". Evidence is provided for these objects having a power-law distribution of sizes within images, from which follows scaling in natural images. It is commonly suggested that scaling instead results from edges, each with power spectrum 1/k2. This hypothesis is refuted by example.