The stochastic structure of images

Abstract

As resolving power increases, image features evolve in an iterative fashion; large scale features will persist, and finer and finer scale features are resolved at each increase in resolution. As such, the observation process is shown to overwhelm natural image statistics. Observation by a linear imaging process imposes natural image statistics to be of random multiplicative nature, rather than additive. The scaling behavior of the random process is driven by the gradient structure in the scene irradiance. From the general structure of multiplicative processes, image statistics are proven to follow a sequential fragmentation process. From these theoretical results, analytical forms for the distributions of image derivative filter responses and gradient magnitude are derived. © Springer-Verlag Berlin Heidelberg 2005.