A Scale-Space Analysis of Multiplicative Texture Processes

Gaussian Scale-space describes the local structure of images. This paper shows a stochastic analysis of the diffusion equation as put forward by Koenderink (1984) for regular images. Important classes of the stochastic process which are structurally described by the diffusion analysis include Brownian fractals, Markovian textures, and fragmentation processes. The analysis shows the diffusion coefficient to relate to the local autocorrelation function over the diffusion process. Diffusion of the multiplicative image formation process directly leads to power-law statistics over the diffusion scale, and to Weibull statistics in the spatial domain.