Fractal modeling and analysis of Poisson processes

This paper describes a new fractal modeling and analysis approach for a point processes based on a previously proposed multiscale model for Poisson processes. A new Bayesian hypothesis testing framework is proposed for detecting or classifying fractal characteristics of an intensity based on observations of the associated point process. The test statistics can be expressed in closed-form, and asymptotic analysis reveals a simple mechanism at work. Applications to photon-limited image edge detection are discussed.