Self-similarity Detection via Multi-scale Image Analysis

Abstract

A dynamic scheme is presented for generating multi-scale images associated with self-similar patterns. By blurring with a small scale parameter, brightness distributions are extended to geometrically singular fractal patterns. Through weighted averaging with respect to scale factors, a multi-scale image is generated as a representation of the conditional probability for capturing unknown attractors. The local structure of the multi-scale image is analyzed to demonstrate the structural consistency of the capturing probability with respect to the imaging process associated with the attractor. By extracting stochastic features based on the capturing probability, a computational scheme is introduced for matching observed attractors with a preassigned dictionary of patterns. Proposed method was verified by simulation studies.