Generic Representation of Self-Similarity via Structure Sensitive Sampling of Noisy Imagery

AbstractAn adaptive sampling scheme is presented for discrete representation of complex patterns in noisy imagery. In this paper, patterns to be observed are assumed to be generated as fractal attractors associated with a fixed set of unknown contraction mappings. To maintain geometric complexity, the brightness distribution of self-similar patterns are counted on 2D array of Gaussian probability density functions. By solving a diffusion equation on the Gaussian array, capturing probability of unknown fractal attractor is generated as a multi-scale image. The totality of local maxima of the capturing probability, then, yields a pattern sensitive sampling of fractal attractors. For eliminating background noise in this sampling process, two filters are introduced: input filter based on local structure analysis on the Gaussian array, and, output filter based on probabilistic complexity analysis at feature points. The sampled image through these filters are structure sensitive so that extracted feature pattrers support invariant subset with respect to mapping sets associated with observed patterns. As the main result, a generic model is established for unknown self-similar patterns in background noise. The detectability of the generic model has been verified through simulation studies