Fractal Dimensions and Random Transformations

Random soups, carpets and fractal dimensions

We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and equal to their expectation dimension. We also estimate their low-intensity limiting behavior. This applies in particular to the “conformal loop en...

FONT DISCRIMINATIO USING FRACTAL DIMENSIONS

One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dime...

Fractal dimensions

Face recognition by fractal transformations

In this paper, we propose a new method for computerized human face recognition using fractal transformations. The popular use of fractal image coding has been for image compression. It is only recently that their uses for object recognition are being explored. We will show that by utilizing the intrinsic properties of block-wise self-similar transformations in fractal image coding we can use it...

Geometric and Fractal Properties of Brownian Motion and Random Walk Paths in Two and Three Dimensions

There is a close relationship between critical exponents for proa-bilities of events and fractal properties of paths of Brownian motion and random walk in two and three dimensions. Cone points, cut points, frontier points, and pioneer points for Brownian motion are examples of sets whose Hausdorr dimension can be given in terms of corresponding exponents. In the latter three cases, the exponent...