Basic properties of 2D-nonlinear scale-space representations of images are considered. First, local-energy filters are used to estimate the Hausdorff dimension, , of images. A new fractal dimension, , defined as a property of 2D-curvature representations on multiple scales, is introduced as a natural extension of traditional fractal dimensions, and it is shown that the two types of fractal dime...

⎯This paper proposes fractal patterns for power quality (PQ) detection using color relational analysis (CRA) based classifier. Iterated function system (IFS) uses the non-linear interpolation in the map and uses similarity maps to construct various fractal patterns of power quality disturbances, including harmonics, voltage sag, voltage swell, voltage sag involving harmonics, voltage swell invo...

In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original time series observation sequence. The result of ...

A fractal is an object or a structure that is self-similar in all length scales. Fractal geometry is an excellent mathematical tool used in the study of irregular geometric objects. The concept of the fractal dimension, D, as a measure of complexity is defined. The concept of fractal geometry is closely linked to scale invariance, and it provides a framework for the analysis of natural phenomen...

The analysis of the effective fractal dimensions corresponding to the fracture parameters points out the existence of at least: a) 8 different effective mechanical fractal dimensions, b) 8 diferent effective topographical fractal dimensions, as well as of: c) 4 different effective lacunarity measures L, corresponding to the mass-radius method and to the methods described by the works. The accom...

Complexity, Risk, and Financial Markets completes a trilogy of books on chaos and fractal analysis. Fractal analysis examines self-similarity or scale invariance, a structure that is often present in seemingly random and otherwise complex processes. Time series, for example, exhibit self-similarity if subsamples resemble compressed versions of longer samples. Pioneered by engineers, mathematici...

A digital grayscale image can be described by intensity or pixel values. The gray levels are spread over the images as irregular or inhomogeneous fashion. A number of proposed methods for calculating the optimal thresholding value for image segmentation, but the fractal analysis is an expeditious and significant mathematical approach that distributes with irregular geometric objects. In the rec...

PURPOSE The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified ...

A novel multiscale framework is introduced for the representation of a clam of fractal point processes. Using this framework, efficient algorithms are developed for the Rynthesis of fractal point processes from a mixture of Poisson processes. Multiscale analysis algorithms are also developed within this framework for computing Maximum-Likelihood fractal dimension estimates of such processes fro...

Fractal geometry has sparked considerable interest for analyzing remote sensing imageries. Fractal models have been used in several image processing and pattern recognition applications such as texture analysis and classification. Applications of fractal geometry in remote sensing rely heavily on estimation of the fractal dimension (D). When land areas are clustered into groups of similar land ...