Related papers: Fractal and Multi-Scale Fractal Dimension analysis…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
In this study, we present a method to measure changes over time of fractal dimension. We confirmed that our method can calculate the fractal dimension with the same precision as conventional methods, and tracking performance of our method…
This work proposes to obtain novel fractal descriptors from gray-level texture images by combining information from interior and boundary measures of the Minkowski dilation applied to the texture surface. At first, the image is converted…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current…
This work proposes the combination of multiscale transform with fractal descriptors employed in the classification of gray-level texture images. We apply the space-scale transform (derivative + Gaussian filter) over the Bouligand-Minkowski…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
This work proposes a texture descriptor based on fractal theory. The method is based on the Bouligand-Minkowski descriptors. We decompose the original image recursively into 4 equal parts. In each recursion step, we estimate the average and…
Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…