Related papers: Fractal Dimension and Retinal Pathology: A Meta-an…
We explored the fractal and multifractal characteristics of breast mammogram micrographs to identify quantitative biomarkers associated with breast cancer progression. In addition to conventional fractal and multifractal analyses, we…
Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation…
Fractal channels have significant applications in fields such as microfluidic chips and in vitro diagnostics. However, there is currently insufficient understanding and recognition of fluid flow within fractal channels. In this paper, the…
Diagnosing different retinal diseases from Spectral Domain Optical Coherence Tomography (SD-OCT) images is a challenging task. Different automated approaches such as image processing, machine learning and deep learning algorithms have been…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. However, limited effort is attempted to calculate the fractal dimension of surfaces computed from precisely known atomic coordinates from…
This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
In this brief report, we present a disordered version of recursive networks. Depending on the structural parameters $u$ and $v$, the networks are either fractals with a finite fractal dimension $d_{f}$ or transfinite fractals (transfractal)…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
Medical image segmentation is an important task for computer aided diagnosis. Pixelwise manual annotations of large datasets require high expertise and is time consuming. Conventional data augmentations have limited benefit by not fully…
The fractal dimension provides a statistical index of object complexity by studying how the pattern changes with the measuring scale. Although useful in several classification tasks, the fractal dimension is under-explored in deep learning…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
Retinal blood vessel segmentation can extract clinically relevant information from fundus images. As manual tracing is cumbersome, algorithms based on Convolution Neural Networks have been developed. Such studies have used small publicly…
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…
Patterns formed by the flow of an inhomogeneous fluid (suspension) over a smooth inclined surface were studied. It was observed that for inclination angle larger than a threshold, global fractal patterns are formed. The fractal dimensions…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…