Related papers: Fractal Dimension and Retinal Pathology: A Meta-an…
Entropy is one of physical bases for fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using fractal dimension, we can describe urban growth and form and characterize spatial complexity. A…
Pulsatile changes in retinal vascular geometry over the cardiac cycle have clinical implications for the diagnosis of ocular and systemic vascular diseases, including ischemia, coronary heart diseases, and diabetes mellitus and its…
Several two-dimensional studies in spiral galaxies show that HII star formation regions have a fractal distribution, with a fractal dimension of approximately 2.3. In this work, the fractal dimension is calculated through the box-counting…
The retinal vascular condition is a reliable biomarker of several ophthalmologic and cardiovascular diseases, so automatic vessel segmentation may be crucial to diagnose and monitor them. In this paper, we propose a novel method that…
The segmentation of the retinal vasculature from eye fundus images represents one of the most fundamental tasks in retinal image analysis. Over recent years, increasingly complex approaches based on sophisticated Convolutional Neural…
We investigate the clinical and prognostic significance of fractal dimension and detrended fluctuation analysis by comparing the group of patients with stable angina pectoris without previous myocardial infarction with the group of…
Self-similar properties of the ribosome in terms of the mass fractal dimension are investigated. We find that both the 30S subunit and the 16S rRNA have fractal dimensions of 2.58 and 2.82, respectively; while the 50S subunit as well as the…
We use a spatially resolved cavity ring-down technique to show that the 2D eigenmode of an unstable optical cavity has a fractal pattern, i.e. it looks the same at different length scales. In agreement with theory, we find that this pattern…
We studied the structural alterations between healthy and diseased brain tissues using a multiparametric framework combining fractal analysis, fractal functional transformation, multifractal analysis, and the Inverse Participation Ratio…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
Transmission intensity of a thin tissue sample produce intensity distribution that is proportional to the refractive index pattern in the thin slice, in turn reflects mass density pattern, and using the intensity pattern, fractal dimension…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
High energy impacts at joint locations often generate highly fragmented, or comminuted, bone fractures. Current approaches for treatment require physicians to decide how to classify the fracture within a hierarchy fracture severity…
This paper serves as a complementary material to a poster presented at the XXXVI Dynamics Days Europe in Corfu, Greece, on June 6th-10th in 2016. In this study, fractal dimension ($D$) of two types of self-affine signals were estimated with…
Cancer is an epidemic worldwide. At present one in four persons has cancer and this statistic will change to one in a two person in the near future. It is now known that war against cancer is the early, curable detection and treatment.…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
Methods for automated retinal vessel segmentation play an important role in the treatment and diagnosis of many eye and systemic diseases. With the fast development of deep learning methods, more and more retinal vessel segmentation methods…
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…