Related papers: Multifractal Analysis of Human Retinal Vessels
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
Demographic studies suggest that changes in the retinal vasculature geometry, especially in vessel width, are associated with the incidence or progression of eye-related or systemic diseases. To date, the main information source for width…
Ophthalmological imaging utilizes different imaging systems, such as color fundus, infrared, fluorescein angiography, optical coherence tomography (OCT) or OCT angiography. Multiple images with different modalities or acquisition times are…
Retinal vessel segmentation is generally grounded in image-based datasets collected with bench-top devices. The static images naturally lose the dynamic characteristics of retina fluctuation, resulting in diminished dataset richness, and…
Retinal imaging has emerged as a promising method of addressing this challenge, taking advantage of the unique structure of the retina. The retina is an embryonic extension of the central nervous system, providing a direct in vivo window…
The geometric characteristics of dust clouds provide important information on the physical processes that structure such clouds. One of such characteristics is the $2D$ fractal dimension $D$ of a cloud projected onto the sky plane. In…
Retinal vessel segmentation plays a vital role in analyzing fundus images for the diagnosis of systemic and ocular diseases. Building on this, classifying segmented vessels into arteries and veins (A/V) further enables the extraction of…
Recent Alzheimer's disease (AD) patient studies have focused on retinal analysis, as the retina is the only part of the central nervous system which can be imaged non-invasively by optical methods. However as this is a relatively new…
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…
Functional connectivity (FC) derived from resting-state fMRI is widely used to characterize large-scale brain network alterations in neurological and psychiatric disorders. However, FC construction critically depends on the choice of brain…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
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…
The choroid is a highly vascularized tissues supplying the retinal pigment epithelium and photoreceptors. Its implication in retinal diseases is gaining increasing interest. However, investigating the anatomy and flow of the choroid remains…
Accurate segmentation of the blood vessels of the retina is an important step in clinical diagnosis of ophthalmic diseases. Many deep learning frameworks have come up for retinal blood vessels segmentation tasks. However, the complex…
The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations.…
It is shown that the heart rate variability (HRV) in healthy and diseased humans possesses a hierarchical structure of the She-Leveque (SL) form. This structure, first found in measurements in turbulent fluid flows, implies further details…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define…
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together…
The multi-scale Frangi vesselness filter is an established tool in (retinal) vascular imaging. However, it cannot cope with crossings or bifurcations, since it only looks for elongated structures. Therefore, we disentangle crossing…