Related papers: Learning Image Fractals Using Chaotic Differentiab…
We examine the optical properties of a system of nano and micro particles of varying size, shape, and material (including metals and dielectrics, and sub-wavelength and super-wavelength regimes). Training data is generated by numerically…
In the process of performing image super-resolution processing, the processing of complex localized information can have a significant impact on the quality of the image generated. Fractal features can capture the rich details of both micro…
Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules.…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
As nature is ascribed as quantum, the fractals also pose some intriguing appearance which is found in many micro and macro observable entities or phenomena. Fractals show self-similarity across sizes; structures that resemble the entire are…
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…
This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…
Field-scale properties of fractured rocks play crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion…
We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…
A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…
When plane waves diffract through fractal-patterned apertures, the resulting far-field profiles or diffractals also exhibit iterated, self-similar features. Here we show that this specific architecture enables robust signal processing and…
Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins'…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
We propose a new network architecture, the Fractal Pyramid Networks (PFNs) for pixel-wise prediction tasks as an alternative to the widely used encoder-decoder structure. In the encoder-decoder structure, the input is processed by an…
Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean…
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces…
Identification of cracks is essential to assess the structural integrity of concrete infrastructure. However, robust crack segmentation remains a challenging task for computer vision systems due to the diverse appearance of concrete…