Related papers: Super Fractal Interpolation Functions
Video Frame Interpolation (VFI) has been extensively explored and demonstrated, yet its application to polarization remains largely unexplored. Due to the selective transmission of light by polarized filters, longer exposure times are…
Iterated Function Systems (IFSs) have been at the heart of fractal geometry almost from its origin, and several generalizations for the notion of IFS have been suggested. Subdivision schemes are widely used in computer graphics and attempts…
Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functions are called local fractal functions and they extend and…
The inclusion of spatial information into spectral classifiers for fine-resolution hyperspectral imagery has led to significant improvements in terms of classification performance. The task of spectral-spatial hyperspectral image…
In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized…
The Taylor Interpolation through FFT (TI-FFT) algorithm for the computation of the electromagnetic wave propagation in the quasi-planar geometry within the half-space is proposed in this article. There are two types of TI-FFT algorithm,…
New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our…
As constituent parts of image objects, superpixels can improve several higher-level operations. However, image segmentation methods might have their accuracy seriously compromised for reduced numbers of superpixels. We have investigated a…
We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted…
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional…
We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for computation of the near-field and far-field in the quasi-cylindrical geometry has been introduced. The modal expansion coefficient of the vector potentials ${\bf F}$…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
In our previous work, On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113-674, we presented a method for finding a finite family of closed balls whose union contains the attractor of a given…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in $\br^d$, and the ``IFS'' refers to…
Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and…
This paper makes a first attempt to bring the Shape from Polarization (SfP) problem to the realm of deep learning. The previous state-of-the-art methods for SfP have been purely physics-based. We see value in these principled models, and…
Conventional methods of imitation learning for variable-speed motion have difficulty extrapolating speeds because they rely on learning models running at a constant sampling frequency. This study proposes variable-frequency imitation…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…