Related papers: Fractal Interpolation over Curves
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the…
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs…
Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast…
We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…
We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying (weak) symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total…
Speckles arise when coherent light interacts with biological tissues. Information retrieval from speckles is desired yet challenging, requiring understanding or mapping of the multiple scattering process, or reliable capability to reverse…
A simple scheme for all-optical time interpolation using spectral interferometry is put forward that is in principle capable of single-shot measurements. In this method, the arrival time of optical timing pulses is encoded into the spectrum…
The problem of finding the convex hull of an IFS fractal is relevant in both theoretical and computational settings. Various methods exist that approximate it, but our aim is its exact determination. The finiteness of extremal points is…
In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This…
Object tracking is a fundamental task in computer vision, requiring the localization of objects of interest across video frames. Diffusion models have shown remarkable capabilities in visual generation, making them well-suited for…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
The new concepts are introduced of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such sequences is relatively norm-compact and we obtain several applications of this fact.
This work presents a supervised learning based approach to the computer vision problem of frame interpolation. The presented technique could also be used in the cartoon animations since drawing each individual frame consumes a noticeable…
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…
Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.
Pseudo-LiDAR point cloud interpolation is a novel and challenging task in the field of autonomous driving, which aims to address the frequency mismatching problem between camera and LiDAR. Previous works represent the 3D spatial motion…
This paper surveys hyperinterpolation, a quadrature-based approximation scheme. We cover classical results, provide examples on several domains, review recent progress on relaxed quadrature exactness, introduce methodological variants, and…
This paper introduces a notion of differential forms on closed, potentially fractal, subsets of Euclidean space by defining pointwise cotangent spaces using the restriction of $C^1$ functions to this set. Aspects of cohomology are…
Diffusion models have achieved remarkable image generation quality surpassing previous generative models. However, a notable limitation of diffusion models, in comparison to GANs, is their difficulty in smoothly interpolating between two…