Related papers: Hermite coordinate interpolation kernels: applicat…
We propose a new class of kernels to simplify the design of filters for image interpolation and resizing. Their properties are defined according to two parameters, specifying the width of the transition band and the height of a unique…
Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even…
Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
Video frame interpolation typically involves two steps: motion estimation and pixel synthesis. Such a two-step approach heavily depends on the quality of motion estimation. This paper presents a robust video frame interpolation method that…
Image interpolation algorithms pervade many modern image processing and analysis applications. However, when their weighting schemes inefficiently generate very unrealistic estimates, they may negatively affect the performance of the end…
Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for…
In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…
Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can…
We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, $J$-Hermitian, Hamiltonian and…
This paper develops a unified theoretical framework for constructing B-spline basis function spaces with structural equivalence to finite element spaces. The theory rigorously establishes that these bases emerge as explicit linear…
Spherical functions appear throughout computer graphics, from spherical harmonic lighting and precomputed radiance transfer to neural radiance fields and procedural planet rendering. Efficient evaluation is critical for real-time…
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered. The splines interpolate points, the corresponding tangent planes and normal curvature forms at domain vertices and approximate tangent…
Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…
We study the problem of the appropriate choice of the interpolating kernel to be used in the evaluation of gradients of functions. Such interpolation technique is often used in applications, e.g. it is typical for Smoothed Particle…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…