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Image Interpolation

Vicent Caselles, Simon Masnou, Jean-Michel Morel, Catalina Sbert (1997/1998)

Séminaire Équations aux dérivées partielles

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolute Minimal Lipschitz Extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range. We...

Interpolating and smoothing biquadratic spline

Radek Kučera (1995)

Applications of Mathematics

The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and...

Interpolation formulas for functions of exponential type

Josef Kofroň, Emílie Moravcová (2001)

Applications of Mathematics

In the paper we present a derivative-free estimate of the remainder of an arbitrary interpolation rule on the class of entire functions which, moreover, belong to the space L ( - ∞ , + ∞ ) 2 . The theory is based on the use of the Paley-Wiener theorem. The essential advantage of this method is the fact that the estimate of the remainder is formed by a product of two terms. The first term depends on the rule only while the second depends on the interpolated function only. The obtained estimate of the remainder of...

Interpolation of non-smooth functions on anisotropic finite element meshes

Thomas Apel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.

Interpolation operators on the space of holomorphic functions on the unit circle

Josef Kofroň (2001)

Applications of Mathematics

The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval [ - a , a ] , a ∈ ( 0 , 1 ) , have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general...

Interpolation with restrictions -- role of the boundary conditions and individual restrictions

Valášek, Jan, Sváček, Petr (2023)

Programs and Algorithms of Numerical Mathematics

The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative...

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