Publication

Linear Interpolation Revitalized

Related publications (36)

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...

2016

Ellipse-Preserving Hermite Interpolation and Subdivision

Michaël Unser

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability t ...

Elsevier2015

MATHICSE Technical Report : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations of PDEs on subdomains featuring non-conforming interfaces

Alfio Quarteroni, Simone Deparis, Davide Forti

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...

MATHICSE2015

Exponential Hermite Splines For The Analysis Of Biomedical Images

Michaël Unser, Ricard Delgado Gonzalo, Virginie Sophie Uhlmann

We present a new exponential B-spline basis that enables the construction of active contours for the analysis of biomedical images. Our functions generalize the well-known polynomial Hermite B-splines and provide us with a direct control over the tangents ...

Ieee2014

Exponential Hermite Splines for the Analysis of Biomedical Images

Michaël Unser, Ricard Delgado Gonzalo, Virginie Sophie Uhlmann

IEEE2014

GPU Prefilter for Accurate Cubic B-spline Interpolation

Philippe Thévenaz

Achieving accurate interpolation is an important requirement for many signal-processing applications. While nearest-neighbor and linear interpolation methods are popular due to their native GPU support, they unfortunately result in severe undesirable artif ...

Oxford University Press2012

Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach

Michaël Unser

Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale inter ...

IEEE2011

A Stochastic Minimum-Norm Approach to Image and Texture Interpolation

Michaël Unser, Hagay Kirshner

We introduce an exponential-based consistent approach to image scaling. Our model stems from Sobolev reproducing kernels, motivated by their role in continuous-domain stochastic autoregressive processes. The proposed approach imposes consistency and applie ...

EURASIP2010

Nonparametric Least Squares Regression for Image Reconstruction on the Sphere

Pascal Frossard, Ivana Tosic, Tamara Tosic

This paper addresses the problem of interpolating signals defined on a 2-d sphere from non-uniform samples. We present an interpolation method based on locally weighted linear and nonlinear regression, which takes into account the differences in importance ...

2009

From Lagrange to Shannon...and Back: Another Look at Sampling

Martin Vetterli, Paolo Prandoni

Classical digital signal processing (DSP) lore tells us the tale of a continuous-time primeval signal, of its brutal sampling, and of the magic sinc interpolation that, under the aegis of bandlimitedness, brings the original signal back to (continuous) lif ...

2009

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