Publications related to Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

Isogeometric mortar methods

The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline spaces but of a diff ...

2015

Statistical Optimality of Hermite Splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Harshit Gupta

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

IEEE2015

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Michaël Unser, John Paul Ward

Motivated by the interior tomography problem, we propose a method for exact reconstruction of a region of interest of a function from its local Radon transform in any number of dimensions. Our aim is to verify the feasibility of a one-dimensional reconstru ...

Siam Publications2015

Exponential convergence of the hp version of isogeometric analysis of 1D

Annalisa Buffa

We establish exponential convergence of the hp-version of isogeometric analysis for second order elliptic problems in one spacial dimension. Specifically, we construct, for functions which are piecewise analytic with a finite number of algebraic singularit ...

Springer, Cham2014

VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles

Jonathan Graves, Wilfred Anthony Cooper, David Pfefferlé, Cyril Misev

Curvilinear guiding-centre drift and full-orbit equations of motion are presented as implemented in the code{VENUS-LEVIS} code. A dedicated interpolation scheme based on Fourier reconstruction in the toroidal and poloidal direction and cubic spline in the ...

Elsevier2014

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Michaël Unser, Ricard Delgado Gonzalo, Virginie Sophie Uhlmann

We propose a novel active contour for the analysis of filament-like structures and boundaries—features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involvin ...

IEEE2014

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Michaël Unser, Virginie Sophie Uhlmann

Cardinal Hermite exponential spline functions are a generalization of the classical cardinal Hermite polynomial splines. In this work we consider the 4-dimensional space

ε _{ 4 }

= {1, x,

e ^{ \alpha x }

,

e ^{ -\alpha x }

} with α ∈ $ ℝ ^{ + } ...

SMAI-SIGMA2014

Local Barycentric Coordinates

Sofien Bouaziz, Bailin Deng

Barycentric coordinates yield a powerful and yet simple paradigm to interpolate data values on polyhedral domains. They represent interior points of the domain as an affine combination of a set of control points, defining an interpolation scheme for any fu ...

Association for Computing Machinery2014

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Annalisa Buffa, Rafael Vazquez Hernandez

In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and following the isogeometric paradigm, we map them on domains which are (piecewise) spline or ...

2014

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry

Pramod Rastogi, Rishikesh Dilip Kulkarni

This Letter proposes a new method for the estimation of the first-and second-order phase derivatives corresponding to strain and curvature from a single fringe pattern in digital holographic interferometry. The method is based on a discrete energy separati ...

Optical Soc Amer2014

Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

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Isogeometric mortar methods

Statistical Optimality of Hermite Splines

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Exponential convergence of the hp version of isogeometric analysis of 1D

VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Local Barycentric Coordinates

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Isogeometric mortar methods

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Statistical Optimality of Hermite Splines

Exponential convergence of the hp version of isogeometric analysis of 1D

VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles

Local Barycentric Coordinates

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry