Publications related to Domain-Informed Spline Interpolation

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

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

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

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

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

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

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

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

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Michaël Unser, John Paul Ward, Aurélien Bourquard, Hagay Kirshner

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

IEEE2013

Domain-Informed Spline Interpolation

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Statistical Optimality of Hermite Splines

Ellipse-Preserving Hermite Interpolation and Subdivision

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

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

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

Exponential Hermite Splines For The Analysis Of Biomedical Images

Exponential Hermite Splines for the Analysis of Biomedical Images

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

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Ellipse-Preserving Hermite Interpolation and Subdivision

Exponential Hermite Splines For The Analysis Of Biomedical Images

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

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

Statistical Optimality of Hermite Splines

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

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Local Barycentric Coordinates

Exponential Hermite Splines for the Analysis of Biomedical Images