Publications related to Splines and Wavelets: New Perspectives for Pattern Recognition

Shortest-support multi-spline bases for generalized sampling

Michaël Unser, Alexis Marie Frederic Goujon, Shayan Aziznejad, Alireza Naderi

Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

2021

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Leello Tadesse Dadi, Shayan Aziznejad

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Spline Shape Processing

Daniel Andreas Schmitter

In this thesis, we present a novel generic and unifying framework for data-adaptive shape modeling. Our work is motivated by the raising need for powerful geometric modeling kernels that are required for shape characterization in biomedical imaging. The on ...

EPFL2017

Landmark Active Contours for Bioimage Analysis

Virginie Sophie Uhlmann

The problem of identifying the outline of objects in images can be approached from two starting points, either by considering localized features (landmarks, keypoints or regions), or by searching for global contours. Features are regions or points of int ...

EPFL2017

Metal artefact reduction in computed tomography images by a fourth-order total variation flow

Alfio Quarteroni, Elena Faggiano

Permanent metallic implants, such as dental fillings and cardiac devices, generate streaks-like artefacts in computed tomography (CT) images. In this article, we propose a strategy to perform metal artefact reduction (MAR) that relies on the total variatio ...

Taylor & Francis Ltd2016

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

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

Image registration for super resolution

Mohamed Taher Nguira

This document presents a mathematical framerwork for delay retrieval between two signals. It treats Global and Local delay cases. It's based on E-splines and Exponential reproducing kernels properties. LCAV1601050917 ...

2015

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

Splines and Wavelets: New Perspectives for Pattern Recognition

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Shortest-support multi-spline bases for generalized sampling

Generating Sparse Stochastic Processes Using Matched Splines

Spline Shape Processing

Landmark Active Contours for Bioimage Analysis

Metal artefact reduction in computed tomography images by a fourth-order total variation flow

Statistical Optimality of Hermite Splines

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

Similarity-Based Shape Priors for 2D Spline Snakes

Image registration for super resolution

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

Landmark Active Contours for Bioimage Analysis

Metal artefact reduction in computed tomography images by a fourth-order total variation flow

Shortest-support multi-spline bases for generalized sampling

Generating Sparse Stochastic Processes Using Matched Splines

Spline Shape Processing

Statistical Optimality of Hermite Splines

Similarity-Based Shape Priors for 2D Spline Snakes

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

Image registration for super resolution

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