Publications related to Multiresolution Segmentation of Natural Images: From linear to Non-Linear Scale-Space Representations

Reduced Order Methods for Modeling and Computational Reduction

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing tech ...

Springer2013

Quotient-method Algorithms for Input-affine Single-input Nonlinear Systems

Willson Sudarsandhari Shibani

Many real-world systems are intrinsically nonlinear. This thesis proposes various algorithms for designing control laws for input-affine single-input nonlinear systems. These algorithms, which are based on the concept of quotients used in nonlinear control ...

EPFL2012

Exponential splines and minimal-support bases for curve representation

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

Joachim Krieger

In this paper we prove the global in time well-posedness of the following non-local diffusion equation with

\alpha\, \varepsilon [0, 2/3)

:

\partial_tu=\{(-\Delta)^{-1}u\}\Delta u+\alpha u^2, \,\, u(t=0)=u_0

. The initial condition

u_0

is positive, rad ...

2012

Subspaces Indexing Model on Grassmann Manifold for Image Search

Xinchao Wang

Conventional linear subspace learning methods like principal component analysis (PCA), linear discriminant analysis (LDA) derive subspaces from the whole data set. These approaches have limitations in the sense that they are linear while the data distribut ...

Institute of Electrical and Electronics Engineers2011

On the efficiency of numerical homogenization methods

Assyr Abdulle

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of num ...

EMS2011

Link between Alginate Reaction Front Propagation and General Reaction Diffusion Theory

Jürgen Brugger, Philippe Renaud, Thomas Michael Braschler, Kristopher Pataky, Ana Valero, Ludovica Colella

We provide a common theoretical framework reuniting specific models for the Ca2+-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differ ...

2011

Audio-driven Nonlinear Video Diffusion

Pierre Vandergheynst, Anna Llagostera Casanovas

In this paper we present a novel nonlinear video diffusion approach based on the fusion of information in audio and video channels. Both modalities are efficiently combined into a diffusion coefficient that integrates the basic assumption in this domain, i ...

Institute of Electrical and Electronics Engineers2011

Model Order Reduction by geometrical parametrization for shape optimization in computational fluid dynamics

Gianluigi Rozza, Andrea Manzoni

Shape Optimization problems governed by partial differential equations result from many applications in computational fluid dynamics; they involve the repetitive evaluation of outputs expressed as functionals of the field variables and usually imply big co ...

2010

Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation

Gianluigi Rozza

In this paper we consider reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear and non-linear parabolic partial differential equations. The essential ingredients are Galerkin projection ...

John Wiley & Sons2010

Multiresolution Segmentation of Natural Images: From linear to Non-Linear Scale-Space Representations

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Reduced Order Methods for Modeling and Computational Reduction

Quotient-method Algorithms for Input-affine Single-input Nonlinear Systems

Exponential splines and minimal-support bases for curve representation

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

Subspaces Indexing Model on Grassmann Manifold for Image Search

On the efficiency of numerical homogenization methods

Link between Alginate Reaction Front Propagation and General Reaction Diffusion Theory

Audio-driven Nonlinear Video Diffusion

Model Order Reduction by geometrical parametrization for shape optimization in computational fluid dynamics

Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

Model Order Reduction by geometrical parametrization for shape optimization in computational fluid dynamics

Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation

Reduced Order Methods for Modeling and Computational Reduction

Subspaces Indexing Model on Grassmann Manifold for Image Search

Audio-driven Nonlinear Video Diffusion

On the efficiency of numerical homogenization methods

Exponential splines and minimal-support bases for curve representation

Link between Alginate Reaction Front Propagation and General Reaction Diffusion Theory

Quotient-method Algorithms for Input-affine Single-input Nonlinear Systems