Publications related to An Inner-Product Calculus for Periodic Functions and Curves

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

We focus on a specific class of curves that can be parametrized using a finite number of variables in two dimensions. The corresponding indicator plane, which is a binary image, has infinite bandwidth and can not be sampled and perfectly reconstructed with ...

2011

Ideal knots and other packing problems of tubes

Henryk Gerlach

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve ...

EPFL2010

Conformational analysis of nucleic acids revisited: Curves

John Maddocks, Daiva Petkeviciute

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algori ...

Oxford University Press2009

Geometrical reconstruction of curves and surfaces using NURBS

Sylvain Rouge

The aim of this project is the analysis of different approaches for curve and surface reconstruction and the development of a related MATLAB library. We initially study the Lagrange polynomial interpolation, then the Bezier, the B-splines and the NURBS cur ...

2008

Direct measurement of drainage curves in infiltration of SiC particle preforms

Andreas Mortensen, Ludger Weber, Maryam Bahraini Hasani

Drainage curves (plots of the non-wetting fluid saturation versus applied pressure) for infiltration of SiC particle preforms with Al and Al-12.2 at.% Si are measured at 1023 K (750 degrees C) with a pressure infiltration apparatus adapted for direct track ...

2008

Global radii of curvature, and the biarc approximation of space curves

Jana Smutny

The distance from self-intersection of a (smooth and either closed or infinite) curve q in three dimensions can be characterised via the global radius of curvature at q(s), which is defined as the smallest possible radius amongst all circles passing throug ...

EPFL2004

Non-linear subdivision using local spherical coordinates

Touradj Ebrahimi, Pierre Vandergheynst, Nicolas Aspert

In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable. The proposed technique is compared to linear subdivision methods hav ...

2003

Unsupervised Selective Anisotropic Feature Diffusion for Cortical Surface Registration

Jean-Philippe Thiran, Olivier Cuisenaire

In this paper we use the theory of geometric curve and surface evolution to diffuse an object preserving their important features. We do that using a curvature flow method with a novel influence function. The proposed influence function takes profit from t ...

EUROCAST2003

Sampling of Periodic Signals: A Quantitative Error Analysis

Michaël Unser, Thierry Blu, Mathews Jacob

We present an exact expression for the

L _{ 2 }

error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schem ...

IEEE2002

An Inner-Product Calculus for Periodic Functions and Curves

Graph Chatbot

Chat with Graph Search

Sampling Curves with Finite Rate of Innovation

Ideal knots and other packing problems of tubes

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Conformational analysis of nucleic acids revisited: Curves

Geometrical reconstruction of curves and surfaces using NURBS

Direct measurement of drainage curves in infiltration of SiC particle preforms

Global radii of curvature, and the biarc approximation of space curves

Non-linear subdivision using local spherical coordinates

Unsupervised Selective Anisotropic Feature Diffusion for Cortical Surface Registration

Sampling of Periodic Signals: A Quantitative Error Analysis

Direct measurement of drainage curves in infiltration of SiC particle preforms

Sampling Curves with Finite Rate of Innovation

Ideal knots and other packing problems of tubes

Global radii of curvature, and the biarc approximation of space curves

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Unsupervised Selective Anisotropic Feature Diffusion for Cortical Surface Registration

Sampling of Periodic Signals: A Quantitative Error Analysis

Conformational analysis of nucleic acids revisited: Curves

Geometrical reconstruction of curves and surfaces using NURBS

Non-linear subdivision using local spherical coordinates