Publication

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst
2008
Journal Articles

Résumé

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give some indications on the CWT on a paraboloid and we introduce a unified approach to the CWT on conic sections.

Source officielle

https://infoscience.epfl.ch/entities/publication/e41bc8a1-e731-443f-a483-7e0c02e9a2e5

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Pierre Vandergheynst, Iva Bogdanova Vandergheynst
2008
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/e41bc8a1-e731-443f-a483-7e0c02e9a2e5

À propos de ce résultat

Concepts associés (32)

Conique

En géométrie euclidienne, une conique est une courbe plane algébrique, définie initialement comme l’intersection d'un cône de révolution (supposé prolongé à l’infini de part et d’autre du sommet) avec un plan. Lorsque le plan de coupe ne passe pas par le sommet du cône, la conique est dite non dégénérée et réalise l’une des trois formes de courbe suivantes : ellipse, parabole ou hyperbole (le cercle étant un cas particulier de l'ellipse, parfois appelé quatrième forme). Ces courbes sont caractérisées par un paramètre réel appelé excentricité.

Confocal conic sections

In geometry, two conic sections are called confocal if they have the same foci. Because ellipses and hyperbolas have two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture of confocal ellipses and hyperbolas, any ellipse intersects any hyperbola orthogonally (at right angles). Parabolas have only one focus, so, by convention, confocal parabolas have the same focus and the same axis of symmetry.

Wavelet transform

In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.

Afficher plus

Publications associées (22)

Teaching Not To

Charlotte Malterre-Barthes

Two design studios were successively taught in two schools of architecture: one at the Harvard Graduate School of Design (GSD) and the other at the Swiss Federal Institute of Technology in Lausanne (EPFL) in Lausanne, Switzerland, based on "A Global Morato ...

Taylor & Francis Inc2024

Rising from rubble - Leveraging existing construction tools for upcycling concrete waste into slender walls

Katrin Beyer, Maxence Grangeot, Corentin Jean Dominique Fivet, Qianqing Wang, Stefana Parascho

In this paper, we present a new method for upcycling concrete rubble waste into slender walls through the lightweight digital augmentation of mainstream construction machines. By using such method, the environmental impact of concrete construction and demo ...

Springer2024

FLO:RE – A new floor system made of reused reinforced concrete and steel elements

Maléna Bastien Masse, Numa Joy Bertola, Célia Marine Küpfer, Corentin Jean Dominique Fivet

Carefully extracting reinforced concrete (RC) elements from soon-to-be demolished structures and reusing them as load-bearing components is an emerging circular low-carbon alternative to building new structures. As floor construction typically accounts for ...

IABSE2024

Afficher plus