• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Aide
  • Connexion
  • Langue 
    • Français
    • English
Consulter le document 
  •   Accueil
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • Consulter le document
  •   Accueil
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • Consulter le document
JavaScript is disabled for your browser. Some features of this site may not work without it.

Afficher

Toute la baseCentres de recherche & CollectionsAnnée de publicationAuteurTitreTypeCette collectionAnnée de publicationAuteurTitreType

Mon compte

Connexion

Enregistrement

Statistiques

Documents les plus consultésStatistiques par paysAuteurs les plus consultés
Thumbnail

How to Apply a Filter Defined in the Frequency Domain by a Continuous Function

Briand, Thibaud; Vacher, Jonathan (2016), How to Apply a Filter Defined in the Frequency Domain by a Continuous Function, Image Processing On Line, 6, p. 183-211. 10.5201/ipol.2016.116

Voir/Ouvrir
article (1).pdf (4.339Mb)
Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
https://doi.org/10.5201/ipol.2016.116
Date
2016
Nom de la revue
Image Processing On Line
Volume
6
Pages
183-211
Identifiant publication
10.5201/ipol.2016.116
Métadonnées
Afficher la notice complète
Auteur(s)
Briand, Thibaud
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Vacher, Jonathan
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
We propose algorithms for filtering real-valued images, when the filter is provided as a continuous function defined in the Nyquist frequency domain. This problem is ambiguous because images are discrete entities and there is no unique way to define the filtering. We provide a theoretical framework designed to analyse the classical and computationally efficient filtering implementations based on discrete Fourier transforms (DFT). In this framework, the filtering is interpreted as the convolution of a distribution, standing for the filter, with a trigonometric polynomial interpolator of the image. The various plausible interpolations and choices of the distribution lead to three equally licit algorithms which can be seen as method variants of the same standard filtering algorithm. In general none should be preferred to the others and the choice depends on the application. In practice, the method differences, which come from the boundary DFT coefficients, are not visible to the naked eye. We demonstrate that claim on several experimental configurations by varying the input image and the considered filter. In some cases however, we discuss how the choice of the variant may affect fundamental properties of the filtering. Source Code The source code and the online demo are accessible at the IPOL web part of this article 1. The C99 implementation of the code that we provide is the one which has been peer reviewed and accepted by IPOL. It contains two modules : one performs the standard filtering algorithm (Algorithm 1) presented in Section 3 and the other performs the comparison detailed in Section 4. The comparison module computes for nine filters the filtered images obtained by applying the three variant methods. For each filter a pairwise comparison of the results is done by computing the (absolute) difference image, the maximum difference and the mean difference. It creates fifty-five images: twenty-seven filtered images, twenty-seven difference images and the modulus of the DFT input in logarithmic scale. See Section 4 and the code documentation for additional information.
Mots-clés
interpolation; trigonometric polynomial; filtering; convolution; Fourier transform; DFT

Publications associées

Affichage des éléments liés par titre et auteur.

  • Vignette de prévisualisation
    The Heeger & Bergen Pyramid Based Texture Synthesis Algorithm 
    Briand, Thibaud; Vacher, Jonathan; Galerne, Bruno; Rabin, Julien (2014) Article accepté pour publication ou publié
  • Vignette de prévisualisation
    The Kalman filter in finance: An application to term structure models of commodity prices and a comparison between the simple and the extended filters 
    Lautier, Delphine (2002) Document de travail / Working paper
  • Vignette de prévisualisation
    Well-being and the Wealth of Nations: How are They to Be Defined? 
    Méda, Dominique; Jany-Catrice, Florence (2013) Article accepté pour publication ou publié
  • Vignette de prévisualisation
    Obstacles to the uptake of breast, cervical, and colorectal cancer screenings: What remains to be achieved by French national programmes? 
    Sicsic, Jonathan; Franc, Carine (2014) Article accepté pour publication ou publié
  • Vignette de prévisualisation
    Synthèse de textures dynamiques pour l'étude de la vision en psychophysique et électrophysiologie 
    Vacher, Jonathan (2017-01-18) Thèse
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Tél. : 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo