Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry. (8th November 2009)

• Record Type: Journal Article
• Authors: Fujinoki Fujinoki, Kensuke Kensuke; Vasilyev Vasilyev, Oleg V. Oleg V.
• Other Names: Fowler Fowler James James Academic Editor.
• Is Part Of: EURASIP journal on image and video processing. Volume 2009(2009)
• Publication Date: 2009-11-08
• Subjects: Image processing -- Digital techniques -- Periodicals; Digital video -- Periodicals; Traitement d'images; Vidéo numérique; Digital video; Image processing -- Digital techniques; Periodicals; Electronic journal; Electronic journals; 621.367
• DOI: 10.1155/2009/248581
• Languages: English
• ISSNs: 1687-5176

Abstract

Abstract : This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.