Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry

Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry

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 generalizatio...

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Main Authors: Kensuke Fujinoki, Oleg V. Vasilyev
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:EURASIP Journal on Image and Video Processing
Online Access:http://dx.doi.org/10.1155/2009/248581
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spelling doaj-353cdaa8ac794363b42e1633751971f82020-11-24T20:59:25ZengSpringerOpenEURASIP Journal on Image and Video Processing1687-51761687-52812009-01-01200910.1155/2009/248581Triangular Wavelets: An Isotropic Image Representation with Hexagonal SymmetryKensuke FujinokiOleg V. VasilyevThis 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. http://dx.doi.org/10.1155/2009/248581
collection DOAJ
language English
format Article
sources DOAJ
author Kensuke Fujinoki
Oleg V. Vasilyev
spellingShingle Kensuke Fujinoki
Oleg V. Vasilyev
Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
EURASIP Journal on Image and Video Processing
author_facet Kensuke Fujinoki
Oleg V. Vasilyev
author_sort Kensuke Fujinoki
title Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
title_short Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
title_full Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
title_fullStr Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
title_full_unstemmed Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
title_sort triangular wavelets: an isotropic image representation with hexagonal symmetry
publisher SpringerOpen
series EURASIP Journal on Image and Video Processing
issn 1687-5176
1687-5281
publishDate 2009-01-01
description 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.
url http://dx.doi.org/10.1155/2009/248581
work_keys_str_mv AT kensukefujinoki triangularwaveletsanisotropicimagerepresentationwithhexagonalsymmetry
AT olegvvasilyev triangularwaveletsanisotropicimagerepresentationwithhexagonalsymmetry
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