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Open Access

Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry

EURASIP Journal on Image and Video Processing20092009:248581

Received: 19 May 2009

Accepted: 14 September 2009

Published: 8 November 2009


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.


HexagonalImage ProcessingPattern RecognitionComputer VisionTensor Product

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Authors’ Affiliations

Department of Mechanical Engineering, University of Colorado, Boulder, USA


© K. Fujinoki and O. V. Vasilyev. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.