Skip to main content
  • Research Article
  • Open access
  • Published:

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 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.

Publisher note

To access the full article, please see PDF.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Kensuke Fujinoki.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Fujinoki, K., Vasilyev, O.V. Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry. J Image Video Proc 2009, 248581 (2009).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: