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Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry

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.

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Correspondence to Kensuke Fujinoki.

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

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Fujinoki, K., Vasilyev, O.V. Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry. J Image Video Proc 2009, 248581 (2009). https://doi.org/10.1155/2009/248581

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Keywords

  • Hexagonal
  • Image Processing
  • Pattern Recognition
  • Computer Vision
  • Tensor Product