Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
© K. Fujinoki and O. V. Vasilyev. 2009
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.
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