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 aimed at preserving isotropy, and a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. 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. Applying our filter to images, we explore applications that truly benefit from our triangular wavelets in comparison with the conventional tensor product transforms.