Construction of triangular biorthogonal wavelets using extended lifting

We present new triangular biorthogonal wavelets by extending two-dimensional lifting, which we call twist. The resulting truly two-dimensional biorthogonal filters defined on a triangular lattice inherit several nice features of the early triangular biorthogonal wavelet filters such as the hexagonal symmetry of low-pass filters, symmetrical arrangement of three high-pass filters on the lattice, both of which contribute to preserve isotropy of images in the muniscale wavelet decomposition. Besides, these filters have much larger support, providing much larger portions of the total energy to three detail components of decomposed images. This plays an important role when extracting the edge structure of an image.