Orthogonal and Biorthogonal FIR Hexagonal Filter Banks With Sixfold Symmetry

Abstract

Recently hexagonal image processing has attracted attention. The hexagonal lattice has several advantages in comparison with the rectangular lattice, the conventionally used lattice for image sampling and processing. For example, a hexagonal lattice needs fewer sampling points; it has better consistent connectivity; it has higher symmetry; its structure is plausible to human vision systems. The multiresolution analysis method has been used for hexagonal image processing. Since the hexagonal lattice has high degree of symmetry, it is desirable that the hexagonal lter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice. The orthogonal or prefect reconstruction (PR) hexagonal lter banks which are available in the literature have only 3-fold symmetry.In this paper we investigate the construction of orthogonal and PR FIR hexagonal lter banks with 6-fold symmetry. We obtain block structures of 7-size re nement (7-channel 2-D) orthogonal and PR FIR hexagonal lter banks with 6-fold rotational symmetry.√ 7-re nement orthogonal and biorthogonal wavelets based on these block structures are constructed. In this paper, we also consider FIR hexagonal lter banks with axial (line) symmetry, and we present a block structure of FIR hexagonal lter banks with pseudo 6-fold axial symmetry.Index TermsHexagonal lattice, hexagonal image, lter bank with 6-fold symmetry, orthogonal hexagonal lter bank, biorthogonal hexagonal lter bank, √ 7-re nement wavelet, 7-size re nement multiresolution decomposition/reconstruction.