Box splines
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
SIAM Journal on Matrix Analysis and Applications
Triangular √3-subdivision schemes: the regular case
Journal of Computational and Applied Mathematics
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition)
Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition)
Biorthogonal loop-subdivision wavelets
Computing - Geometric modelling dagstuhl 2002
Hexagonal Parallel Pattern Transformations
IEEE Transactions on Computers
Orthogonal and Biorthogonal FIR Hexagonal Filter Banks With Sixfold Symmetry
IEEE Transactions on Signal Processing
√3-Subdivision-Based Biorthogonal Wavelets
IEEE Transactions on Visualization and Computer Graphics
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
Isotropic polyharmonic B-splines: scaling functions and wavelets
IEEE Transactions on Image Processing
FIR Filter Banks for Hexagonal Data Processing
IEEE Transactions on Image Processing
| Hi-index | 35.68 |
The hexagonal lattice was proposed as an alternative method for image sampling. The hexagonal sampling has certain advantages over the conventionally used square sampling. Hence, the hexagonal lattice has been used in many areas. A hexagonal lattice allows √3, dyadic and √7 refinements, which makes it possible to use the multiresolution (multiscale) analysis method to process hexagonally sampled data. The √3-refinement is the most appealing refinement for multiresolution data processing due to the fact that it has the slowest progression through scale, and hence, it provides more resolution levels from which one can choose. This fact is the main motivation for the study of √3-refinement surface subdivision, and it is also the main reason for the recommendation to use the √3-refinement for discrete global grid systems. However, there is little work on compactly supported √3-refinement wavelets. In this paper, we study the construction of compactly supported orthogonal and biorthogonal √3-refinement wavelets. In particular, we present a block structure of orthogonal FIR filter banks with twofold symmetry and construct the associated orthogonal √3-refinement wavelets. We study the sixfold axial symmetry of perfect reconstruction (biorthogonal) FIR filter banks. In addition, we obtain a block structure of sixfold symmetric √3-refinement filter banks and construct the associated biorthogonal wavelets.