Multirate systems and filter banks
Multirate systems and filter banks
Box splines
Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
European Journal of Combinatorics
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines
An evaluation of reconstruction filters for volume rendering
VIS '94 Proceedings of the conference on Visualization '94
Linear and Cubic Box Splines for the Body Centered Cubic Lattice
VIS '04 Proceedings of the conference on Visualization '04
Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition)
Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition)
Discrete Topology of (An*) Optimal Sampling Grids. Interest in Image Processing and Visualization
Journal of Mathematical Imaging and Vision
Topology Preserving Marching Cubes-like Algorithms on the Face-Centered Cubic Grid
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
Optimal sampling lattices and trivariate box splines
Optimal sampling lattices and trivariate box splines
Box Spline Reconstruction On The Face-Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
A computable fourier condition generating alias-free sampling lattices
IEEE Transactions on Signal Processing
Approximation orders of shift-invariant subspaces of W2s(Rd)
Journal of Approximation Theory
Symmetric box-splines on root lattices
Symmetric box-splines on root lattices
A box spline calculus for computed tomography
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
IEEE Transactions on Information Theory
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
Quasi-Interpolating Spline Models for Hexagonally-Sampled Data
IEEE Transactions on Image Processing
Rendering in shift-invariant spaces
Proceedings of Graphics Interface 2013
| Hi-index | 35.68 |
-We introduce a framework for construction of non-separable multivariate splines that are geometrically tailored for general sampling lattices. Voronoi splines are B-spline-like elements that inherit the geometry of a sampling lattice from its Voronoi cell and generate a lattice-shift-invariant spline space for approximation in Rd. The spline spaces associated with Voronoi splines have guaranteed approximation order and degree of continuity. By exploiting the geometric proplerties of Voronoi polytopes and zonotopes, we establish the relationship between Voronoi splines and box splines which are used for a closed-form characterization of the former. For Cartesian lattices, Voronoi splines coincide with tensor-product B-splines and for the 2-D hexagonal lattice, the proposed approach offers a reformulation of hex-splines in terms of multi-box splines. While the construction is for general multidimensional lattices, we particularly characterize bivariate and trivariate Voronoi splines for all 2-D and 3-D lattices and specifically study them for body centered cubic and face centered cubic lattices.