Discrete-time signal processing
Discrete-time signal processing
Design of accurate and smooth filters for function and derivative reconstruction
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Mastering windows: improving reconstruction
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
Reconstruction filters in computer-graphics
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Optimal regular volume sampling
Proceedings of the conference on Visualization '01
Frequency Analysis of Gradient Estimators in Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
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
IEEE Transactions on Visualization and Computer Graphics
An Evaluation of Prefiltered Reconstruction Schemes for Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
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
Quasi-interpolation on the body centered cubic lattice
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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Recently, it has been demonstrated that the optimality of the Body-Centered Cubic (BCC) lattice can be utilized also in practice by using either non-separable box-spline filters or tensor-product B-spline filters for reconstructing an originally continuous signal from its discrete BCC-sampled representation. In order to study the frequency-domain behavior of these filters, a 3D analysis of their frequency responses is required. In this paper, we show that direct volume rendering offers a natural tool for such a 3D analysis. As the frequency responses are analytically known, their characteristic isosurfaces can be rendered separately in the pass band and in the stop band. The visualization of the frequency responses conveys information not just on the absolute postaliasing and oversmoothing effects, but also on their direction dependence. In this sense, the frequency-domain behavior of the non-separable box splines and the tensor-product B-splines on the BCC lattice is evaluated for the first time in this paper. Furthermore, we also analyze how the frequency responses are influenced by a discrete prefiltering, which is necessary to fully exploit the approximation power of the higherorder box-spline and B-spline filters.