Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice

Authors:
Alireza Entezari;Torsten Moller
Affiliations:
-;IEEE
Venue:
IEEE Transactions on Visualization and Computer Graphics
Year:
2006

Citing 8
Cited 4

Analytic antialiasing with prism splines

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A comparison of normal estimation schemes

VIS '97 Proceedings of the 8th conference on Visualization '97
Design of accurate and smooth filters for function and derivative reconstruction

VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Splatting Errors and Antialiasing

IEEE Transactions on Visualization and Computer Graphics
C2 Surfaces Built from Zero Sets of the 7-Direction Box Spline

Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Hardware-Accelerated High-Quality Reconstruction on PC Hardware

VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Linear and Cubic Box Splines for the Body Centered Cubic Lattice

VIS '04 Proceedings of the conference on Visualization '04
A granular three dimensional multiresolution transform

EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization

Technical Section: Efficient volume rendering on the body centered cubic lattice using box splines

Computers and Graphics
3D frequency-domain analysis of non-separable reconstruction schemes by using direct volume rendering

Proceedings of the 26th Spring Conference on Computer Graphics
On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains

Computer Aided Geometric Design
Symmetric box-splines on root lattices

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this article we propose a box spline and its variants for reconstructing volumetric data sampled on the Cartesian lattice. In particular we present a tri-variate box spline reconstruction kernel that is superior to tensor product reconstruction schemes in terms of recovering the proper Cartesian spectrum of the underlying function. This box spline produces a $C^2$ reconstruction that can be considered as a three dimensional extension of the well known Zwart-Powell element in 2D. While its smoothness and approximation power are equivalent to those of the tri-cubic B-spline, we illustrate the superiority of this reconstruction on functions sampled on the Cartesian lattice and contrast it to tensor product B-splines. Our construction is validated through a Fourier domain analysis of the reconstruction behavior of this box spline.Moreover, we present a stable method for evaluation of this box spline by means of a decomposition. Through a convolution, this decomposition reduces the problem to evaluation of a four directional box spline that we previously published in its explicit closed form [8].