Entezari Alireza, Möller Torsten
School of Computing Science, Simon Fraser University.
IEEE Trans Vis Comput Graph. 2006 Sep-Oct;12(5):1337-44. doi: 10.1109/tvcg.2006.141.
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 C2 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.
在本文中，我们提出了一种盒样条及其变体，用于重建在笛卡尔格点上采样的体数据。特别地，我们给出了一种三变量盒样条重建核，在恢复底层函数的正确笛卡尔频谱方面，它优于张量积重建方案。这种盒样条产生一个(C^2)重建，可以看作是二维中著名的Zwart-Powell元在三维中的扩展。虽然它的光滑性和逼近能力与三三次B样条相当，但我们展示了这种重建在笛卡尔格点上采样的函数上的优越性，并将其与张量积B样条进行对比。我们的构造通过对这种盒样条重建行为的傅里叶域分析得到验证。此外，我们提出了一种通过分解来稳定评估这种盒样条的方法。通过卷积，这种分解将问题简化为对我们之前以显式封闭形式发表的四向盒样条的评估。
