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arXiv 1105.4477cs.CV
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三维数字图像的上同调

On the Cohomology of 3D Digital Images

Universidad de Sevilla(塞维利亚大学)

Rocio Gonzalez-Diaz, Pedro Real

摘要:

提出了一种计算三维数字二值图像上同调环的方法。通过一个单纯复形K(I)拓扑地表示(直到图像的同构)一个三维数字二值图像$I$的上同调环.的有用性的简单描述的“数字”上同调环的三维数字二进制值的图片测试通过一个小程序可视化的方法的不同步骤。给出了拓扑细化、(余)同调生成元的代表(余)圈的可视化以及简单图上同调的杯积计算等方面的一些实例。

英文摘要:

We propose a method for computing the cohomology ring of three--dimensional (3D) digital binary-valued pictures. We obtain the cohomology ring of a 3D digital binary--valued picture $I$, via a simplicial complex K(I)topologically representing (up to isomorphisms of pictures) the picture I. The usefulness of a simplicial description of the "digital" cohomology ring of 3D digital binary-valued pictures is tested by means of a small program visualizing the different steps of the method. Some examples concerning topological thinning, the visualization of representative (co)cycles of (co)homology generators and the computation of the cup product on the cohomology of simple pictures are showed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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