Computational Topology for Point Data: Betti Numbers of α-Shapes
Computational Topology for Point Data: Betti Numbers of α-Shapes
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点数据的计算拓扑：α 形状的 Betti 数
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
V. Robins
中科院分区：
文献类型：
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作者：
V. Robins
下面要考虑的问题是，在给定X的有限点近似值的情况下，确定一个子集X∧R n的拓扑信息。基本方法是在一系列分辨率下计算拓扑属性——比如组件的数量和孔的数量，然后进行外推。取这一极限的理论基础来自于形状理论的逆极限系统和Cech同调。计算机实现涉及离散几何结构，如alpha形状和最小生成树。
The problem considered below is that of determining information about the topology of a subset X ⊂ R n given only a finite point approximation to X. The basic approach is to compute topological properties - such as the number of components and number of holes - at a sequence of resolutions, and then to extrapolate. Theoretical foundations for taking this limit come from the inverse limit systems of shape theory and ˇ Cech homology. Computer implementations involve constructions from discrete geometry such as alpha shapes and the minimal spanning tree.