Persistence-sensitive simplification functions on 2-manifolds
Persistence-sensitive simplification functions on 2-manifolds
复制标题
2-流形上的持久敏感简化函数
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Valerio Pascucci
中科院分区：
文献类型：
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作者：
H. Edelsbrunner;D. Morozov;Valerio Pascucci
我们继续研究拓扑持久性[5]，通过研究简化函数<i>f</i>的问题，以消除由其持久性图[2]确定的拓扑噪声。为了说明我们的结果，我们称一个函数<i>g</i>是另一个函数<i>f</i>的ε-<i>简化，</i>如果f<i>−</i><sub>g</sub> ≤ ε，并且<i>g</i>的持久性图与<i>f</i>的持久性图相同，只是从对角线上去掉了<sub>L1</sub><i></i>我们证明了对于2-流形上的函数<i>f</i>存在这样的ε-化简，并给出了在分段线性情形下构造它们的算法.
We continue the study of topological persistence [5] by investigating the problem of simplifying a function <i>f</i> in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function <i>g</i> an ε-<i>simplification</i> of another function <i>f</i> if ¦¦<i>f−g</i>¦¦<sub>∞</sub>≤ε, and the persistence diagrams of <i>g</i> are the same as those of <i>f</i> except all points within <i>L</i><sub>1</sub>-distance at most ε from the diagonal have been removed. We prove that for functions <i>f</i> on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.