Computing Minimum Area Homologies
Computing Minimum Area Homologies
复制标题
计算最小面积同源性
DOI：
10.1111/cgf.12514
复制
发表时间：
2014
影响因子：
2.5
通讯作者：
Mikael Vejdemo
中科院分区：
文献类型：
--
作者：
E. Chambers;Mikael Vejdemo
曲线相似性的计算和分类是一个基本问题，最近引起了人们的兴趣。然而，到目前为止，还没有实现这些算法的曲面上的曲线与可证明的保证质量的措施。在本文中，我们提出了一个相似性度量的任何两个循环是同源的，我们计算的最小面积的任何同源性（或连接的边界链）之间的两个循环。最小面积的同源性存在于更广泛的类的周期比以前的措施是基于同伦。它也比以前定义的度量更容易计算，从而产生基于线性代数工具的有效实现。我们展示了我们的算法在一系列的输入，显示的例子，突出了这种相似性度量的可行性。
Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on the quality of the measure. In this paper, we present a similarity measure for any two cycles that are homologous, where we calculate the minimum area of any homology (or connected bounding chain) between the two cycles. The minimum area homology exists for broader classes of cycles than previous measures which are based on homotopy. It is also much easier to compute than previously defined measures, yielding an efficient implementation that is based on linear algebra tools. We demonstrate our algorithm on a range of inputs, showing examples which highlight the feasibility of this similarity measure.