Conformal Wasserstein distances: Comparing surfaces in polynomial time
Conformal Wasserstein distances: Comparing surfaces in polynomial time
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共形 Wasserstein 距离：在多项式时间内比较表面
DOI：
10.1016/j.aim.2011.01.020
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发表时间：
2011
影响因子：
1.7
通讯作者：
I. Daubechies
中科院分区：
文献类型：
--
作者：
Y. Lipman;I. Daubechies
我们提出了一种可由多项式时间算法实现的曲面比较的构造性方法。我们通过解决两个给定表面的共形密度之间的质量输运问题来确定它们的“相似性”。这个大规模运输问题与标准情况的不同之处在于，我们要求解在全局Möbius变换下是不变的。我们详细介绍了要比较的曲面是圆盘状的情况；我们还概述了如何将该方法推广到其他类型的曲面。
We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the “similarity” of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global Möbius transformations. We present in detail the case where the surfaces to compare are disk-like; we also sketch how the approach can be generalized to other types of surfaces.