论文标题
2D滤波功能的匹配距离的几何形状
Geometry of the matching distance for 2D filtering functions
论文作者
论文摘要
在本文中，我们利用了扩展的帕累托电网的概念来研究$ \ mathbb {r}^2 $值定义在Riemannian封闭歧管上定义的常规功能的匹配距离的几何特性。特别是，我们证明在这种情况下，匹配距离是在特殊值或对应于垂直，水平或斜率1行的值下实现的。
In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for $\mathbb{R}^2$-valued regular functions defined on a Riemannian closed manifold. In particular, we prove that in this case the matching distance is realised either at special values or at values corresponding to vertical, horizontal or slope 1 lines.
