悬赏，求大神解释一下Fréchet distance和Hausdorff Distance

Janus槑

最近写paper被这两个概念折腾的死去活来的，有么有大神能教教我这两个距离的概念还有他们之间的区别是什么

悬赏一下，意思意思

败家娘们你好

我是文科生，这是我在维基百科上看到的。
In mathematics, the Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves.
The Fréchet distance between two curves is the minimum length of a leash required to connect a dog and its owner, constrained on two separate paths, as they walk without backtracking along their respective curves from one endpoint to the other. The definition is symmetric with respect to the two curves. Imagine a dog walking along one curve and the dog's owner walking along the other curve, connected by a leash. Both walk continuously along their respective curve from the prescribed start point to the prescribed end point of the curve. Both may vary their speed, and even stop, at arbitrary positions and for arbitrarily long. However, neither can backtrack. The Fréchet distance between the two curves is the length of the shortest leash (not the shortest leash that is sufficient for all walks, but the shortest leash of all the leashes) that is sufficient for traversing both curves in this manner.
EXAMPLE
The Fréchet distance between two concentric circles of radius r_1 and r_2 respectively is |r_1 - r_2|. The longest leash is required when the owner stands still and the dog travels to the opposite side of the circle (r_1 + r_2), and the shortest leash when both owner and dog walk at a constant speed around the circle (|r_1 - r_2|).

败家娘们你好

完全看不懂呢！
豪斯多夫距离量度度量空间中真子集之间的距离。
设X和Y是度量空间M的两个真子集。那麽豪斯多夫距离dH(X,Y)是最小的数r使得X的闭r—邻域包含Y，Y的闭r—邻域也包含X。
这距离函数令M的所有真子集组成的集成为度量空间，且记为F(M)。F(M)的拓扑只是依赖于M的拓扑。若M是非空的，则F(M)也是。
豪斯多夫空间也可以照样定义在M的闭非真子集上，但距离可能是无限大，F(M)的拓扑不只依赖于M的拓扑，也依赖于M的特有度量。非闭子集间的豪斯多夫距离可以定义为它们的闭包的豪斯多夫距离。这给予M的所有子集组成的集一个伪度量。（两个有相同闭包的子集的豪斯多夫距离是零）。
在欧几里得几何常用一个类似概念，称为等距同构下的豪斯多夫距离。设X 和Y是欧几里得空间中两个紧的图形，则DH(X,Y)是dH(I(X),Y)取所有欧几里得空间的保距变换I的最小值。这距离量度X和Y离等距差多少。

pogoplug

LZ保重 我在metric space课里听到过这两个概念。。。。。。。。。

Janus槑

pogoplug 发表于 2014-8-3 12:16
LZ保重 我在metric space课里听到过这两个概念。。。。。。。。。

这样啊，那你还记得你的教科书是什么吗，我拿来看看