地球移动距离(EMD)是一种衡量D区域上两个概率分布之间距离的度量，等同于第一Wasserstein距离。当分布具有相同总量时，EMD可以通过解决运输问题来计算，例如在离散域中使用匈牙利算法。它在统计、图像处理和数据比较中有广泛应用。
以下内容为罗方炜译：
Earth mover’s distance
In computer science, the earth mover’s distance (EMD) is a measure of the distance between two probability distributions over a region D. In mathematics, this is known as the Wasserstein metric. Informally, if the distributions are interpreted as two different ways of piling up a certain amount of dirt over the region D, the EMD is the minimum cost of turning one pile into the other; where the cost is assumed to be amount of dirt moved times the distance by which it is moved [1].
在计算机科学与技术中，地球移动距离(EMD)是一种在D区域两个概率分布距离的度量，就是被熟知的Wasserstein度量标准。不正式的说，如果两个分布被看作在D区域上两种不同方式堆积一定数量的山堆，那么EMD就是把一堆变成另一堆所需要移动单位小块最小的距离之和。
The above definition is valid only if the two distributions have the same integral (informally, if the two piles have the same amount of dirt), as in normalized histograms orprobability density functions. In that case, the EMD is equivalent to the 1st Mallows distance or 1st Wassers
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