SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2088-A2107, January 2020.
This paper deals with the 3/4-discrete 2-Wasserstein optimal transport between two measures, where one is supported on a set of line segments and the other is supported on a set of points. We select the most suitable optimization procedure that computes the optimal transport. Then we address the problem of projecting point clouds on the set of measures supported on segments for the optimal transportation distance. We provide numerical examples of approximation of point clouds by segments.

中文翻译：

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3/4离散最优运输

SIAM科学计算杂志，第42卷，第4期，第A2088-A2107页，2020年1月。
本文讨论了两个量度之间的3/4离散2-Wasserstein最优输运，其中一个在一组线段上得到支持，并且另一点在一组点上受支持。我们选择最合适的优化程序来计算最佳运输。然后，我们解决了在点上投影点云的问题，这些点在为最佳运输距离而支持的路段上得到支持。我们提供了按分段逼近点云的数值示例。