论文标题
切成薄片的最佳部分运输
Sliced Optimal Partial Transport
论文作者
论文摘要
最佳运输（OT）在机器学习，数据科学和计算机视觉中变得极为流行。 OT问题中的核心假设是源和目标度量的质量总量相等，这限制了其应用。最佳部分运输（OPT）是最近提出的解决此限制的解决方案。与OT问题相似，OPT的计算依赖于解决线性编程问题（通常在高维度），这可能会在计算上变得过于刺激。在本文中，我们提出了一种有效的算法，用于计算一个维度的两个非负测度之间的OPT问题。接下来，遵循切片的距离距离的想法，我们利用切片来定义切片的OPT距离。最后，我们在各种数值实验中证明了基于切片的方法的计算和准确性好处。特别是，我们在嘈杂的点云注册中展示了我们所提出的切片OPT的应用。
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its application. Optimal Partial Transport (OPT) is a recently proposed solution to this limitation. Similar to the OT problem, the computation of OPT relies on solving a linear programming problem (often in high dimensions), which can become computationally prohibitive. In this paper, we propose an efficient algorithm for calculating the OPT problem between two non-negative measures in one dimension. Next, following the idea of sliced OT distances, we utilize slicing to define the sliced OPT distance. Finally, we demonstrate the computational and accuracy benefits of the sliced OPT-based method in various numerical experiments. In particular, we show an application of our proposed Sliced-OPT in noisy point cloud registration.
