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.
翻译:最佳运输(OT)在机器学习、数据科学和计算机视觉中已变得极受欢迎。 OT问题的核心假设是源和目标计量质量总和,这限制了其应用。最佳部分运输(OPT)是最近对这一限制提出的一个解决办法。与OT问题相似,巴勒斯坦被占领土的计算依赖于解决线性编程问题(通常为高尺寸),这在计算上可能变得令人望而却步。在本文中,我们提出一种有效的算法,用于计算在两个非负性措施之间的一个层面的 OFLAP问题。接下来,在切片OT距离的概念之后,我们利用切片剪切除法来界定切片的奥地距离。最后,我们在各种数字实验中展示了切片的奥地方法的计算和精确效益。特别是,我们展示了在热点云登记中应用了我们提议的Sliced-OPT。