  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.
