Sliced Optimal Partial Transport
This work addresses a computational bottleneck in OPT for researchers in machine learning and computer vision, offering an incremental improvement over existing methods.
The paper tackles the computational inefficiency of Optimal Partial Transport (OPT) by proposing a one-dimensional algorithm and extending it to a sliced OPT distance, demonstrating improved computational speed and accuracy in experiments, including a 30% faster registration with comparable accuracy in noisy point cloud registration.
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.