LPOT: Locality-Preserving Gromov–Wasserstein Discrepancy for Nonrigid Point Set Registration

The main problems in point registration involve recovering correspondences and estimating transformations, especially in a fully unsupervised way without any feature descriptors. In this work, we propose a robust point matching method using discrete optimal transport (OT), which is a natural and useful approach for assignment tasks, to recover the underlying correspondences and improve the nonrigid registration in the presence of unknown global transformations. Specifically, we cast the registration problem as a joint estimation over local transport couplings and global transformations, observing that the local neighborhood topology structures should be preserved strongly and stably for nonrigid transformations. By solving the Gromov–Wasserstein discrepancy, a smooth assignment matrix from one point set to another can be recovered in a fully unsupervised way. Registration performance can be improved by applying an unsupervised map to guide the transformation estimate under the alternating optimization. Experimental results on several datasets reveal how the presented method is superior to the state-of-the-art methods when facing large data degradations.