Initial Bounding of Partial Optimal Transport for Point Cloud Co-Registration

Abstract. Recently published work on the use of partial optimal transport (POT) has shown promise as a robust, fully-automated means to co-register point cloud data sets where either the spatial extent does not fully overlap or where one or more elements appear within only one of the scans due to temporal-based changes. However, understanding the ultimate robustness of such an approach requires further analysis of the relationship between its performance and the sensitivity of the user-defined hyperparameters that determine which elements in the partially-overlapped data set are included in the final correspondence map. Presented herein are a set of experiments formulated to investigate this relationship. The resulting outputs show a robustness to approximately 25% outliers, beyond which even carefully tuned hyperparameters cannot reliably achieve proper mass assignment. For practitioners, exponential regression models derived from controlled experiments provide reliable starting points for hyperparameter tuning in scenes with outlier proportions below 25%. When outlier content approaches or exceeds the 25% threshold, preprocessing through rough segmentation or filtering is recommended. Spatially-aware sampling improves robustness at low outlier percentages but degrades performance at high proportions. While hyperparameter value selection has negligible computational impact, runtime exhibits exponential growth with data size. POT’s robust performance independent of point cloud sparsity suggests temporary downsampling strategies can effectively reduce computational burden without compromising final registration quality.