Point cloud registration is a fundamental problem in robotics, critical for tasks like localization and mapping. Most approaches to this problem use feature based techniques. However, these approaches are limited when dealing with un-structured environments where meaningful features are difficult to extract. Recently, an innovative global point cloud registration algorithm, PHASER, which does not rely on geometric features or point correspondences, has been introduced. It leverages Fourier transforms to identify the optimal rigid transform that maximizes cross-correlation between source and target point clouds. PHASER can also incorporate additional data channels, like LiDAR intensity, to enhance registration results. Because it does not rely on local features and because of its ability to exploit additional data, PHASER is particularly useful when dealing with very noisy point clouds or with many outliers. For this reasons, we propose an extension to PHASER that considers multiple plausible rototranslation hypotheses. Our extended approach outperforms the original PHASER algorithm, especially in challenging scenarios where point clouds are widely separated. We validate its effectiveness on the DARPA SubT, and the Newer College datasets, showcasing its potential for improving registration accuracy in complex environments.
