  The problem of simultaneous rigid alignment of multiple unordered point sets
which is unbiased towards any of the inputs has recently attracted increasing
interest, and several reliable methods have been newly proposed. While being
remarkably robust towards noise and clustered outliers, current approaches
require sophisticated initialisation schemes and do not scale well to large
point sets. This paper proposes a new resilient technique for simultaneous
registration of multiple point sets by interpreting the latter as particle
swarms rigidly moving in the mutually induced force fields. Thanks to the
improved simulation with altered physical laws and acceleration of globally
multiply-linked point interactions with a 2^D-tree (D is the space
dimensionality), our Multi-Body Gravitational Approach (MBGA) is robust to
noise and missing data while supporting more massive point sets than previous
methods (with 10^5 points and more). In various experimental settings, MBGA is
shown to outperform several baseline point set alignment approaches in terms of
accuracy and runtime. We make our source code available for the community to
facilitate the reproducibility of the results.
