Accelerated Gravitational Point Set Alignment With Altered Physical Laws

This work describes Barnes-Hut Rigid Gravitational Approach (BH-RGA) -- a new rigid point set registration method relying on principles of particle dynamics. Interpreting the inputs as two interacting particle swarms, we directly minimise the gravitational potential energy of the system using non-linear least squares. Compared to solutions obtained by solving systems of second-order ordinary differential equations, our approach is more robust and less dependent on the parameter choice. We accelerate otherwise exhaustive particle interactions with a Barnes-Hut tree and efficiently handle massive point sets in quasilinear time while preserving the globally multiply-linked character of interactions. Among the advantages of BH-RGA is the possibility to define boundary conditions or additional alignment cues through varying point masses. Systematic experiments demonstrate that BH-RGA surpasses performances of baseline methods in terms of the convergence basin and accuracy when handling incomplete, noisy and perturbed data. The proposed approach also positively compares to the competing method for the alignment with prior matches.