NRGA: Gravitational Approach for Non-rigid Point Set Registration

Recovery of correspondences between point sets which differ by some non-rigid transformation is an ill-posed problem. Many existing methods underperform on noisy or corrupted input data. In this study, a novel physics-based approach -- Non-Rigid Gravitational Approach (NRGA) -- for non-rigid point set registration is introduced which is robust to the mentioned artifacts. Thereafter, a distributed N-body simulation and iterative Procrustes alignment non-rigidly transform and register the template point set. Furthermore, in the force field evolution, per-point Gaussian curvature serves as a shape matching descriptor whereas the displacement fields are regularized by coherent collective motion. The optimal alignment is referred to as the state of minimum gravitational potential energy between the point sets. A thorough experimental evaluation and comparison are provided with widely used state-of-the-art methods on 2D and 3D data sets. Experiments show NRGA's robustness against uniform outliers and missing data.