  Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way
to align with a target 3D shape, is a classical problem in computer vision.
Such problems can be challenging because of imperfect data (noise, outliers and
partial overlap) and high degrees of freedom. Existing methods typically adopt
the $\ell_p$ type robust norm to measure the alignment error and regularize the
smoothness of deformation, and use a proximal algorithm to solve the resulting
non-smooth optimization problem. However, the slow convergence of such
algorithms limits their wide applications. In this paper, we propose a
formulation for robust non-rigid registration based on a globally smooth robust
norm for alignment and regularization, which can effectively handle outliers
and partial overlaps. The problem is solved using the majorization-minimization
algorithm, which reduces each iteration to a convex quadratic problem with a
closed-form solution. We further apply Anderson acceleration to speed up the
convergence of the solver, enabling the solver to run efficiently on devices
with limited compute capability. Extensive experiments demonstrate the
effectiveness of our method for non-rigid alignment between two shapes with
outliers and partial overlaps, with quantitative evaluation showing that it
outperforms state-of-the-art methods in terms of registration accuracy and
computational speed. The source code is available at
https://github.com/yaoyx689/AMM_NRR.
