  Imperfect data (noise, outliers and partial overlap) and high degrees of
freedom make non-rigid registration a classical challenging problem in computer
vision. Existing methods typically adopt the $\ell_{p}$ type robust estimator
to regularize the fitting and smoothness, and the proximal operator is used to
solve the resulting non-smooth problem. However, the slow convergence of these
algorithms limits its wide applications. In this paper, we propose a
formulation for robust non-rigid registration based on a globally smooth robust
estimator for data fitting and regularization, which can handle outliers and
partial overlaps. We apply the majorization-minimization algorithm to the
problem, which reduces each iteration to solving a simple least-squares problem
with L-BFGS. Extensive experiments demonstrate the effectiveness of our method
for non-rigid alignment between two shapes with outliers and partial overlap,
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/Juyong/Fast_RNRR.
