  Point set registration is defined as a process to determine the spatial
transformation from the source point set to the target one. Existing methods
often iteratively search for the optimal geometric transformation to register a
given pair of point sets, driven by minimizing a predefined alignment loss
function. In contrast, the proposed point registration neural network (PR-Net)
actively learns the registration pattern as a parametric function from a
training dataset, consequently predict the desired geometric transformation to
align a pair of point sets. PR-Net can transfer the learned knowledge (i.e.
registration pattern) from registering training pairs to testing ones without
additional iterative optimization. Specifically, in this paper, we develop
novel techniques to learn shape descriptors from point sets that help formulate
a clear correlation between source and target point sets. With the defined
correlation, PR-Net tends to predict the transformation so that the source and
target point sets can be statistically aligned, which in turn leads to an
optimal spatial geometric registration. PR-Net achieves robust and superior
performance for non-rigid registration of point sets, even in presence of
Gaussian noise, outliers, and missing points, but requires much less time for
registering large number of pairs. More importantly, for a new pair of point
sets, PR-Net is able to directly predict the desired transformation using the
learned model without repetitive iterative optimization routine. Our code is
available at https://github.com/Lingjing324/PR-Net.
