  Registration of point clouds related by rigid transformations is one of the
fundamental problems in computer vision. However, a solution to the practical
scenario of aligning sparsely and differently sampled observations in the
presence of noise is still lacking. We approach registration in this scenario
with a fusion of the closed-form Universal Mani-fold Embedding (UME) method and
a deep neural network. The two are combined into a single unified framework,
named DeepUME, trained end-to-end and in an unsupervised manner. To
successfully provide a global solution in the presence of large
transformations, we employ an SO(3)-invariant coordinate system to learn both a
joint-resampling strategy of the point clouds and SO(3)-invariant features.
These features are then utilized by the geometric UME method for transformation
estimation. The parameters of DeepUME are optimized using a metric designed to
overcome an ambiguity problem emerging in the registration of symmetric shapes,
when noisy scenarios are considered. We show that our hybrid method outperforms
state-of-the-art registration methods in various scenarios, and generalizes
well to unseen data sets. Our code is publicly available.
