  Inspired by the recent PointHop classification method, an unsupervised 3D
point cloud registration method, called R-PointHop, is proposed in this work.
R-PointHop first determines a local reference frame (LRF) for every point using
its nearest neighbors and finds its local attributes. Next, R-PointHop obtains
local-to-global hierarchical features by point downsampling, neighborhood
expansion, attribute construction and dimensionality reduction steps. Thus, we
can build the correspondence of points in the hierarchical feature space using
the nearest neighbor rule. Afterwards, a subset of salient points of good
correspondence is selected to estimate the 3D transformation. The use of LRF
allows for hierarchical features of points to be invariant with respect to
rotation and translation, thus making R-PointHop more robust in building point
correspondence even when rotation angles are large. Experiments are conducted
on the ModelNet40 and the Stanford Bunny dataset, which demonstrate the
effectiveness of R-PointHop on the 3D point cloud registration task. R-PointHop
is a green and accurate solution since its model size and training time are
smaller than those of deep learning methods by an order of magnitude while its
registration errors are smaller. Our codes are available on GitHub.
