  We present PPF-FoldNet for unsupervised learning of 3D local descriptors on
pure point cloud geometry. Based on the folding-based auto-encoding of well
known point pair features, PPF-FoldNet offers many desirable properties: it
necessitates neither supervision, nor a sensitive local reference frame,
benefits from point-set sparsity, is end-to-end, fast, and can extract powerful
rotation invariant descriptors. Thanks to a novel feature visualization, its
evolution can be monitored to provide interpretable insights. Our extensive
experiments demonstrate that despite having six degree-of-freedom invariance
and lack of training labels, our network achieves state of the art results in
standard benchmark datasets and outperforms its competitors when rotations and
varying point densities are present. PPF-FoldNet achieves $9\%$ higher recall
on standard benchmarks, $23\%$ higher recall when rotations are introduced into
the same datasets and finally, a margin of $>35\%$ is attained when point
density is significantly decreased.
