  We present an approach to learning features that represent the local geometry
around a point in an unstructured point cloud. Such features play a central
role in geometric registration, which supports diverse applications in robotics
and 3D vision. Current state-of-the-art local features for unstructured point
clouds have been manually crafted and none combines the desirable properties of
precision, compactness, and robustness. We show that features with these
properties can be learned from data, by optimizing deep networks that map
high-dimensional histograms into low-dimensional Euclidean spaces. The
presented approach yields a family of features, parameterized by dimension,
that are both more compact and more accurate than existing descriptors.
