  The processing, storage and transmission of large-scale point clouds is an
ongoing challenge in the computer vision community which hinders progress in
the application of 3D models to real-world settings, such as autonomous
driving, virtual reality and remote sensing. We propose a novel, one-shot point
cloud simplification method which preserves both the salient structural
features and the overall shape of a point cloud without any prior surface
reconstruction step. Our method employs Gaussian processes suitable for
functions defined on Riemannian manifolds, allowing us to model the surface
variation function across any given point cloud. A simplified version of the
original cloud is obtained by sequentially selecting points using a greedy
sparsification scheme. The selection criterion used for this scheme ensures
that the simplified cloud best represents the surface variation of the original
point cloud. We evaluate our method on several benchmark and self-acquired
point clouds, compare it to a range of existing methods, demonstrate its
application in downstream tasks of registration and surface reconstruction, and
show that our method is competitive both in terms of empirical performance and
computational efficiency.
