  In this paper we address the task of finding representative subsets of points
in a 3D point cloud by means of a point-wise ordering. Only a few works have
tried to address this challenging vision problem, all with the help of hard to
obtain point and cloud labels. Different from these works, we introduce the
task of point-wise ordering in 3D point clouds through self-supervision, which
we call self-ordering. We further contribute the first end-to-end trainable
network that learns a point-wise ordering in a self-supervised fashion. It
utilizes a novel differentiable point scoring-sorting strategy and it
constructs an hierarchical contrastive scheme to obtain self-supervision
signals. We extensively ablate the method and show its scalability and superior
performance even compared to supervised ordering methods on multiple datasets
and tasks including zero-shot ordering of point clouds from unseen categories.
