  Point clouds upsampling is a challenging issue to generate dense and uniform
point clouds from the given sparse input. Most existing methods either take the
end-to-end supervised learning based manner, where large amounts of pairs of
sparse input and dense ground-truth are exploited as supervision information;
or treat up-scaling of different scale factors as independent tasks, and have
to build multiple networks to handle upsampling with varying factors. In this
paper, we propose a novel approach that achieves self-supervised and
magnification-flexible point clouds upsampling simultaneously. We formulate
point clouds upsampling as the task of seeking nearest projection points on the
implicit surface for seed points. To this end, we define two implicit neural
functions to estimate projection direction and distance respectively, which can
be trained by two pretext learning tasks. Experimental results demonstrate that
our self-supervised learning based scheme achieves competitive or even better
performance than supervised learning based state-of-the-art methods. The source
code is publicly available at https://github.com/xnowbzhao/sapcu.
