  This paper addresses the problem of generating dense point clouds from given
sparse point clouds to model the underlying geometric structures of
objects/scenes. To tackle this challenging issue, we propose a novel end-to-end
learning-based framework. Specifically, by taking advantage of the linear
approximation theorem, we first formulate the problem explicitly, which boils
down to determining the interpolation weights and high-order approximation
errors. Then, we design a lightweight neural network to adaptively learn
unified and sorted interpolation weights as well as the high-order refinements,
by analyzing the local geometry of the input point cloud. The proposed method
can be interpreted by the explicit formulation, and thus is more
memory-efficient than existing ones. In sharp contrast to the existing methods
that work only for a pre-defined and fixed upsampling factor, the proposed
framework only requires a single neural network with one-time training to
handle various upsampling factors within a typical range, which is highly
desired in real-world applications. In addition, we propose a simple yet
effective training strategy to drive such a flexible ability. In addition, our
method can handle non-uniformly distributed and noisy data well. Extensive
experiments on both synthetic and real-world data demonstrate the superiority
of the proposed method over state-of-the-art methods both quantitatively and
qualitatively.
