Deep Magnification-Arbitrary Upsampling over 3D Point Clouds

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, namely MAPU-Net. 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 and normal-guided displacements, by analyzing the local geometry of the input point cloud. MAPU-Net 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, MAPU-Net, a single neural network with one-time training, can handle an arbitrary upsampling factor, which is highly desired in real-world applications. In addition, we propose a simple yet effective training strategy to drive such a flexible ability. Extensive experiments on both synthetic and real world data demonstrate the superiority of the proposed MAPU-Net over state-of-the-art methods both quantitatively and qualitatively. To the best of our knowledge, this is the first end-to-end learning based method that is capable of achieving magnification-arbitrary upsampling over 3D point clouds.