PUNO: A Neural Operator Framework for Point Cloud Upsampling

We propose PUNO, a novel deep operator-based framework for point cloud upsampling, addressing the challenge of reconstructing high-resolution geometries from sparse point clouds. PUNO generalizes the neural operators proven effective in image super-resolution to 3D point cloud upsampling. Moreover, it first designs a network for point cloud tasks to achieve vertex displacement and manifold parameterization, thereby forming a coarse geometric representation that is compatible with super-resolution neural operators. This is followed by iterative kernel integral approximations in the function space and backprojection to generate the target coordinates, fully utilizing the high-frequency information in the function space. Unlike prior work, PUNO performs transformations in both the data domain and the function domain, with the solution space containing richer basis functions, yielding finer results that mitigate the ill-posed nature of sparse data. It also benefits global continuity. Extensive experiments demonstrate its superior accuracy, robustness, and generalization ability.