  Point cloud is a collection of 3D coordinates that are discrete geometric
samples of an object's 2D surfaces. Using a low-cost 3D scanner to acquire data
means that point clouds are often in lower resolution than desired for
rendering on high-resolution displays. Building on recent advances in graph
signal processing, we design a local algorithm for 3D point cloud
super-resolution (SR). First, we initialize new points at centroids of local
triangles formed using the low-resolution point cloud, and connect all points
using a k-nearestneighbor graph. Then, to establish a linear relationship
between surface normals and 3D point coordinates, we perform bipartite graph
approximation to divide all nodes into two disjoint sets, which are optimized
alternately until convergence. For each node set, to promote piecewise smooth
(PWS) 2D surfaces, we design a graph total variation (GTV) objective for nearby
surface normals, under the constraint that coordinates of the original points
are preserved. We pursue an augmented Lagrangian approach to tackle the
optimization, and solve the unconstrained equivalent using the alternating
method of multipliers (ADMM). Extensive experiments show that our proposed
point cloud SR algorithm outperforms competing schemes objectively and
subjectively for a large variety of point clouds.
