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Point cloud is a collection of 3D coordinates that are discrete geometricsamples of an object's 2D surfaces. Using a low-cost 3D scanner to acquire datameans that point clouds are often in lower resolution than desired forrendering on high-resolution displays. Building on recent advances in graphsignal processing, we design a local algorithm for 3D point cloudsuper-resolution (SR). First, we initialize new points at centroids of localtriangles formed using the low-resolution point cloud, and connect all pointsusing a k-nearestneighbor graph. Then, to establish a linear relationshipbetween surface normals and 3D point coordinates, we perform bipartite graphapproximation to divide all nodes into two disjoint sets, which are optimizedalternately until convergence. For each node set, to promote piecewise smooth(PWS) 2D surfaces, we design a graph total variation (GTV) objective for nearbysurface normals, under the constraint that coordinates of the original pointsare preserved. We pursue an augmented Lagrangian approach to tackle theoptimization, and solve the unconstrained equivalent using the alternatingmethod of multipliers (ADMM). Extensive experiments show that our proposedpoint cloud SR algorithm outperforms competing schemes objectively andsubjectively for a large variety of point clouds.

3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals