Super-Resolution of 3D Color Point Clouds Via Fast Graph Total Variation

3D point clouds acquired by low-cost sensors are often in lower spatial resolutions than desired for rendering images on high-resolution displays. In this paper, we propose a fast super-resolution (SR) algorithm for color 3D point clouds. We first populate a target low-res point cloud with added interior points. We refine the newly added 3D coordinates and their RGB values by minimizing a graph total variation (GTV) term of connected points' surface normals and RGB values respectively. Unlike non-local methods that require computation-intensive searches of similar patches in a large defined space, our algorithm is inherently local and performs smoothing of newly inserted points only with respect to neighboring points. Moreover, differing from our previous GTV-based SR algorithm that employs gradient descent procedures with sensitive step size parameters due to GTV's non-smooth l
₁
-norm, we rewrite the l
₁
objective into a linear proxy, so that together with constraints on surface normals / RGB values, it can be solved efficiently as a parameter-free linear program (LP). Experimental results show that our algorithm outperforms competing non-graph-based point cloud SR schemes, and is significantly faster than our previous graph-based SR method.