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Point set is arguably the most direct approximation of an object or scenesurface, yet its practical acquisition often suffers from the shortcoming ofbeing noisy, sparse, and possibly incomplete, which restricts its use for ahigh-quality surface recovery. Point set upsampling aims to increase itsdensity and regularity such that a better surface recovery could be achieved.The problem is severely ill-posed and challenging, considering that theupsampling target itself is only an approximation of the underlying surface.Motivated to improve the surface approximation via point set upsampling, weidentify the factors that are critical to the objective, by pairing the surfaceapproximation error bounds of the input and output point sets. It suggests thatgiven a fixed budget of points in the upsampling result, more points should bedistributed onto the surface regions where local curvatures are relativelyhigh. To implement the motivation, we propose a novel design ofCurvature-ADaptive Point set Upsampling network (CAD-PU), the core of which isa module of curvature-adaptive feature expansion. To train CAD-PU, we followthe same motivation and propose geometrically intuitive surrogates thatapproximate discrete notions of surface curvature for the upsampled point set.We further integrate the proposed surrogates into an adversarial learning basedcurvature minimization objective, which gives a practically effective learningof CAD-PU. We conduct thorough experiments that show the efficacy of ourcontributions and the advantages of our method over existing ones. Ourimplementation codes are publicly available athttps://github.com/JiehongLin/CAD-PU.

CAD-PU: A Curvature-Adaptive Deep Learning Solution for Point Set Upsampling