CAD-PU：一种用于点集上采样的曲率自适应深度学习解决方案
CAD-PU: A Curvature-Adaptive Deep Learning Solution for Point Set Upsampling
摘要：
点集可以说是物体或场景表面最直接的近似，但它的实际获取往往受到噪声，稀疏，并可能不完整的缺点，这限制了其用于高质量的表面恢复。点集上采样旨在增加其密度和规则性，以便可以实现更好的表面恢复。考虑到上采样目标本身只是底层表面的近似，该问题是严重不适定和具有挑战性的。为了通过点集上采样提高表面近似，我们通过配对输入和输出点集的表面近似误差范围来确定对目标至关重要的因素。这表明，给定上采样结果中的点的固定预算，更多的点应该分布到局部曲率相对较高的表面区域上。为了实现这一动机，我们提出了一种新的曲率自适应点集上采样网络（CAD-PU）的设计，其核心是一个曲率自适应特征扩展模块。为了训练CAD-PU，我们遵循相同的动机，并提出几何直观的代理人，近似离散的概念，表面曲率的上采样点集。我们进一步将所提出的代理集成到基于曲率最小化目标的对抗学习中，这给出了CAD-PU的实际有效学习。我们进行彻底的实验，显示我们的贡献和我们的方法比现有的优势的功效。我们的实现代码可在https://github.com/JiehongLin/CAD-PU上公开获取。
英文摘要：
Point set is arguably the most direct approximation of an object or scene surface, yet its practical acquisition often suffers from the shortcoming of being noisy, sparse, and possibly incomplete, which restricts its use for a high-quality surface recovery. Point set upsampling aims to increase its density and regularity such that a better surface recovery could be achieved. The problem is severely ill-posed and challenging, considering that the upsampling target itself is only an approximation of the underlying surface. Motivated to improve the surface approximation via point set upsampling, we identify the factors that are critical to the objective, by pairing the surface approximation error bounds of the input and output point sets. It suggests that given a fixed budget of points in the upsampling result, more points should be distributed onto the surface regions where local curvatures are relatively high. To implement the motivation, we propose a novel design of Curvature-ADaptive Point set Upsampling network (CAD-PU), the core of which is a module of curvature-adaptive feature expansion. To train CAD-PU, we follow the same motivation and propose geometrically intuitive surrogates that approximate discrete notions of surface curvature for the upsampled point set. We further integrate the proposed surrogates into an adversarial learning based curvature minimization objective, which gives a practically effective learning of CAD-PU. We conduct thorough experiments that show the efficacy of our contributions and the advantages of our method over existing ones. Our implementation codes are publicly available at https://github.com/JiehongLin/CAD-PU.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
