It is an important task to reconstruct surfaces from 3D point clouds. Current methods are able to reconstruct surfaces by learning Signed Distance Functions (SDFs) from single point clouds without ground truth signed distances or point normals. However, they require the point clouds to be dense, which dramatically limits their performance in real applications. To resolve this issue, we propose to reconstruct highly accurate surfaces from sparse point clouds with an on-surface prior. We train a neural network to learn SDFs via projecting queries onto the surface represented by the sparse point cloud. Our key idea is to infer signed distances by pushing both the query projections to be on the surface and the projection distance to be the minimum. To achieve this, we train a neural network to capture the on-surface prior to determine whether a point is on a sparse point cloud or not, and then leverage it as a differentiable function to learn SDFs from unseen sparse point cloud. Our method can learn SDFs from a single sparse point cloud without ground truth signed distances or point normals. Our numerical evaluation under widely used benchmarks demonstrates that our method achieves state-of-the-art reconstruction accuracy, especially for sparse point clouds.

翻译：从 3D 点云重建地表是一项重要任务。 目前的方法可以通过从没有地面真相签名的距离或点正常值的单点云中学习签名远程函数( SDFs) 来重建地表。 但是, 它们要求点云密度高, 从而在实际应用中大大限制其性能 。 为了解决这个问题, 我们建议从点云稀疏的云中和在地表之前的表面云重建高度准确的表面。 我们训练一个神经网络, 通过将查询结果投射到以稀薄点云为代表的表面来学习 SDFs 。 我们的关键想法是通过将查询预测推到地表上和投射距离最小来推到最低, 来推入签名的距离。 为了实现这一点, 我们训练一个神经网络, 在确定某个点是否在微点云上, 之前先捕捉到点云层, 然后将它作为一种不同的功能来从看不见的点云中学习 SDFs。 我们的方法可以从一个小点云中学习 SDFs, 没有地面真相签名的距离或点正常。 我们根据广泛使用的基准进行的数字评估, 我们的数值评估表明我们的方法实现了状态重建的准确度,, 特别是小云。