In this paper, we propose a normal estimation method for unstructured 3D point clouds. In this method, a feature constraint mechanism called Local Plane Features Constraint (LPFC) is used and then a multi-scale selection strategy is introduced. The LPFC can be used in a single-scale point network architecture for a more stable normal estimation of the unstructured 3D point clouds. In particular, it can partly overcome the influence of noise on a large sampling scale compared to the other methods which only use regression loss for normal estimation. For more details, a subnetwork is built after point-wise features extracted layers of the network and it gives more constraints to each point of the local patch via a binary classifier in the end. Then we use multi-task optimization to train the normal estimation and local plane classification tasks simultaneously. Via LPFC, the normal estimation network could obtain more distinguish point-wise plane-aware features that can describe the differences of each point on the local patch. Finally, thanks to the distinguish features constraint, we can obtain a more robust and meaningful global feature that can be used to regress the normal of the local patch. Also, to integrate the advantages of multi-scale results, a scale selection strategy is adopted, which is a data-driven approach for selecting the optimal scale around each point and encourages subnetwork specialization. Specifically, we employed a subnetwork called Scale Estimation Network to extract scale weight information from multi-scale features. The multi-scale method can well reduce the cost time while persevere the estimation accuracy. More analysis is given about the relations between noise levels, local boundary, and scales in the experiment. These relationships can be a better guide to choosing particular scales for a particular model. Besides, the experimental result shows that our network can distinguish the points on the fitting plane accurately and this can be used to guide the normal estimation and our multi-scale method can improve the results well. Compared to some state-of-the-art surface normal estimators, our method is robust to noise and can achieve competitive results.

在本文中，我们提出了一种非结构化3D点云的法线估计方法。在这种方法中，使用了称为局部平面特征约束（LPFC）的特征约束机制，然后引入了多尺度选择策略。LPFC可以用于单尺度点网络体系结构，以更稳定地估计非结构化3D点云。特别是，与仅使用回归损失进行正常估计的其他方法相比，它可以部分克服噪声对大采样规模的影响。有关更多详细信息，在网络的逐点特征提取之后建立一个子网，最后通过二进制分类器为本地补丁的每个点提供更多约束。然后，我们使用多任务优化来同时训练正常估计和局部平面分类任务。通过LPFC，法线估计网络可以获得更多区分点的平面感知特征，这些特征可以描述局部补丁上每个点的差异。最后，由于区别特征约束，我们可以获得更健壮和有意义的全局特征，可用于回归局部补丁的法线。此外，为了整合多尺度结果的优势，采用尺度选择策略，这是一种数据驱动的方法，用于在每个点附近选择最佳尺度，并鼓励子网专业化。具体来说，我们使用了一个称为Scale Estimation Network的子网来从多尺度特征中提取尺度权重信息。多尺度方法可以在保持估计精度的同时很好地减少成本时间。实验中对噪声水平，局部边界和尺度之间的关系进行了更多分析。这些关系可以更好地指导为特定模型选择特定比例。实验结果表明，我们的网络可以准确地区分拟合平面上的点，可以用来指导正态估计，我们的多尺度方法可以很好地改善结果。与某些最新的表面法线估计器相比，我们的方法对噪声具有鲁棒性，并且可以取得有竞争力的结果。这些关系可以更好地指导为特定模型选择特定比例。实验结果表明，我们的网络可以准确地区分拟合平面上的点，可以用来指导正态估计，而多尺度方法可以很好地改善结果。与某些最新的表面法线估计器相比，我们的方法对噪声具有鲁棒性，并且可以取得有竞争力的结果。这些关系可以更好地指导为特定模型选择特定比例。实验结果表明，我们的网络可以准确地区分拟合平面上的点，可以用来指导正态估计，我们的多尺度方法可以很好地改善结果。与某些最新的表面法线估计器相比，我们的方法对噪声具有鲁棒性，并且可以取得有竞争力的结果。