[论文解读] Improvement of Normal Estimation for PointClouds via Simplifying Surface Fitting

Jun Zhou, Wei Jin+4 more|arXiv (Cornell University)|Apr 21, 2021

Advanced Numerical Analysis Techniques参考文献 28被引用 4

一句话总结

本文提出两种轻量级、高效的方法——动态top-k选择与点更新，以增强神经网络与经典曲面拟合在点云法向估计中的兼容性。通过聚焦关键点选择与预拟合点平滑，简化局部曲面拟合过程，该方法在尖锐特征和噪声数据上实现了最先进（SOTA）的精度，相较于DeepFit在512个点的点云块上最高提升5.64%。

ABSTRACT

With the burst development of neural networks in recent years, the task of normal estimation has once again become a concern. By introducing the neural networks to classic methods based on problem-specific knowledge, the adaptability of the normal estimation algorithm to noise and scale has been greatly improved. However, the compatibility between neural networks and the traditional methods has not been considered. Similar to the principle of Occam's razor, that is, the simpler is better. We observe that a more simplified process of surface fitting can significantly improve the accuracy of the normal estimation. In this paper, two simple-yet-effective strategies are proposed to address the compatibility between the neural networks and surface fitting process to improve normal estimation. Firstly, a dynamic top-k selection strategy is introduced to better focus on the most critical points of a given patch, and the points selected by our learning method tend to fit a surface by way of a simple tangent plane, which can dramatically improve the normal estimation results of patches with sharp corners or complex patterns. Then, we propose a point update strategy before local surface fitting, which smooths the sharp boundary of the patch to simplify the surface fitting process, significantly reducing the fitting distortion and improving the accuracy of the predicted point normal. The experiments analyze the effectiveness of our proposed strategies and demonstrate that our method achieves SOTA results with the advantage of higher estimation accuracy over most existed approaches.

研究动机与目标

• 解决学习型神经网络与经典曲面拟合方法在点云法向估计中的不兼容性问题。
• 降低在尖锐拐角或复杂图案区域的拟合复杂度与失真。
• 在噪声和采样密度变化条件下提升法向估计精度。
• 开发轻量级、高效策略，在不增加模型复杂度的前提下简化曲面拟合过程。

提出的方法

• 提出一种动态top-k选择策略，学习识别局部点云块中的关键点，将曲面拟合聚焦于对法向估计最相关的点，提升精度。
• 提出一种点更新策略，在拟合前对点位置进行形变，生成更平滑、更接近平面的点云块，降低拟合失真。
• 使用神经网络预测点选择权重与位置调整量，实现自适应、基于学习的拟合过程优化。
• 在预处理后采用低阶参数化曲面（如切平面）进行简化拟合，提升鲁棒性与精度。
• 将两种策略整合进统一框架，增强深度学习与传统几何拟合之间的兼容性。
• 端到端训练网络，采用回归损失预测法向，同时优化拟合的简洁性与精度。

实验结果

研究问题

• RQ1 简化曲面拟合过程是否能提升法向估计精度，尤其是在尖锐拐角等挑战性区域？
• RQ2 如何更好地将神经网络与经典曲面拟合结合，以减少拟合失真并提升鲁棒性？
• RQ3 在局部点云块中动态选择关键点是否比均匀或固定选择方式带来更精确的法向估计？
• RQ4 在拟合前对点位置进行调整是否能显著降低曲面拟合的复杂度与误差？
• RQ5 与最先进方法相比，这些轻量级策略在平滑与尖锐特征区域的性能提升程度如何？

主要发现

• 所提方法达到最先进性能，在512个点的采样点云块上相较DeepFit精度提升5.64%。
• 点更新策略在512个点的点云块上使法向估计精度提升4.38%，显著降低尖锐边缘附近的拟合失真。
• top-k选择策略在256个点的点云块上提升性能4.66%，在512个点的点云块上提升5.64%，尤其显著增强复杂特征区域的精度。
• 该方法在PGP10（法向误差小于10°的点比例）上优于DeepFit，最高提升出现在尖锐与噪声区域。
• 在256个点点云块中采用k=50、512个点点云块中采用k=100时取得最优结果，表明方法对采样密度具有鲁棒性。
• 简化拟合过程——通常仅需一阶曲面——显著提升精度，验证了‘越简单，越有效’的原则。