论文标题
从点云的曲率正则表面重建
Curvature Regularized Surface Reconstruction from Point Cloud
论文作者
论文摘要
我们提出了一种变性功能和快速算法，以从点云数据与曲率约束重建隐式表面。最小化功能可以平衡距点云和平均曲率项的距离函数。仅使用点位置，每个点没有任何局部正常或曲率估计。随着曲率约束的增加，计算变得特别具有挑战性。为了提高计算效率，我们通过新型操作员分裂方案解决了问题。它用脱钩的PDE系统替代了原始的高阶PDE，该系统通过半平绘法解决。我们还使用增强的拉格朗日方法讨论方法。所提出的方法显示出对噪声的鲁棒性，与没有曲率约束的模型相比，恢复凹形特征和尖角更好。在两个和三维数据集中进行数值实验，嘈杂和稀疏的数据被提出以验证模型。
We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature term. Only the point location is used, without any local normal or curvature estimation at each point. With the added curvature constraint, the computation becomes particularly challenging. To enhance the computational efficiency, we solve the problem by a novel operator splitting scheme. It replaces the original high-order PDEs by a decoupled PDE system, which is solved by a semi-implicit method. We also discuss approach using an augmented Lagrangian method. The proposed method shows robustness against noise, and recovers concave features and sharp corners better compared to models without curvature constraint. Numerical experiments in two and three dimensional data sets, noisy and sparse data are presented to validate the model.
