Implicit Surface Reconstruction with a Curl-free Radial Basis Function Partition of Unity Method
Implicit Surface Reconstruction with a Curl-free Radial Basis Function Partition of Unity Method
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DOI：
10.1137/22m1474485
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Kathryn P. Drake;E. Fuselier;G. Wright
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文献类型：
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作者：
Kathryn P. Drake;E. Fuselier;G. Wright
从一组分散点或点云中重建的表面重建，有许多应用程序，从计算机图形到遥感，我们为此任务提供了一种新的方法仅使用（近似）向表面的信息来利用矢量计算的基本结果，即通向隐式表面无卷曲径向基函数（RBF）插值的插值，我们可以为零级表面近似的矢量场提取潜力，我们使用基于多谐波的curl rbfs来实现该任务。形状或支持参数。 （CFPU）我们显示了CFPU如何适应点云的精确插值，并可以正规化以处理正常位置和点位置。随着采样密度的增加，如何处理噪声数据，以及该方法在文献中发现的各种问题。
. Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set) approximation for an oriented point cloud using only information about (approximate) normals to the surface. The technique exploits the fundamental result from vector calculus that the normals to an implicit surface are curl-free. By using curl-free radial basis function (RBF) interpolation of the normals, we can extract a potential for the vector field whose zero-level surface approximates the point cloud. We use curl-free RBFs based on polyharmonic splines for this task, since they are free of any shape or support parameters. To make this technique efficient and able to better represent local sharp features, we combine it with a partition of unity (PU) method. The result is the curl-free partition of unity (CFPU) method. We show how CFPU can be adapted to enforce exact interpolation of a point cloud and can be regularized to handle noise in both the normals and the point positions. Numerical results are presented that demonstrate how the method converges for a known surface as the sampling density increases, how regularization handles noisy data, and how the method performs on various problems found in the literature.