Spectral sampling of manifolds
Spectral sampling of manifolds
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DOI：
10.1145/1866158.1866190
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
A. C. Öztireli;M. Alexa;M. Gross
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文献类型：
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作者：
A. C. Öztireli;M. Alexa;M. Gross
计算机图形学的一个中心问题是找到给定表面表示的最佳采样条件。我们提出了一种基于流形谱分析的新方法来解决这个问题，该方法可以实现忠实的重建和高质量的各向同性采样，高效、核外、特征敏感、控制直观且易于实现。我们利用谱分析、核方法和矩阵微扰理论的结果，以一种新颖的方式解决这个问题。由单点引起的流形变化通过局部测量来量化，该局部测量限制了流形的拉普拉斯-贝尔特拉米谱的变化。因此，我们不需要显式计算频谱或任何全局量，这使得我们的算法非常高效。尽管我们的主要重点是采样表面，但分析和算法是通用的，可用于简化和重新采样位于任意维度流形附近的点云。
A central problem in computer graphics is finding optimal sampling conditions for a given surface representation. We propose a new method to solve this problem based on spectral analysis of manifolds which results in faithful reconstructions and high quality isotropic samplings, is efficient, out-of-core, feature sensitive, intuitive to control and simple to implement. We approach the problem in a novel way by utilizing results from spectral analysis, kernel methods, and matrix perturbation theory. Change in a manifold due to a single point is quantified by a local measure that limits the change in the Laplace-Beltrami spectrum of the manifold. Hence, we do not need to explicitly compute the spectrum or any global quantity, which makes our algorithms very efficient. Although our main focus is on sampling surfaces, the analysis and algorithms are general and can be applied for simplifying and resampling point clouds lying near a manifold of arbitrary dimension.