Spectral Sampling of Manifolds: Extended Version Cengiz Öztireli∗

Figure 1: From left to right: The original model with 14 million samples is adaptively subsampled to 300k samples and reconstructed, total time including out-of-core simplification and reconstruction is 6 minutes. Detail from uniform resampling of the model to 21k samples. Uniform and adaptive samplings. Remeshing obtained by using sampled points as vertices. A central problem in computer graphics is finding optimal sam-pling 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, intu-itive 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