Abstract: We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection (LOP) operator. Our algorithm includes two new developments. First, a weight term related to surface variation at each point is introduced to the classic LOP operator. It produces output points with a spatially adaptive distribution. Second, for speeding up the convergence of our method, an initialization process is proposed based on geometry-aware stochastic sampling. Owing to the initialization, the relaxation process achieves a faster convergence rate than those initialized by uniform sampling. Our simplification method possesses a number of distinguishing features. In particular, it provides resilience to noise and outliers, and an intuitively controllable distribution of simplification. Finally, we show the results of our approach with publicly available point cloud data, and compare the results with those obtained using previous methods. Our method outperforms these methods on raw scanned data.

Key words: Point-sampled geometry, Particle simulation, Locally optimal projection, Simplification

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