Scale Selection for Geometric Fitting in Noisy Point Clouds

In recent years, there has been a resurgence in the use of raw point cloud data as the geometric primitive of choice for several modeling tasks such as rendering, editing and compression. Algorithms using this representation often require reliable additional information such as the curve tangent or surface normal at each point. Estimation of these quantities requires the selection of an appropriate scale of analysis to accommodate sensor noise, density variation and sparsity in the data. To this goal, we present a new class of locally semi-parametric estimators that allows analysis of accuracy with finite samples, as well as explicitly addresses the problem of selecting optimal support volume for local fitting. Experiments on synthetic and real data validate the behavior predicted by the model, and show competitive performance and improved stability over leading alternatives that require a preset scale.

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