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Local Neighborhoods for Shape Classification and Normal Estimation

We introduce the concept of local neighborhoods, a generalization of the one-ring on a mesh to unlabeled 3D data points arising from sampling a 2D surface embedded in 3D. The local neighborhood supports both local shape classification and robust normal estimation. In particular, local neighborhoods out-perform traditional approaches in unevenly sampled, curved regions. We show that the local neighborhood can be used in place of a full mesh structure for applications such as smoothing, moving least-squares reconstruction, and