L₁-Medial Skeleton Of Point Cloud

We introduce1-medial skeleton as a curve skeleton representation for3D point clouddata. The1-median is well-known as a robust global center of an arbitrary set of points. Wemake the key observation that adapting1-medians locally to a point set representing a3Dshape gives rise to a one-dimensional structure, which can be seen as a localized center of theshape. The primary advantage of our approach is that it does not place strong requirements onthe quality of the input point cloud nor on the geometry or topology of the captured shape. Wedevelop a1-medial skeleton construction algorithm, which can be directly applied to anunoriented raw point scan with significant noise, outliers, and large areas of missing data. Wedemonstrate1-medial skeletons extracted from raw scans of a variety of shapes, includingthose modeling high-genus3D objects, plant-like structures, and curve networks.