Abstract: We introduce $L_1$-medial skeleton as a curve skeleton representation for 3D point cloud data. The $L_1$-median is well-known as a robust global center of an arbitrary set of points. We make the key observation that adapting $L_1$-medians locally to a point set representing a 3D shape gives rise to a one-dimensional structure, which can be seen as a localized center of the shape. The primary advantage of our approach is that it does not place strong requirements on the quality of the input point cloud nor on the geometry or topology of the captured shape. We develop a $L_1$-medial skeleton construction algorithm, which can be directly applied to an unoriented raw point scan with significant noise, outliers, and large areas of missing data. We demonstrate $L_1$-medial skeletons extracted from raw scans of a variety of shapes, including those modeling high-genus 3D objects, plant-like structures, and curve networks.