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Abstract: This paper presents a novel technique for estimating normals on unorganized point clouds. Methods from robust statistics are used to detect the best local tangent plane for each point. Therefore the algorithm is capable to deal with points located in high curvature regions or near/on complex sharp features, while being highly robust with respect to noise and outliers. In particular, the presented method reliably recovers sharp features but does not require tedious manual parameter tuning as done by current methods. The key ingredients of our approach are a robust noise-scale estimator and a kernel density estimation (KDE) based objective function. In contrast to previous approaches the noise-scale estimation is not affected by sharp features and achieves high accuracy even in the presence of outliers. In addition, our normal estimation procedure allows detection and elimination of outliers. We confirm the validity and reliability of our approach on synthetic and measured data and demonstrate applications to point cloud denoising. [Copyright &y& Elsevier]