  This paper presents an end-to-end differentiable algorithm for robust and
detail-preserving surface normal estimation on unstructured point-clouds. We
utilize graph neural networks to iteratively parameterize an adaptive
anisotropic kernel that produces point weights for weighted least-squares plane
fitting in local neighborhoods. The approach retains the interpretability and
efficiency of traditional sequential plane fitting while benefiting from
adaptation to data set statistics through deep learning. This results in a
state-of-the-art surface normal estimator that is robust to noise, outliers and
point density variation, preserves sharp features through anisotropic kernels
and equivariance through a local quaternion-based spatial transformer. Contrary
to previous deep learning methods, the proposed approach does not require any
hand-crafted features or preprocessing. It improves on the state-of-the-art
results while being more than two orders of magnitude faster and more parameter
efficient.
