  We propose a robust normal estimation method for both point clouds and meshes
using a low rank matrix approximation algorithm. First, we compute a local
feature descriptor for each point and find similar, non-local neighbors that we
organize into a matrix. We then show that a low rank matrix approximation
algorithm can robustly estimate normals for both point clouds and meshes.
Furthermore, we provide a new filtering method for point cloud data to smooth
the position data to fit the estimated normals. We show applications of our
method to point cloud filtering, point set upsampling, surface reconstruction,
mesh denoising, and geometric texture removal. Our experiments show that our
method outperforms current methods in both visual quality and accuracy.
