Patch-space Beltrami denoising of 3D point clouds

The Beltrami framework has been shown to be an effective and efficient denoising filter for color images, treating them as two dimensional manifolds embedded in a hybrid spatial-spectral space. Recent work using this framework on the patchspace of an image has demonstrated that including neighboring pixels in the feature space can significantly improve the technique's denoising performance. In this paper we demonstrate an extension of the patch-space Beltrami filter to unstructured point sets. We achieve this by extracting the neighborhood about each point, and using the resulting canonical local frame to perform an explicit iteration of the patch-space Beltrami flow on the normal coordinates. As we demonstrate on real 3D data, the resulting iterative scheme denoises the point set while preserving the underlying manifold structure.