Robust Denoising of Piece-Wise Smooth Manifolds

Abstract

A common smoothness model used in graph based regularization approaches is to require the energy of signals to be small with respect to the graph Laplacian of the graph. In this paper, we suggest an alternative approach which can effectively incorporate the high frequency information of the graph for unsupervised piece-wise smooth manifold denoising using Spectral Graph Wavelets. Our approach is based on a novel technique to remove noise from SGW coefficients estimated from a local tangent space based graph, which allows us to effectively regularize manifolds with singularities, such as for example intersecting manifolds. Experimental results on synthetic and real datasets in computer vision applications show that our proposed approach outperforms the state of the art, and is an effective tool to remove noise from manifolds with complex structures without over-smoothing at discontinuities.