Structured Low-Rank Matrix Factorization for Point-Cloud Denoising

摘要

In this work we address the problem of point-cloud denoising where we assume that a given point-cloud comprises (noisy) points that were sampled from an underlying surface that is to be denoised. We phrase the point-cloud denoising problem in terms of a dictionary learning framework. To this end, for a given point-cloud we (robustly) extract planar patches covering the entire point-cloud, where each patch contains a (noisy) description of the local structure of the underlying surface. Based on the general assumption that many of the local patches (in the noise-free point-cloud) contain redundant information (e.g. due to smoothness of the surface, or due to repetitive structures), we find a low-dimensional affine subspace that (approximately) explains the extracted (noisy) patches. Computationally, this is achieved by solving a structured low-rank matrix factorization problem, where we impose smoothness on the patch dictionary and sparsity on the coefficients. We experimentally demonstrate that our method outperforms existing denoising approaches in various noise scenarios.