  3D point cloud - a new signal representation of volumetric objects - is a
discrete collection of triples marking exterior object surface locations in 3D
space. Conventional imperfect acquisition processes of 3D point cloud - e.g.,
stereo-matching from multiple viewpoint images or depth data acquired directly
from active light sensors - imply non-negligible noise in the data. In this
paper, we adopt a previously proposed low-dimensional manifold model for the
surface patches in the point cloud and seek self-similar patches to denoise
them simultaneously using the patch manifold prior. Due to discrete
observations of the patches on the manifold, we approximate the manifold
dimension computation defined in the continuous domain with a patch-based graph
Laplacian regularizer and propose a new discrete patch distance measure to
quantify the similarity between two same-sized surface patches for graph
construction that is robust to noise. We show that our graph Laplacian
regularizer has a natural graph spectral interpretation, and has desirable
numerical stability properties via eigenanalysis. Extensive simulation results
show that our proposed denoising scheme can outperform state-of-the-art methods
in objective metrics and can better preserve visually salient structural
features like edges.
