3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model

Understand

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.