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

Abstract

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., stereomatching from multiple viewpoint images or depth data acquired directly from active light sensors-imply non-negligible noise in the data. In this paper, we extend a previously proposed lowdimensional manifold model for the image patches to 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 leads to speedy implementation and has desirable numerical stability properties given its natural graph spectral interpretation. Extensive simulation results show that our proposed denoising scheme outperforms state-of-the-art methods in objective metrics and better preserves visually salient structural features like edges.

Feature Graph Learning for 3D Point Cloud Denoising

“…Finally, we optimize the point cloud and the underlying graph alternately until convergence. Extensive experiments show that we achieve state-of-the-art performance compared to competing methods [39]- [41].…”

“…Moreover, they established a linear relationship between normals and 3D point coordinates via bipartite graph approximation for ease of optimization. [41] proposed graph Laplacian regularization (GLR) of a low dimensional manifold model (LDMM), and sought self-similar patches to denoise them simultaneously. Instead of directly smoothing the coordinates or normals of 3D points, [62] estimated a local tangent plane at each 3D point based on a graph and then reconstructed each 3D point by weighted averaging of its projections on multiple tangent planes.…”

“…Mimicking a fixed-size image patch with a center pixel, we first define a patch V i in a point cloud P as done in [41]: Definition 1. A patch V i in a point cloud is a local point set of k + 1 points, consisting of a center point c i ∈ R 3 and its k-nearest-neighbors in terms of Euclidean distance.…”

“…Next, for each center point c i we construct a patch by identifying c i 's k nearest neighbors. To exploit the assumed similarity among patches for denoising, we align patches via 4 https://www.intelrealsense.com/ 5 https://www.teledyneoptech.com/en/products/static-3d-survey/ 6 [41] formally defined patch similarity based on projections on parallel planes, but it is computation-intensive. translation so each patch has its center at the origin.…”

“…We compare the proposed approach with seven competing point cloud denoising algorithms, including APSS [47], RIMLS [48], AWLOP [51], non-local denoising algorithm (NLD) [55], MRPCA [39], LR [40], and GLR [41]. Further, to validate the necessity of optimizing edge weights, we compare with a Baseline scheme of our method, where we randomly set edge weights in range [0, 1] instead of optimizing via feature graph learning.…”