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., 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.

References in corpus (4)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain
• Fast Resampling of 3D Point Clouds via Graphs
• From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

Cited by in corpus (9)

• Differentiable Manifold Reconstruction for Point Cloud Denoising
• Hypergraph Spectral Analysis and Processing in 3D Point Cloud
• PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds
• 3D Point Cloud Processing and Learning for Autonomous Driving
• MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches
• 3D Point Cloud Denoising via Deep Neural Network based Local Surface Estimation
• Deep Surface Normal Estimation with Hierarchical RGB-D Fusion
• Large-scale 3D point cloud representations via graph inception networks with applications to autonomous driving
• Point cloud denoising based on tensor Tucker decomposition