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

Area of Science:

• Computer Vision
• Geometric Modeling
• Signal Processing

Background:

• 3D point clouds are essential representations of volumetric objects.
• Acquisition processes often introduce noise into 3D point cloud data.
• Existing denoising methods may struggle with preserving fine structural details.

Purpose of the Study:

• To develop an effective denoising technique for 3D point clouds.
• To extend manifold models to surface patches for noise reduction.
• To preserve salient structural features during the denoising process.

Main Methods:

• Extending low-dimensional manifold models to 3D point cloud surface patches.
• Utilizing self-similar patches for simultaneous denoising via patch manifold prior.
• Approximating manifold dimension with a graph Laplacian regularizer for discrete data.
• Proposing a novel, noise-robust discrete patch distance measure for graph construction.

Main Results:

• The proposed graph Laplacian regularizer offers efficient implementation and numerical stability.
• The denoising scheme outperforms existing state-of-the-art methods in objective metrics.
• Visually salient structural features, such as edges, are well-preserved.

Conclusions:

• The developed method provides a robust and effective solution for 3D point cloud denoising.
• The approach demonstrates superiority over current techniques in both quantitative and qualitative evaluations.
• This work contributes a valuable tool for processing noisy 3D geometric data.