Point Cloud Denoising via Feature Graph Laplacian Regularization.

Area of Science:

• Computer Vision
• Geometric Processing
• Signal Processing

Background:

• Point clouds are discrete 3D coordinate samples of surfaces, often corrupted by noise during acquisition.
• Graph signal processing offers advanced techniques for analyzing and processing point cloud data.
• Existing denoising methods may struggle with different types of noise present in point clouds.

Purpose of the Study:

• To develop advanced local algorithms for effective 3D point cloud denoising.
• To introduce a signal-dependent feature graph Laplacian regularizer (SDFGLR) for noise reduction.
• To address the challenge of removing both Gaussian and Laplacian noise from point cloud data.

Main Methods:

• Formulation of an optimization problem using SDFGLR as a signal prior.
• Inclusion of a general 'p-norm fidelity term to handle different noise types ('2 for Gaussian, '1 for Laplacian).
• Bipartite graph approximation for linear relationship between normals and coordinates, with alternate optimization of node sets.

Main Results:

• Iterative optimization using unconstrained quadratic programming (QP) for '2-norm fidelity.
• Iterative minimization of an '1-'2 cost function using accelerated proximal gradient (APG) for '1-norm fidelity.
• State-of-the-art denoising performance demonstrated through extensive experiments compared to existing local methods.

Conclusions:

• The proposed SDFGLR-based algorithms effectively denoise 3D point clouds.
• The method successfully handles both sparse and non-sparse additive noise.
• The developed techniques offer significant improvements in point cloud quality for various applications.