Denoising for 3D Point Cloud Based on Regularization of a Statistical Low-Dimensional Manifold.

Area of Science:

• Computer Vision
• Computational Geometry
• Data Science

Background:

• Three-dimensional (3D) point clouds from stereo matching or scanners often contain complex noise.
• This noise degrades the accuracy of surface reconstruction and visualization.
• Existing denoising methods may struggle with complex noise patterns.

Purpose of the Study:

• To propose a novel regularization algorithm for effectively denoising 3D point clouds.
• To address the challenge of complex noise affecting 3D data processing.
• To develop a method that preserves essential geometric features during denoising.

Main Methods:

• Established a statistical low-dimensional manifold (SLDM) model leveraging the inherent low-dimensional structure of 3D point clouds.
• Formulated the denoising problem as an optimization task by regularizing manifold dimensions.
• Employed discrete sampling to construct a low-dimensional smooth manifold model.
• Utilized statistical and alternating iterative methods for solving the optimization problem.

Main Results:

• The proposed SLDM-based denoising method demonstrated superior performance compared to Algebraic Point-Set Surface (APSS), Non-Local Denoising (NLD), and Feature Graph Learning (FGL) algorithms.
• Quantitative evaluation showed increased mean Signal-to-Noise Ratio (SNR) by 1.22 dB (vs. APSS), 1.81 dB (vs. NLD), and 1.20 dB (vs. FGL).
• The method achieved decreased mean Mean Square Error (MSE) and Mean Structural Similarity Index Measure (SSIM), effectively removing Gaussian and Laplace noise while preserving geometric information.

Conclusions:

• The proposed statistical low-dimensional manifold (SLDM) regularization algorithm is highly effective for denoising 3D point clouds.
• It significantly improves denoising performance metrics like SNR and MSE.
• The algorithm successfully preserves critical geometric features of the point cloud during the noise elimination process.