Point Cloud Sampling via Graph Balancing and Gershgorin Disc Alignment.

Area of Science:

• Computer Vision and Graphics
• Computational Geometry
• Machine Learning

Background:

• Point clouds (PCs) are large, making subsequent operations computationally expensive.
• Existing PC sub-sampling methods lack generalization and sufficient shape preservation.
• Model-based and data-driven approaches have limitations in adaptability and performance.

Purpose of the Study:

• To develop a fast and generalizable point cloud sub-sampling algorithm.
• To minimize global reconstruction error during the sub-sampling process.
• To improve the efficiency and quality of 3D point selection.

Main Methods:

• Proposed a linear-time complexity algorithm for point cloud sub-sampling.
• Formulated sub-sampling as maximizing the smallest eigenvalue of H^T H + μL, related to super-resolution reconstruction.
• Employed graph sampling techniques, approximating the graph Laplacian and utilizing Gershgorin Disc Perfect Alignment (GDPA).

Main Results:

• The algorithm achieves linear time complexity for point cloud sub-sampling.
• Experimental results demonstrate superior numerical and visual reconstruction quality compared to competing methods.
• The selected 3D points effectively preserve the overall shape and details of the original point cloud.

Conclusions:

• The proposed graph sampling-based approach offers an efficient and effective solution for point cloud sub-sampling.
• The method generalizes well across different point cloud sizes and sub-sampling rates.
• This work advances the state-of-the-art in point cloud processing by improving reconstruction accuracy and computational efficiency.