Discrete Geodesic Distribution-Based Graph Kernel for 3D Point Clouds

Area of Science:

• Computational geometry
• Machine learning
• Data science

Background:

• Graph kernels are effective for analyzing discrete geometric data, preserving topological structures.
• They enable machine learning on evolving graph-based vector data.
• Point cloud data analysis is crucial for various applications.

Purpose of the Study:

• To formulate a unique kernel function for similarity determination in point cloud data structures.
• To leverage graph properties for enhanced point cloud analysis.
• To demonstrate the kernel's utility in similarity measures and categorization.

Main Methods:

• Developed a novel graph kernel function tailored for point clouds.
• The kernel quantifies similarity based on geodesic route distributions within graph representations.
• Utilized discrete geometry principles to define the kernel's properties.

Main Results:

• The proposed kernel effectively captures the underlying discrete geometry of point clouds.
• Demonstrated high efficiency in similarity determination tasks for point cloud data.
• Achieved accurate categorization of point clouds using the developed kernel function.

Conclusions:

• The novel graph kernel offers a powerful tool for point cloud structural analysis.
• This approach enhances machine learning applications involving geometric data.
• The method provides a robust solution for point cloud similarity and classification.