Topological Signal Processing from Stereo Visual SLAM.

Area of Science:

• Computer Vision
• Signal Processing
• Computational Geometry

Background:

• Graph Signal Processing (GSP) models connectivity using nodes and edges.
• Visual Simultaneous Localization and Mapping (V-SLAM) generates rich point clouds typically processed with graph-based methods.
• Existing methods often overlook higher-order connectivity structures.

Purpose of the Study:

• Introduce a Topological Signal Processing (TSP) framework, TSP-SLAM, for V-SLAM.
• Integrate texture information into TSP for enriched point cloud representation.
• Extend graph-based point cloud processing to advanced TSP techniques.

Main Methods:

• Developed the TSP-SLAM framework integrating V-SLAM texture data.
• Represented point clouds by associating signals with vertices, edges, and faces of a mesh.
• Exploited the mapping between 3D mesh elements and their 2D image projections for filtering.

Main Results:

• TSP-SLAM enables richer point cloud representations beyond traditional graph methods.
• Demonstrated successful association of signals with mesh vertices, edges, and faces.
• Showcased the design of topological filtering algorithms leveraging 3D-2D mappings.

Conclusions:

• TSP-SLAM offers a novel approach for topological signal processing of V-SLAM data.
• The framework enriches point cloud representation by incorporating higher-order connectivity.
• TSP-SLAM shows significant potential for challenging V-SLAM environments.