# Topological Signal Processing from Stereo Visual SLAM

## TL;DR

This paper introduces TSP-SLAM, a new method that enhances point cloud processing in visual SLAM by using topological signal processing techniques.

## Contribution

The novel TSP-SLAM framework integrates texture information from V-SLAM into topological signal processing.

## Key findings

- TSP-SLAM allows signals to be associated with vertices, edges, and faces of a 3D mesh.
- Numerical results show TSP-SLAM supports advanced topological filtering algorithms.
- The method improves point cloud representation in challenging V-SLAM environments.

## Abstract

Topological signal processing is emerging alongside Graph Signal Processing (GSP) in various applications, incorporating higher-order connectivity structures—such as faces—in addition to nodes and edges, for enriched connectivity modeling. Rich point clouds acquired by multi-camera systems in Visual Simultaneous Localization and Mapping (V-SLAM) are typically processed using graph-based methods. In this work, we introduce a topological signal processing (TSP) framework that integrates texture information extracted from V-SLAM; we refer to this framework as TSP-SLAM. We show how TSP-SLAM enables the extension of graph-based point cloud processing to more advanced topological signal processing techniques. We demonstrate, on real stereo data, that TSP-SLAM enables a richer point cloud representation by associating signals not only with vertices but also with edges and faces of the mesh computed from the point cloud. Numerical results show that TSP-SLAM supports the design of topological filtering algorithms by exploiting the mapping between the 3D mesh faces, edges and vertices and their 2D image projections. These findings confirm the potential of TSP-SLAM for topological signal processing of point cloud data acquired in challenging V-SLAM environments.