Persistent Homology in LiDAR-Based Ego-Vehicle Localization

Recently, various applications leveraging topological data analysis, in particular, persistent homology (PH), have been presented in many fields since PH provides a novel point cloud analysis method. In this work, we apply PH to LiDAR-based ego-vehicle localization applications. PH can extract translation and rotation invariant features from a point cloud. These features do not maintain local information of the point cloud, such as the edges and lines; however, they can abstract the global structure of the point cloud. A persistence image (PI) vectorizes the features and allows us to obtain fixed-size vectors despite the sizes of the source point clouds being different. Additionally, the size of the PI is not large even though the source point cloud is extremely big. We consider that these advantages are effective to loop closure detection, place categorization, and end-to-end global localization applications. Results reveal that it is difficult to improve the localization accuracy by simply applying PH owing to the basic concept of the topology that does not focus on exact shapes of the geometry. Therefore, we discuss how the advantages of PH can be utilized for the localization.