Extracting Geometric Representations Of Trajectories Using Topological Data Analysis

Object tracking fi nds applications in many research areas. Examples include tracking weather phenomena such as a snow storm and tracking migration data and identifying migration patterns of bird species. However, tracking objects is a challenging task since an object's topological
properties can change over time. Previous research proposed a method for tracking objects with dynamic topology, based on using zig-zag persistent homology principles. Our paper builds on that research by using the method for identifying objects within a dataset in order to extract and visualise trajectories of the moving objects. We create the trajectories based on the centroids of the objects in each time step. We also perform trajectory clustering for reducing noise in data and identifying main movement patterns. The approach is demonstrated with respect to
tracking rain clouds in radar imagery.