  Many complex flows such as those arising from ocean plastics in geophysics or
moving cells in biology are characterized by sparse and noisy trajectory
datasets. We introduce techniques for identifying Lagrangian Coherent
Structures (LCSs) of hyperbolic and elliptic nature in such datasets.
Hyperbolic LCSs, which represent surfaces with maximal attraction or repulsion
over a finite amount of time, are computed through a regularized least-squares
approximation of the flow map gradient. Elliptic LCSs, which identify regions
of coherent motion such as vortices and jets, are extracted using DBSCAN - a
popular data clustering algorithm - combined with a systematic approach to
choose parameters. We deploy these methods on various benchmark analytical
flows and real-life experimental datasets ranging from oceanography to biology
and show that they yield accurate results, despite sparse and noisy data. We
also provide a lightweight computational implementation of these techniques as
a user-friendly and straightforward Python code.
