  In this paper, we present an algorithm that computes the topological
signature for a given periodic motion sequence. Such signature consists of a
vector obtained by persistent homology which captures the topological and
geometric changes of the object that models the motion. Two topological
signatures are compared simply by the angle between the corresponding vectors.
With respect to gait recognition, we have tested our method using only the
lowest fourth part of the body's silhouette. In this way, the impact of
variations in the upper part of the body, which are very frequent in real
scenarios, decreases considerably. We have also tested our method using other
periodic motions such as running or jumping. Finally, we formally prove that
our method is robust to small perturbations in the input data and does not
depend on the number of periods contained in the periodic motion sequence.
