The analysis of human gait is more and more investigated due to its large panel of potential applications in various domains, like rehabilitation, deficiency diagnosis, surveillance and movement optimization. In addition, the release of depth sensors offers new opportunities to achieve gait analysis in a non-intrusive context. In this paper, we propose a gait analysis method from depth sequences by analyzing separately each step so as to be robust to gait duration and incomplete cycles. We analyze the shape of the motion trajectory as signature of the gait and consider shape variations within a Riemannian manifold to learn step models. During classification, the derivation of each performed step is evaluated in an online manner to qualitatively analyze the gait. Experiments are carried out in the context of abnormal gait detection and person re-identification trough gait recognition. Results demonstrated the potential of the method in both scenarios.