Figure 3.

Geometric description of the construction of the mean and individual spatiotemporal trajectories in the space of measurement, which is the Riemannian Manifold M that embeds both the real observations and the trajectories. (A) Three-dimensional space embedding individual observations (blue points) of two individuals and the mean spatiotemporal trajectory γ₀ (red curve). (B) The spatial variations from the group-average trajectory γ₀ to the individual observations are captured in individual vectors w_i and w_j, called space shifts. (C) The vector w_i is parallel-transported along γ₀ (orange vectors) to define a parallel curve η_i that characterizes the individual spatiotemporal trajectory.