  When analyzing cell trajectories, we often have to deal with noisy data due
to the random motion of the cells and possible imperfections in cell center
detection. To smooth these trajectories, we present a mathematical model and
numerical method based on evolving open-plane curve approach in the Lagrangian
formulation. The model contains two terms: the first is the smoothing term
given by the influence of local curvature, while the other attracts the curve
to the original trajectory. We use the flowing finite volume method to
discretize the advection-diffusion partial differential equation. The PDE
includes the asymptotically uniform tangential redistribution of curve grid
points. We present results for macrophage trajectory smoothing and define a
method to compute the cell velocity for the discrete points on the smoothed
curve.
