We propose a novel approach to pedestrian flow characterization. The definitions of density, flow and velocity existing in the literature are extended through a data-driven spatio-temporal discretization framework. The framework is based on three-dimensional Voronoi diagrams. Synthetic data is used to empirically investigate the performance of the approach and to illustrate its advantages. Our approach outperforms the considered approaches from the literature in terms of the robustness with respect to the simulation noise and with respect to the sampling frequency. Additionally, the proposed approach is by design (i) independent from an arbitrarily chosen discretization; (ii) appropriate for the multidirectional composition of pedestrian traffic; (iii) able to reflect the heterogeneity of the pedestrian population; and (iv) applicable to pedestrian trajectories described either analytically or as a sample of points.