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. The new definitions are (i) independent from an arbitrarily chosen discretization; (ii) appropriate for the multi-directional 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. Synthetic data is used to empirically investigate the performance of the approach and to illustrate its advantages.