An automated method to estimate vector fields of propagation velocity from observed epicardial extracellular potentials is introduced. The method relies on fitting polynomial surfaces T(x, y) to the space-time (x, y, t) coordinates of activity. Both speed and direction of propagation are computed from the gradient of the local polynomial surface. The components of velocity, which are total derivatives, are expressed in terms of the partial derivatives which comprise the gradient of T. The method was validated on two-dimensional (2-D) simulations of propagation and then applied to cardiac mapping data. Conduction velocity was estimated at multiple epicardial locations during sinus rhythm, pacing, and ventricular fibrillation (VF) in pigs. Data were obtained via a 528-channel mapping system from 23 x 22 and 24 x 21 arrays of unipolar electrodes sutured to the right ventricular epicardium. Velocity estimates are displayed as vector fields and are used to characterize propagation qualitatively and quantitatively during both simple and complex rhythms.