Image-based algorithms have become a powerful tool for estimating flow velocities in rivers. In this study, we generalize the space-time image velocimetry (STIV) framework for reach-scale application rather than along a cross section. The new algorithm provides information on both the magnitude and orientation of velocity vectors, and we refer to the algorithm as two-dimensional STIV, or 2D-STIV. The workflow involves setting up a grid, using centreline tangent vectors as initial estimates of flow direction, and then extracting space-time images (STIs) along search lines radiating from each grid node. The autocorrelation function is used to infer the inclination of streak lines present in STIs, which represents the advection of water surface features. Information on flow direction is obtained by evaluating various candidate search lines and identifying that which yields the highest velocity. This search can be performed exhaustively or via optimization. We applied the new 2D-STIV algorithm to three test cases, one simulated data set and two natural channels, and compared image-derived velocities to modelled or measured values. We also applied two established particle image velocimetry (PIV) algorithms to the same data sets. 2D-STIV performed as well as the two PIV algorithms for simulated images. For a natural river with distinct water surface features, 2D-STIV was effective for much of the channel but also led to a more patchy, irregular velocity field than the two PIV algorithms. For a site lacking obvious surface features, exhaustive 2D-STIV led to velocity estimates uncorrelated with field data while the optimization-based version produced erratic flow directions. 2D-STIV also required greater image sequence durations, higher frame rates, and generally longer computational run times. Overall, ensemble PIV was the most reliable algorithm.