We address the problem of tracking points in dense vector fields. Such vector fields may come from computational fluid dynamics simulations, environmental monitoring sensors, or dense point tracking of video data. To track points in vector fields, we capture the distribution of higher-order properties (e.g., properties derived from the gradient of the velocity vector field) in a novel local descriptor called a vector spin-image. Our distribution-based approach has a number of advantages over methods that use topology analysis to track points in vector fields. The local distributions are robust to noise, adaptable to changes in the feature, and can be used to extrapolate the location of features after they have disappeared. We describe the vector spin-image data structure, the higher-order properties we record to track vector field points, and show results of tracking points in the simulated flow through a diesel engine cylinder.