A data-driven method for choosing smoothing parameters in optical flow problems

In optical flow estimation, an additional constraint to the constant brightness assumption is required to uniquely determine both components of the flow. Typically, these constraints impose a smoothness requirement on the flow estimate. Since the smoothness constraint may be inconsistent with the brightness constraint, a smoothing parameter is introduced to control the tradeoff between satisfying the requirements of both constraints. Previously, there have only been heuristic discussions on how to choose the smoothing parameter. We show that the choice of the smoothing parameter can have a significant effect on the flow estimate and present a data-driven method based on estimated risk to select the smoothing parameter in the Horn and Schunck (1981) algorithm