The paper considers making inferences about the underlying true 2-D motion when only evaluations of a local block-based cost function, the mean of absolute or squared differences, for a set of motion candidates are available. Considering bounds for these criteria, it is shown that simple local image gradient measures provide useful information for interpreting the criterion values. Based on analysis, a thresholding scheme for the criteria is proposed. Using a Gaussian approximation for the thresholding result, estimates of local motions and related uncertainties can be obtained.