Optical flow methods are among the most accurate techniques for estimating displacement and velocity fields in a number of applications that range from neuroscience to robotics. The performance of any optical flow method will naturally depend on the configuration of its parameters, and for different applications there are different trade-offs between the corresponding evaluation criteria (e.g. the accuracy and the processing speed of the estimated optical flow). Beyond the standard practice of manual selection of parameters for a specific application, in this article we propose a framework for automatic parameter setting that allows searching for an approximated Pareto-optimal set of configurations in the whole parameter space. This final Pareto-front characterizes each specific method, enabling proper method comparison and proper parameter selection. Using the proposed methodology and two open benchmark databases, we study two recent variational optical flow methods. The obtained results clearly indicate that the method to be selected is application dependent, that in general method comparison and parameter selection should not be done using a single evaluation measure, and that the proposed approach allows to successfully perform the desired method comparison and parameter selection. (C) 2016 Elsevier B.V. All rights reserved.