  Optical flow estimation remains challenging due to untextured areas, motion
boundaries, occlusions, and more. Thus, the estimated flow is not equally
reliable across the image. To that end, post-hoc confidence measures have been
introduced to assess the per-pixel reliability of the flow. We overcome the
artificial separation of optical flow and confidence estimation by introducing
a method that jointly predicts optical flow and its underlying uncertainty.
Starting from common energy-based formulations, we rely on the corresponding
posterior distribution of the flow given the images. We derive a variational
inference scheme based on mean field, which incorporates best practices from
energy minimization. An uncertainty measure is obtained along the flow at every
pixel as the (marginal) entropy of the variational distribution. We demonstrate
the flexibility of our probabilistic approach by applying it to two different
energies and on two benchmarks. We not only obtain flow results that are
competitive with the underlying energy minimization approach, but also a
reliable uncertainty measure that significantly outperforms existing post-hoc
approaches.
