  Optical flow refers to the visual motion observed between two consecutive
images. Since the degree of freedom is typically much larger than the
constraints imposed by the image observations, the straightforward formulation
of optical flow as an inverse problem is ill-posed. Standard approaches to
determine optical flow rely on formulating and solving an optimization problem
that contains both a data fidelity term and a regularization term, the latter
effectively resolves the otherwise ill-posedness of the inverse problem. In
this work, we depart from the deterministic formalism, and instead treat
optical flow as a statistical inverse problem. We discuss how a classical
optical flow solution can be interpreted as a point estimate in this more
general framework. The statistical approach, whose "solution" is a distribution
of flow fields, which we refer to as Bayesian optical flow, allows not only
"point" estimates (e.g., the computation of average flow field), but also
statistical estimates (e.g., quantification of uncertainty) that are beyond any
standard method for optical flow. As application, we benchmark Bayesian optical
flow together with uncertainty quantification using several types of prescribed
ground-truth flow fields and images.
