Bayesian Methods for Optical Flow Estimation Using a Variational Approximation, with Applications to Ultrasound

We develop a unified Bayesian framework for optical flow (OF) estimation that uses a variational lower bound to obtain a variational approximation of the posterior probability distribution. Our framework enables the incorporation of domain-specific knowledge as well as a quantification of the uncertainty of OF estimation, and it encompasses existing maximum a posteriori (MAP) and variational Bayes (VB) methods as special cases. We leverage this flexibility for the ultrasound modality by using ultrasound-specific likelihood functions within both MAP and VB methods. Numerical results for the problem of cardiac motion estimation demonstrate that VB methods outperform MAP methods, in addition to providing a more faithful uncertainty measure.