Statistical Inverse Formulation of Optical Flow with Uncertainty Quantification

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 inference is an ill-posed problem. By setting some type of additional “regularity” constraints, classical approaches formulate a well-posed optical flow inference problem in the form of a parameterized set of variational equations. In this work we build a mathematical connection, focused on optical flow methods, between classical variational optical flow approaches and Bayesian statistical inversion. A classical optical flow solution is in fact identical to a maximum a posteriori estimator under the assumptions of linear model with additive independent Gaussian noise and a Gaussian prior distribution. Unlike classical approaches, the statistical inversion approach to optical flow estimation not only allows for “point” estimates, but also provides a distribution of solutions which can be used for ensemble estimation and in particular uncertainty quantification.