Optical-Flow Estimation while Preserving Its Discontinuities: A Variational Approach

This paper describes a variational approach devised for the purpose of estimating optical flow from a sequence of images with the constraint to preserve the flow discontinuities. This problem is set as a regularization and minimization of a non quadratic functional. The Tikhonov quadratic regularization term usually used to recover smooth solution is replaced by a particular function of the gradient flow specifically derived to allow flow discontinuities formation in the solution. Conditions to be fulfilled by this specific regularizing term, to preserve discontinuities and insure stability of the regularization problem, are also derived. To minimize this non quadratic functional, two different methods have been investigated. The first one is an iterative scheme to solve the associated non-linear Euler-Lagrange equations. The second solution introduces dual variables so that the minimization problem becomes a quadratic or a convex functional minimization problem. Promising experimental results on synthetic and real image sequences will illustrate the capabilities of this approach.