Variational approach to optical flow estimation managing discontinuities

Projection of the 3D velocity of real objects on the image plane. is often cal/ed the 'velocity field'. The estimation of thlS fleld lS one of the most important research top ics in computer vision. In the literature, there are numerous solutions which adopt a sort of continuity equation called optical flow constrain (O FC). The solution of this constraint equation is usually called the 'optical flow' field, and can be considered equal to the velocity field under particular assumptions. The structure of the OFC equation makes the oprical flow estimation an ill-posed problem, like many other inverse problems in earlyvision. For this reason, many reglarization techniques were used in the past for estimating optical flow. The major drawback of these solutions is the presence of propagation effects which produce the loss of the information associated to the discontinuities. On the other hand, the dicontinuities are very important for estimating precise optical flow fields, and detecting the shape of moving objects. In this paper, we propose a new solution based on variational techniques for optical flow estimation and regularization, which takes into account the discontinuities, and strongly reduces the related problems. The proposed method is called 'discontinuity-dependent variational solution'.