Clarifying the implementation of warping in the combined local global method for optic flow computation

The field of optical flow techniques in vision is presently dominated by global variational techniques based on pixel-wise matching costs, ie. based on the Horn & Schunck paradigm, as opposed to local window based matching costs, ie. based on the Lucas-Kanade paradigm. Motivated by the needs of some difficult real world data we underline the practical interest of the combined local global (CLG) method proposed by Bruhn et al. that combines both approaches. We will show that embedding the basic first order CLG equations in a large displacement iterative framework leads to a technical difficulty. We shall see how Bruhn et al. implicitly deal with this difficulty and we will propose an alternative approximation that yields fewer computations and performs equally well.