Motion estimation from equation of continuity. The well-conditioned computation point of view

In the last years, different variational approaches have been used to compute optical flow and the attention was essentially concentrated on additional regularization terms. However, almost all these methods use the classical optical flow constraint (OFC). In order to extend these variational approaches to elastic deformable motion, we recently proposed a new functional built from physical considerations and based on the Equation of Continuity EOC. We have addressed the problem to use EOC rather than OFC in terms of well-conditioned computation, which may be essential for the accuracy of the results. We demonstrate, EOC leads to a better conditioned problem than OFC and this better conditioning increases with the intensity of the pixels. Under some restrictions the same condition quality from numerical point of view, may be obtained with OFC but, in this case, the OFC solution may be over smoothed.