Symmetric Optical Flow

One of the main technique used to recover motion analysis from two images or to register them is variational optical flow, where the pixels of one image are matched to the pixels of the second image by minimizing an energy functional. In the standard formulation of variational optical flow, the estimated motion vector field depends on the reference image and is asymmetric. However, in most application the solution should be independent of the reference image. Only few symmetrical formulations of the optical flow has been proposed in the literature, where the solution is constraint to be symmetric using a combination of the flow in both directions. We propose a new symmetric variational formulation of the optical flow problem, where the flow is naturally symmetric. Results on the Yosemite sequence show an improved accuracy of our symmetric flow with respect to standard optical flow algorithm.