Primal-dual optimization strategies in Huber-L1 optical flow with temporal subspace constraints for non-rigid sequence registration

This work studies the application of Fenchel-Duality principles to general convex optimization problems and their corresponding relaxed versions in the context of optical flow estimation. We derive the associated primal-dual optimization strategies in the problem of Huber-L1 optical flow with temporal consistency for non-rigid sequence registration. Temporal consistency is imposed using a recently proposed approach that characterizes the optical flow using temporal subspace constraints, yielding solutions in a space spanned by a non-rigid orthogonal trajectory basis. The performance of the resulting optical flow methods has been studied in a framework for non-rigid sequence registration evaluation. In addition, we have compared the solution of the different methods in other challenging datasets. We have found that the strategies with the best outcome are among the ways of applying Fenchel-Duality principles that were not considered in previous works for the optical flow model with temporal subspace constraints. Indeed, our experiments have shown the simplest optimization strategy as the best performing one.