2020/07/06 by Vogt, Thomas, Haase, Roland, Bednarski, Danielle +1
#Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2007.02587
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the space of pointwise probability measures over a fixed range Γ. Interestingly, this approach can be derived as a generalization of the theory of dynamical optimal transport. Imposing the established continuity equation as a constraint corresponds to variational models with first-order regularization. By modifying the continuity equation, the approach can also be extended to models with higher-order regularization.