A Convex Solution to Spatially-Regularized Correspondence Problems

We propose a convex formulation of the correspondence problem between two images with respect to an energy function measuring data consistency and spatial regularity. To this end, we formulate the general correspondence problem as the search for a minimal two-dimensional surface in R4. We then use tools from geometric measure theory and introduce 2-vector fields as a representation of two-dimensional surfaces in R4. We propose a discretization of this surface formulation that gives rise to a convex minimization problem and compute a globally optimal solution using an efficient primal-dual algorithm.