Variational Model for Depth Estimation from Images

We propose a variant of convex reformulation of the standard variational model with non-convex data terms. The proposed convex relaxation of multilabel problems is a continuous formulation of Ishikawa's method for extension of the graph min-cut to the multilabel problems. Our convex continuous reformulation is based upon functional lifting to a higher-dimensional space using superlevel functions. We solve the resulting convex variational problem by the augmented Lagrangian method. The most time consuming part of this method is the numerical solution of a boundary value problem for the Poisson equation in three-dimensional space, which is implemented by means of a fast Poisson solver. We illustrate the developed theory with several numerical examples for the standard correspondence problem for a rectified stereo image pair.