Variational Model for Depth Estimation from Images We propose a variant of convex reformulation of the standard variational model with nonconvex data terms. The proposed convex relaxation of multilabel problems is a continuous formulation of Ishikawaxe2x80x99s method for extension of the graph mincut to the multilabel problems. Our convex continuous reformulation is based upon functional lifting to a higherdimensional 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 threedimensional 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.

LocalConvexity Reinforcement for Scene Reconstruction from Sparse Point Clouds Several methods reconstruct surfaces from sparse point clouds that are estimated from images. Most of them build 3D Delaunay triangulation of the points and compute occupancy labeling of the tetrahedra thanks to visibility information and surface constraints. However their most notable errors are falselylabeled freespace tetrahedra. We present labeling corrections of these errors based on a new shape constraint: localconvexity. In the simplest case, this means that a freespace tetrahedron of the Delaunay is relabeled matter if its size is small enough and all its vertices are in matter tetrahedra. The allowed corrections are more important in the vertical direction than in the horizontal ones to take into account the anisotropy of usual scenes. In the experiments, our corrections improve the results of previous surface reconstruction methods applied to videos taken by a consumer 360 camera.