Several methods reconstruct surfaces from sparse point clouds that are estimated from images. Most of them build 3D De-launay triangulation of the points and compute occupancy labeling of the tetrahedra thanks to visibility information and surface constraints. However their most notable errors are falsely-labeled freespace tetrahedra. We present labeling corrections of these errors based on a new shape constraint: local-convexity. 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 aniso-tropy 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.